PIAGET'S CONCEPT OF FORMAL OPERATIONAL REASONING

AND WHOLE BRAIN FUNCTION: EVIDENCE FROM

EEG ALPHA COHERENCE DURING TRANSCENDENTAL MEDITATION

by

John W. Sorflaten

An Abstract

Of a thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Education

(Instructional Design and Technology)in the Graduate College of

The University of Iowa

May 1994

Thesis co-supervisors: Professor Barry BrattonProfessor Darrell G. Phillips

1

ABSTRACT

No clear relationships have been drawn between Piaget’s concept of formal

operation reasoning and neuropsychological models of brain function such as left-right

hemisphere specialization. At least one popular science educator suggests that formal

reasoning is solely a left-hemisphere function and fails to tap aptitudes for right

hemisphere intuitive and metaphoric thought. On the other hand, Piaget’s writings

describe the “structured whole” and the need for “all possibilities” in a way that suggests

that formal reasoning indeed requires right as well as left hemisphere functions.

An EEG alpha coherence index of F3F4 + F3C3 + F4C4 - O1O2 (FLR-O index)

was measured on 58 college students during a “standard cognitive state,” Transcendental

Meditation (TM). Greater mean FLR-O indexes were found for groups scored formal on

three clinically administered tasks: Shadows (testing for quantitative proportional

reasoning), Correlations, and Chemicals Combinations. The group scored formal on the

Communicating Vessels tasks, a test of the INRC group schema, demonstrated

significantly greater (p ≤ .05) FLR-O index than the non-formal group. As expected,

significantly more males passed the Shadows task than females. Surprisingly, no

significant interaction was found between gender and task on the FLR-O index or any of

the individual derivations.

These results give weak but positive support for the hypothesis. However,

additional support was found when studying the neuropsychological correlates of a

formal operational “stage.” Subjects failing all four tasks were considered to lack the

logical relations characteristic of the formal stage. Fail group subjects measured less on

the FLR-O index than subjects who passed at least one of the tasks (p = .0558, and p

= .050 when adjusted for age and gender). These results lend credence to the hypothesis

that formal reasoning is a “whole-brain” activity.

In a speculating on neuropsychological theory of equilibration and development

of formal reasoning, I suggest that improvement in frontal executive control enhances

pre-attentive orientation towards a task and simultaneous pre-attentive habituation to

distraction. This dual process supports accomodation and permits the cycle of

differentiation and integration to continue unimpeded leading, ultimately, to formal

operational reasoning. I suggest that EEG alpha anterior coherence represents temporal

and spatial coordination that supports improved information transfer and global brain

functioning.

Abstract approved: _______________________________Thesis supervisor

_______________________________Title and department

_______________________________Date

_______________________________Thesis co-supervisor

_______________________________Title and department

_______________________________Date

3

PIAGET’S CONCEPT OF FORMAL OPERATIONAL REASONING

AND WHOLE BRAIN FUNCTION: EVIDENCE FROM

EEG ALPHA COHERENCE DURING TRANSCENDENTAL MEDITATION

by

John W. Sorflaten

A thesis submitted in partial fulfillment of the requirementsfor the Doctor of Philosophy degree in Education

(Instructional Design and Technology)in the Graduate College of

The University of Iowa

May 1994

Thesis co-supervisors: Professor Barry BrattonProfessor Darrell G. Phillips

Copyright by

JOHN W. SORFLATEN1994

All Rights Reserved

Graduate CollegeThe University of Iowa

Iowa City, Iowa

CERTIFICATE OF APPROVAL

_____________________

PH.D. THESIS

__________

This is to certify that the Ph.D. thesis of

John W. Sorflaten

has been approved by the Examining Committee for thethesis requirement for the Doctor of Philosophydegree in Education at the May 1994 graduation

Thesis committee: ____________________________________Thesis supervisor

____________________________________Thesis co-supervisor

____________________________________Member

____________________________________Member

_____________________________________Member

_____________________________________Member

To the memory of my mother and to my father.

3

There is no greater kindness than the kindness of nature. All the laws of nature function in the direction of evolution. This inevitable flow of nature is a flow into which the individual can consciously put himself to let nature work on him for his evolution in accord with the natural flow of cosmic evolution.

Maharishi Mahesh YogiThe Science of Being and Art of Living

5

ACKNOWLEDGMENTS

I wish to thank all those who have encouraged and supported this work.

Archimedes claimed he could move the world if he were given a place to stand, a

sufficiently long lever, and an immovable pivot. My parents, who engendered that

primal cause, whatever it may have been, led me to pursue and complete the Ph.D. They

gave me a place to stand. I whole-heartedly thank the Eastman Kodak Company whose

far-sighted grant provided the “pivot.” They funded the Visual Scholars Program at the

University of Iowa, which in turn provided me the time and resources to pursue research

into the “role of visuals in learning, thinking, and communication,” whatever my

definition might be. The lever in this analogy is, of course, the group of faculty advisors

who have encouraged me and who truly helped me leverage my own ideas. Special

thanks to Dr. Darrell Phillips, the thesis co-supervisor, who graciously extended the

welcome and time of the U. of I. Science Education Department to this study, and who

insightfully advised me on the Piagetian theory and protocols. I also thank my other

dissertation committee members who reviewed this work and, in the spirit of enlightened

science education, let me chart my own path through the territory I chose to study. These

include Dr. Barry Bratton, thesis supervisor, and Dr. Lowell Schoer both from the

Division of Quantitative and Psychological Foundations of Education, home of the

Instructional Design and Technology graduate program as well as the Visual Scholars

Program. Other members from the Division of Curriculum and Instruction include Dr.

Jim Shymansky, Science Education, and Dr. John McLure, Curriculum and Supervision.

7

All the above are from the College of Education. The “outside faculty” member of my

committee is Dr. Thor Yamada from the U. of Iowa Hospital’s EEG facilities.

Thanks to each of my Visual Scholars Program advisors for believing that this

study could be interesting, and even be completed. This includes Dr. Kathryn

Alessandrini Lutz who served several years as the Director of the Visual Scholars

Program and Dr. Bikar Randhawa, Director at the time I was selected for the program.

Also, my heartfelt appreciation to Dr. William Coffman and Lida Cochran, who nurtured

my own progress even as they nurtured the Visual Scholars Program, not only with the

right ideas, but also with the right feeling behind the ideas. I also thank the Iowa City

Chapter of Phi Delta Kappa, which honored me with the yearly local Young Researchers

award for an outstanding dissertation topic. The award included funds toward research

expenses. Special thanks to Dr. Eric Schaffer, President of Human Factors International,

Inc. and my employer over the last 6 years, who provided not only friendly

encouragement, but also valuable time during work hours for completing this work.

Additionally, I extend my gratitude to Dr. William Vesely, and Susanne Arass-

Vesely, who supervised the EEG recording at Maharishi International University as part

of their responsibilities in the International Center for Scientific Research. I also thank

the students who participated in the study. Over time, I’ve had the chance to meet with

various EEG authorities who graciously answered my questions and made me feel “at

home” including Drs. Robert Thatcher, Alan Gevins, Don Walter (now deceased), Dulio

Giannitrapani and Hilton Stowell, who took time from his busy schedule to make a

delightful visit at my request.

Last, I wish to express my deepest appreciation to my wife, Theresa Olson-

Sorflaten, whose love and devotion allowed me to bring this work to a close.

TABLE OF CONTENTS

Page

LIST OF TABLES.............................................................................................................................................................................................................................. x

LIST OF FIGURES........................................................................................................................................................................................................................... xii

CHAPTER

I. INTRODUCTION...............................................................................1

General Rationale.........................................................................................................................................................................1

Justification..................................................................................................................................................................................1Theory....................................................................................

..................................................................................... 4Piaget’s Four Stages of Development.....................................

..................................................................................... 5First Three Stages.............................................................

...............................................................................5The Fourth Stage: Formal Operational Reasoning.............

...............................................................................6Developing the Structured Whole.....................................

...............................................................................7Cognitive Evolution: Experience (Objects and Logico-

Mathematical).........................................................................................................................................7

Cognitive Evolution—Social Transmission......................................................................................................8

Cognitive Evolution—Biological Maturation...................................................................................................9

Cognitive Evolution—Equilibration.................................................................................................................9

The Direction of Cognitive Growth - Greater Equilibrium.............................................................................10

Greater Adaptability.......................................................................................................................................10

Logic and the Left Hemisphere - Fact vs. Fancy............................................................................................12

The Measurable Left Hemisphere..................................................................................................................14

9

The Structured Whole and EEG Coherence...............................................................................................................14

Agreement on Value of “Wholeness”.............................................................................................................14

EEG Studies of Piagetian Theory...................................................................................................................15

EEG Coherence as Measure of Whole-Brain Integration. ..............................................................................17

EEG Alpha Coherence and Psychological Measures......................................................................................18

Statement of the Problem...............................................................................................................................21

Statement of Research Hypotheses.................................................................................................................23

II. REVIEW OF RELEVANT LITERATURE.........................................24

Writings of Jean Piaget...............................................................................................................................................................24

Reviews of Piaget’s Equilibration Model...................................................................................................................................28

Reviews of Research on Formal Operational Tasks....................................................................................................................29

Replication vs. Group Tests........................................................................................................................................................33

Projection of Shadows Task, Gender, Spatial Skills, and Achievement......................................................................................................................................................................33Research with the University of Iowa Grouping Model..........

...................................................................................33College and 12th Grade Subjects......................................

.............................................................................34Elementary and Middle School Subjects...........................

.............................................................................40Summary..........................................................................

.............................................................................42Other Research Using the Shadows Task................................

...................................................................................42Other Research on Spatial Reasoning and Gender...................

...................................................................................46Correlations Task............................................................................

...........................................................................................49University of Iowa Studies......................................................

...................................................................................49

Other Research Using the Correlations Task..............................................................................................................50

Combinations of Colored and Colorless Chemical Bodies Task.................................................................................................52

Communicating Vessels Task.....................................................................................................................................................54

Brain Localization and Piagetian Studies....................................................................................................................................55

EEG Coherence Studies..............................................................................................................................................................57Standard Cognitive State (Transcendental Meditation) and

EEG Coherence Studies....................................................................................................................................57

Studies Related to EEG Alpha Coherence and Intelligence........................................................................................59

Posterior Coherence Inversely Related to Intelligence....................................................................................59

Anterior Coherence Positively Related to Intelligence...................................................................................63

TM-Related Anterior Coherence Changes......................................................................................................64

EEG Alpha Coherence and Frontal Lobe Activation..................................................................................................68

III. METHODS AND PROCEDURES......................................................72

Pilot Study..................................................................................................................................................................................72

Sample Selection........................................................................................................................................................................72

EEG Measurement.....................................................................................................................................................................73Equipment..............................................................................

...................................................................................73Procedures..............................................................................

...................................................................................74Task Measurement...........................................................................

...........................................................................................74Task Selection Criteria....................................................................

...........................................................................................75Chemicals Task...............................................................................

...........................................................................................77Colored and Colorless Chemical Bodies Protocol...................

...................................................................................78

11

Equipment.....................................................................................................................................................78

Instructions....................................................................................................................................................78

Narrative Scoring Criteria for Colored and Colorless Chemical Bodies Task.......................................................................................................................................80

Communicating Vessels Task.....................................................................................................................................................80Communicating Vessels Protocol............................................

...................................................................................81Equipment........................................................................

.............................................................................81Instructions.......................................................................

.............................................................................82Narrative Scoring Criteria for the Communicating Vessels

Task..................................................................................................................................................................84

Projection of Shadows Task.......................................................................................................................................................85Projection of Shadows Protocol..............................................

...................................................................................86Equipment........................................................................

.............................................................................86Instructions.......................................................................

.............................................................................87Narrative Scoring Criteria for the Projection of Shadows

Task..................................................................................................................................................................89

Correlations Task.......................................................................................................................................................................90Correlations Protocol..............................................................

...................................................................................90Equipment........................................................................

.............................................................................90Instructions.......................................................................

.............................................................................91Narrative Scoring Criteria for the Correlations Task...............

...................................................................................94Analysis of Data..............................................................................

...........................................................................................94

IV. RESULTS............................................................................................96

Results of Subject Selection.......................................................................................................................................................96

Sample.......................................................................................................................................................................................97

Measurement Reliability.............................................................................................................................................................99Task Scoring Reliability.........................................................

...................................................................................99EEG Artifact Analysis............................................................

.................................................................................100Summary of Data............................................................................

.......................................................................................... 100Summary of Task Scores........................................................

.................................................................................100Summary of EEG Alpha Coherence Measures........................

.................................................................................105Analysis 1 - Unitary Composition of Task Index.............................

.......................................................................................... 105Analysis 2 - Relationship Between Gender and Task Performance. .

.......................................................................................... 111Analysis 2 - Relationship Between Coherence Index and Task

Performance..................................................................................................................................................................... 112

Analysis 3 - Relationship between Coherence Index and Task Performance Controlling for Age and Gender................................................................................................................... 115

Follow-up Analysis 1 - Analysis of Differences in Various Coherence Measures Between Pass and Fail Subjects....................................................................................................... 118Follow-up Analysis 2: Tests for Relationships Between

Preferences and Task Performance..................................................................................................................126

Follow-up Analysis 3: Tests for Relationships Between Preferences and Gender...................................................................................................................................128

Differences in Preference, by Gender, Without Regard to Task................................................................................................................................................................128

Differences Between Males and Females Within Each Task (Pass Groups Tested Separately From Fail Groups)........................................................................................130

Differences Between Pass and Fail Groups (Female Groups Tested Separately From Male Groups)............................................................................................................133

13

Conclusions Regarding Gender, Task Performance, and Preference Measures.......................................................................................................................................134

Follow-up Analysis 4 - Tests for Relationships Between Preferences and Other Variables....................................................................................................................................... 135

V. DISCUSSION AND CONCLUSION..................................................137

Review of Purpose and Procedures............................................................................................................................................ 137

Discussion of the Data............................................................................................................................................................... 140Proportion Passing the Tasks..................................................

.................................................................................140Formal Stage Criterion......................................................

...........................................................................140Shadows Task...................................................................

...........................................................................141Correlations Task..............................................................

...........................................................................142Combinations of Colored and Colorless Chemical Bodies

Task....................................................................................................................................................143

Communicating Vessels Task......................................................................................................................143

Hierarchical Ordering of Task Difficulty.................................................................................................................144

Inhelder and Piaget......................................................................................................................................146

EEG Coherence Measures........................................................................................................................................148

Task and EEG Alpha Coherence Index Relationships................................................................................................................ 150

Follow-up Analysis of Relationships Between Tasks and Other EEG Measures.................................................................................................................................................................. 155Summary of Follow-up Analyses in Various Coherence

Measures: The Effect of the TM Instructional Set...........................................................................................158

Limitations of the Study............................................................................................................................................................ 159

Long-term Effects of the Practice of Transcendental Meditation on Cognitive Functioning: Toward an Organicist Reduction

Theory of Piaget’s Constructivist Principles..................................................................................................................... 161Regulation of Selective Attention and the Mechanics of TM. .

.................................................................................162Cognitive Effects of the Practice of TM..................................

.................................................................................164Development of ORs to Significant Events and Habituation

to Distraction..................................................................................................................................................166

Implications of Frontal Functions for the OR and Adaptive “Stability”.......................................................................................................................................................169

“Integration of the Transcended in its Transcendence” (Piaget, 1986)..................................................................................................................................................172

Educational Implications of theTheory....................................................................................................................180

Summary of the Theory...........................................................................................................................................185

Recommendations for Future Research..................................................................................................................................... 189The Question of Bilateral Occipital Coherence.......................

.................................................................................189The Question of Information Transfer....................................

.................................................................................193

VI. TOWARD A NEUROPSYCHOLOGY OF EQUILIBRATION..........

199

Orienting and the “Transcending Reflex”........................................199

The Adaptive Significance of the Orienting Response.....................203

ORs Support Cognitive Success..............................................204

Stable Evoked Potentials Support ORs...................................207

IQ and Evoked Potentials (EPs) in Relation to Orienting of Attention.................................................................................

208Gating Out Distractions...................................................................

211Decentration Consists of Resistance to Involuntary ORs.................

215

15

A Role for Coherence in Accommodation and Reequilibration.......................................................................

217Relationships Between EEG Alpha Coherence and Increased EPs (i.e., ORs)........................................................................

220Conclusion–A Neuropsychology of Equilibration Processes

in the Context of TM........................................................................................................................................................ 223

APPENDIX............................................................................................................225

REFERENCES.......................................................................................................233

LIST OF TABLES

Table Page

1. Description of Color Schemes for Correlation Task.......................................................................................................................... 93

2. Percentage Agreement on Pass/Fail Ratings By Two Independent Judges (N=14)................................................................................................................................................................................. 101

3. Data Summary: Number of Subjects Scoring Each Level For Each of the Four Tasks and the Formal Stage Criterion.................................................................................................................. 102

4. Data Summary: Number and Proportion of Subjects Passing Each Task, the Combination of Tasks, and the Formal Stage Criterion.................................................................................................... 103

5. Data Summary: EEG Data By Total Subjects................................................................................................................................. 106

6. Data Summary: EEG Data By Gender............................................................................................................................................ 107

7. Analysis of Relative Difficulty of Task Pairs: McNemar Chi-Square Test for the Equality of Two Correlated Proportions (with Bonferroni Correction).................................................................................................................................................................... 108

8. Analysis of Differences in Male and Female Performance on the Four Tasks...................................................................................................................................................................................... 113

9. Results of Unpaired T-Test of Differences in Coherence Index Means between Pass and Fail Groups.............................................................................................................................................. 114

10. Results of Tests of the Assumption of Homogeneity of Slopes for Age as a Covariant with Task and Gender....................................................................................................................................... 116

11. Results of Analysis of Covariance in Coherence Index Between Tasks, Controlling for Age and Gender........................................................................................................................................... 117

12. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Formal Stage Criterion Pass and Fail Groups*.................................................................................................. 120

13. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Vessels Task Pass and Fail Groups*.................................................................................................................. 121

14. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Shadows Task Pass and Fail Groups*............................................................................................................... 122

15. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Correlations Task Pass and Fail Groups*.......................................................................................................... 123

16. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Combination Task Pass and Fail Groups*......................................................................................................... 124

17. Results of Tests of Differences in Preference Measures Between Task Pass and Fail Groups.............................................................................................................................................................. 129

18. Results of Tests of Differences in Preference Measures Between Male and Females........................................................................................................................................................................... 130

17

19. Results of Tests of Gender Differences in Preference Measures Taken Separately for Each Task Pass Group................................................................................................................................... 131

20. Results of Tests of Gender Differences in Preference Measures Taken Separately for Each Task Fail Group.................................................................................................................................... 132

21. Results of Tests for Relationships between Preference Measures and Non-task Variables................................................................................................................................................................... 136

22. Coherence Results for Orme-Johnson, Wallace, and Dillbeck (1982)............................................................................................................................................................................................. 149

23. Coherence Results for Nidich, Ryncarz, Abrams, Orme-Johnson, and Wallace (1983)......................................................................................................................................................................... 150

24. Results Summary............................................................................................................................................................................ 157

LIST OF FIGURES

Figure Page

1. Placement of the Derivations Used in TM EEG Alpha Coherence Studies.............................................................................................................................................................................................. 20

2. Chart of Concrete Operational Structures.......................................................................................................................................... 36

3. Contingency Relationships for Subjects With Scores on Both Tasks................................................................................................................................................................................................. 78

4. Ordering Diagram for Four Tests of Formal Reasoning: Arrow Indicates Direction of Logical Prerequisite........................................................................................................................................ 79

19

1

CHAPTER I

INTRODUCTION

General Rationale

The object of this research is to examine the possible relationship between two

major currents of educational theory that have developed over the last two decades. The

first trend involves a neurophysiological approach to cognitive skills, specifically in

terms of hemispheric lateralization of brain function. The second trend involves a

genetic-epistemological approach to cognitive development, specifically in terms of

Piaget’s theory of formal operational reasoning. Indeed it is difficult to imagine that a

relationship does not exist between these two theoretically attractive and empirically

convincing trends. While no literature has yet developed measures of one theory in

terms of the other, Inhelder and Piaget (1958) expressed the opinion that maturation of

the nervous system must certainly be a necessary, although not sufficient, condition for

the presence of the formal operational stage of logical thought (p. 281).

The primary purpose of this research is to test the hypothesis that some degree of

neurological coordination between the two hemispheres can be defined which is at least a

necessary, if not sufficient, condition for development of formal operational thinking.

Justification

Research on so-called “split brain” patients began in earnest with publications by

Gazanniga, Bogen, and Sperry on the effects of surgical sectioning of the corpus

collosum—the nerve fiber bundle which connects the two major masses of brain tissue.

Since these studies voluminous research has been done on both sectioned and

normal subjects toward the end of determining hemispheric correlates of psychological

attributes. Neurological approaches to educational issues have stimulated wide-spread

interest by educators and researchers since the mid-seventies. Bogen (1975), one of the

original researchers on split-brain patients found great encouragement for education now

that it has a fact about the brain—lateralization—from which we can begin to

systematically develop educational pedagogy. An entire issue of the UCLA Educator

(1975), edited by M.C. Wittrock, was devoted to educational applications of

lateralization studies.

Further interest was exemplified by the International Visual Literacy Association

which devoted its 1979 conference to the theme of integrated brain functioning and the

American Educational Research Association which has a special interest group devoted

to “Mind/Body Education,” including left/right hemisphere studies. More recently,

Waber (1989) explores the educational implications of not only left and right hemisphere

functioning, but also two other “axes” of brain function, frontal/posterior and

cortical/subcortcial. Waber points to evidence that frontal lobe activity modulates left and

right hemisphere biases that lead to differences in “cognitive styles” such as field

dependent vs. independent and impulsive vs. reflective behaviors.

As already mentioned, Inhelder and Piaget postulate an important role for

neurological development in the growth of logical thinking. To whatever degree that

educators advocate the ability to think rationally as the central goal of education, they

also presuppose development of neurological functioning as a necessary condition of

rational thinking (Educational Policies Commission, 1961). It should be noted that

logical thought is not solely the province of scientific reasoning; it belongs to the realm

3

of daily adult logical discourse as well, and for this reason has been adopted as an

explicit educational goal by various educators and curriculum authorities.

Therefore, an issue arises when after 8 to 10 years of formal education, many

high school students still have not attained the stage of formal operations (Haley and

Good, 1976). Even more dramatic is the evidence that 50% or more of college

undergraduates may not possess formal operations reasoning (Haley and Good, 1976).

Therefore, it will be important to seek neurological evidence of maturational differences

in early college populations. Such evidence may come from studies of hemispheric brain

functioning with special reference to interhemispheric activity and Piagetian stages of

logical development (Dennen, 1985; Dilling, Wheatley and Mitchell, 1976; Kraft, 1976;

Unruh, 1978).

Note that debate can be raised regarding the precise definition of “formal

operation reasoning, ” especially in the context of reports that 50% or more of college

undergraduates may lack formal reasoning. Such reports imply that a subject may not

have attained a “stage” of formal reasoning. However, such reports are misleading since

often they are based on the proportion of subjects passing a test of a given, single logical

structure, of which Piaget has identified ten. Failure on any given task should not be

taken as evidence for lack of “formal reasoning.” For example, Piaget has indicated that

“the developmental stages are not established by the development of single logical

structures as such. (Which one should we so privilege?)” (Italics by the author, Piaget

and Garcia, 1991. p. 130).

What, then, defines a “stage?” Piaget‘s approach suggests a wider perspective,

one that inquires whether the subject has undergone a re-organization of cognitive

structures in general, above and beyond success or failure on a test of a single logical

structure. Garcia writes “Here we find the core of the problem we are discussing: Each

stage cannot be conceived as simply a natural growth of the preceding one; each stage re-

organizes the whole of the instruments already used by the subject” (Italics by the author,

Piaget and Garcia, 1991, p. 136).

Further, Garcia explains:

Logical relations are not built in isolation, nor are they constructed all at once...(L)ogical relations are slowly being built up as fragments of structure which are gradually coordinated among themselves until some new structures with more coherent internal organization emerge...The way such coordinations take place represents a very complex process not yet studied in full detail. At a given moment, there is a convergence of various structural fragments in what we referred to above as a “structural kernel,” and, as already pointed out, each “fragment” may find itself at a different “level of development“ from the others. The stage is therefore not defined by any of those single lines of development but rather by what the child is able to do with all the fragments of structures he has built so far. (Piaget and Garcia, 1991, p. 140)

The “emergent” properties of stages reflect a discontinuity that may ultimately be

best explained by research into neurological readiness for higher stages of reasoning.

This is the thrust of the current study. I will examine both “stage” development and four

of the structures subsumed within the stage of formal operational reasoning.

Theory

One outcome of hemispheric brain functioning research has been heightened

awareness that current educational practices may discriminate against students who lack

aptitude in the verbal-analytic mode of instruction which predominates in most

classrooms today. The skills involved in such “left-hemisphere tasks” tend to reflect

processes associated with linear, time-dependent, or time-ordered stimulus or production

sequences such as speech or mathematical calculation. This is termed "propositional"

cognition in contrast to right hemisphere, “appositional” cognition (Bogen, 1975, p.26).

Appositional cognition excels at time-independent processing such as configuration

recognition and facial or figural pattern recognition (Ibid.). It seems reasonable that the

aptitudes used in logical thinking fall somewhere on this left-right hemisphere

5

continuum. At least one educational researcher who utilizes left/right brain explanations

of pedagogical theory has suggested that formal operational reasoning is a left-brain

process (Samples, 1975).

As will be demonstrated, there are many theoretical and empirical reasons to

suspect that a formal system of logical thought is very much a whole-brain process. The

following will first discuss important aspects of Piaget’s theory of cognitive

development, then relate it to brain functions.

Piaget’s Four Stages of Development

First Three Stages

Over several decades of research, Piaget and his colleagues amassed evidence of

four major stages of intellectual development: the sensory-motor, pre-operational,

concrete operational, and formal operational stages. Intellectual development begins

with the stage of sensory-motor orientation. During this stage, beginning at birth and

lasting until roughly 18 months, the child begins to separate objects from one another and

find relationships between his physical actions and their effects on objects. The child

realizes that objects continue to exist even though they pass from view.

The second stage of development continues the child’s developing understanding

of his environment in terms of his actions on objects. This is primarily manifested in the

development of language, or symbolic representation of objects and events. However,

the child mentally represents his world in terms of static configurations; that is, he cannot

mentally predict what will happen during the process of transforming something. Since

the child cannot yet deal with mental operations, the stage is called pre-operational

thought.

After about seven years, the child begins to apprehend mentally the operational

process of objects transforming or changing from one configuration to another. Thus, for

example, water poured from a short squat beaker into a tall thin beaker will be known to

maintain the same amount of water. Prior to this, the child would have said the amount

of water had changed as it was poured from one beaker to the other. The child’s ability

to grasp such transformations and, further, the ability to deal in terms of classes and

ordered relationships implies operational ability. However, these operations are limited

at first to experience of concrete objects rather than their mental representations. Also,

the operations remain uncoordinated between themselves.

This stage, which lasts until adolescence or later, is termed concrete operational.

A useful generalization is that the concrete operational thinker subordinates any thought

of what is possible to the actuality of his concrete experience.

The Fourth Stage: Formal Operational Reasoning

In contrast, the next stage, formal operations, is characterized by the

generalization that actuality is subordinated to what is possible. This is exemplified by

the system of formal logic and the possible relationships between two variables such as

“p” and “q.” For instance, given “p” and its negation “not-p,” and “q” with its negation

“not-q” there exist 16 possible combinations depending on whether the pairs are taken

one-by-one, two-by-two, three-by-three, the four together, or none at all. Logical

thought derives from possession of the implicit set of relationships represented by this

integrated “structured whole,” as Piaget calls it.

Making use of such combinations can result from either trial and error

experimentation, as is done by the concrete operational thinker, or by mentally

combining the variables in a hypothetical-deductive mode of thought, as is done by the

formal operational thinker. The formal operational thinker will feel quite spontaneous in

7

this thought process. If he is able to proceed to the heart of the problem, generate all

possible relations of variables, and outline for himself a systematic experimental

procedure to test the truth value of each relation, then that individual has access to a

formal system of logical thought. Such an individual can perform mental operations

which relate logical operations one to another. Access to this second-order ability to

perform operations on operations is the hallmark of the formal operational stage.

[In formal thinking, the subject seeks all possible combinations] so as to select the true and discard the false. In the course of this selective activity he intuitively constructs a combinatorial system. It is for this reason that he repeatedly passes from one propositional operation to another. [Propositional operations]...form a system or structured whole: such as the lattice or the group INRC (Piaget, 1957, p. 39).

Developing the Structured Whole

To fully understand what Piaget means by the “structured whole,” I turn to the

factors which Piaget has identified as contributing to the development of intelligence.

The most important of these in terms of a theory of formal operations will be covered last

under the topic of “equilibrium.” Piaget suggests four main factors supporting the

process of cognitive evolution: experience, social transmission, maturation and

equilibrium.

Cognitive Evolution: Experience (Objects and Logico-Mathematical)

Experience has two forms: object-oriented experience and logico-mathematical

experience. Object-oriented experience involves situations over which the child has no

overt control such as the conditions of his environment, objects present within his field of

activity, cognitive challenges, etc. Logico-mathematical experience involves events

which the child constructs for himself and which are applied to objects or events around

him.

Experience with objects can lead to figurative knowledge, (i.e. knowledge about

objects) or logico-mathematical knowledge, (i.e. knowledge of what can be done with

objects). For instance, the child who has pebbles before him utilizes figurative

knowledge by using the color names or shape names. The child utilizes operational or

logico-mathematical knowledge when he experiments in classifying the rocks by color or

shape or when he applies the number system to the succession of pebbles to see how

“many” pebbles are present. Through both kinds of experience the child eventually gains

the ability to “undo” an action mentally, leading to development of internal

representations, operations and ultimately operations on operations. Action on objects

particularly aids the child in eliminating contradictions in his thought and building

consistency among his mental structures.

Cognitive Evolution—Social Transmission

Accompanying the child’s experience with objects and logico-mathematical

concepts is the process of social transmission. The child’s attention is guided by the

values and challenges presented in his social environment. Social transmission can occur

via example, verbal precept, or any other means of acculturation. Piaget has suggested

that many of the ills of modern education can be traced to over reliance on verbal modes

of information transfer when dealing with pre-operational and concrete operational

students (Piaget, 1970, p. 72). Faced with teacher-centered, verbal learning, Piaget

suggests that many students substitute memorization of concepts and relationships in

place of operational comprehension of the logico-mathematical elements involved. As

many educators are finding, rote learning remains a fragile companion, and students

forget verbally founded “facts” because they have not developed the abstract reasoning

abilities necessary to support verbalization. For these reasons, curriculum developers

9

have advocated experience-based learning, typically referred to as inquiry-based or

discovery mode learning (Lawson and Renner, 1975; Matthews, Phillips, Good, 1977).

Cognitive Evolution—Biological Maturation

However, a problem remains with experience-based learning. The problem is

that certain experiences will be meaningful only if the information-processing capacity of

the central nervous system is sufficiently developed to accommodate to a challenging

situation. Thus the study of the growth of logical thinking presupposes a developmental

sequence of neurological learning readiness as a necessary, but not sufficient condition of

growth. Without such biological maturational readiness, no amount of instructional

planning, either student-centered or teacher-centered, can bring about advanced stages of

reasoning.

Cognitive Evolution—Equilibration

Neurological readiness returns us to our main topic of discussion: equilibration.

Piaget specifically addresses the role of nervous system maturation in relation to the

abstract psychological processes associated with formal structures as follows:

If someone wanted to say that an a priori form of reasoning accounts for the development of formal structures, he would have to accept the burden of proof of the fact that this a priori form emerges so late. Of course, he could always call on the effect of a late-maturing nervous structure, and such a structure is probably a necessary condition for the development of combinatorial operations. But the neurological explanation cannot in itself be sufficient because the occurrence of transitional phases shows that the new operations derive from earlier ones. Given this fact, it must be that a continuously operating equilibration factor plays a role beyond that of purely internal conditions of maturation, and the problem is to understand how a tendency toward equilibrium or its results can lead the subject to organize a formal combinatorial system. (Inhelder and Piaget, 1958, p. 281).

Piaget’s discussions of equilibrium cover several chapters in The Growth of

Logical Thought (Inhelder and Piaget, 1958) and he utilizes a monograph Logic and

Psychology (1957) and a book The Development of Thought (1979) to develop the

concept fully. It seems reasonable to cover the most salient points as they relate to our

specific topic of interest (the “structured whole”) and let other definitions and lines of

reasoning be read in their original sources.

The “Structured Whole”

The most direct path to understanding the structured whole emerges from our

previous discussion of the combinatorial system. That is, a subject who is formal

operational actively seeks to construct all possible combinations of the variables at hand

in order to systematically test each for its truth value. This method of problem solving is

so powerful that philosophers of science have independently given it a descriptive title:

hypothetical-deduction.

The Direction of Cognitive Growth - Greater Equilibrium

As Piaget has shown through many studies of child reasoning, hypothetical-

deductive reasoning does not appear until adolescence (and, as we have seen, even later

in many college students). Piaget’s research specifically attempts to trace the causal

origins of the development of formal operations. He concludes that formal thinking

represents the most stable form of adaptive response to the logico-mathematical

environment. In this sense, stability, or equilibrium in cognitive structures, takes on a

causal role in structural evolution by directing cognitive growth toward greater stability

or greater equilibrium.

Greater Adaptability

The drive toward equilibrium is initiated by the subject and not by his

environment. Cognitive adaptation in any other direction does not diminish

contradictions or increase the success of rational thought as much as the direction toward

the system of formal operations. Thus Piaget suggests that operational equilibrium

11

increases in adaptive mobility as it increases in stability. Growth in this direction of

increased number of possible transformations results from the use of mental reality or

mental representations of reality (Inhelder and Piaget, 1958, p. 331). Therefore,

equilibrium may have a neurological basis in the sense that any organism must have

some drive toward adaptive or “coordinated behavior”:

The empirical reality behind [symbolic logic] is the field of coordinated behavior. The concept of equilibrium proves indispensable to causal explanation from this standpoint; it makes it possible for us to understand how at a given level of development intelligence takes up simultaneously all of the directions opened up in this field as a function of the potential transformations which characterize it [as a “structured whole”], as well as of the portions already structured. If neurological considerations come to round out our explanation at some later date...these laws of equilibrium will prove to be more general than when linked to behavior patterns alone (Ibid., p. 333).

The Boundaries of Awareness

Piaget notes that a subject will not be aware of the general structure as a totality

because the totality is formed out of simple possibilities. Only the operations and

operational schemata actually used in some performances are manifest at any one time.

“The others must exist only as latent transformations which may appear in performance

in the appropriate situation.” (Ibid., p.330).

Logic Governed by “Field” of Structured Whole

Thus we can conclude this outline of Piaget's theory with remarks regarding the

necessary relationship between the development of cognition and the structured whole of

propositional logic.

The different schemata [of formal operations which subjects acquire] imply not merely isolated propositional operations, but the structured wholes themselves...which propositional operations exemplify. The structured whole, considered as the form of equilibrium of the subject’s operational behavior, is therefore of fundamental psychological importance, which is why the logical (algebraic) analysis of such structures gives the psychologist an indispensable instrument of explanation and prediction....[The state of equilibration is] one in which all the virtual transformations compatible with the relationships of the

system compensate each other. From a psychological point of view, the logical structures correspond precisely to this view. On the one hand, these structures appear in the form of a set of virtual transformations, consisting of all the operations which it would be possible to carry out starting from a few actually defined operations. On the other, these structures are essentially reversible; that is to say, the virtual transformations which they permit are always self-compensatory as a consequence of inversions and reciprocities. In this way we can explain why the subject is affected by such structures, without being conscious of them. When starting from an actually performed propositional operation, or endeavoring to express the characteristics of a given situation by an operation, he cannot proceed in any way he likes. He finds himself, as it were, in a field of force governed by the laws of equilibrium, carrying out transformations or operations determined not only by occurrences in the immediate past, but by the laws of the whole operational field of which these past occurrences form a part. (Piaget, 1957, pp. 41 & 45)

The notion of two largely lateralized modes of thought suggests that teaching by

either precept or percept affects primarily one or the other hemisphere. Learning of

almost any idea is likely to be better if both methods are used. Since education is

effective only in so far as it affects the working of the brain, we can see that an

elementary school program narrowly restricted to reading, writing, and arithmetic will

educate mainly one hemisphere, leaving half of an individual’s high-level potential

unschooled (Bogen, 1975, p. 27).

Thus, on the one hand, we find an important link between Piaget’s emphasis on

experience with objects and Bogen’s previously mentioned emphasis on right-brain

education. Both Piaget and Bogen suggest that development of intelligence can be

influenced by the types of experience gained by students. Both researchers imply that

experience is mediated by neurological functioning. Both researchers would agree that

experience also influences the degree to which brain function potential is manifested

developmentally.

Logic and the Left Hemisphere - Fact vs. Fancy

On the other hand, however, there appears to be some disagreement about the

precise relationship between the development of logical thought and the correlates of

13

logical thought relative to left/right brain lateralization. At least one researcher appears

to equate reasoning skills with left-hemisphere educational practices. Robert Samples

(1975) suggests that Piaget’s developmental hierarchy deals only with left-brain

rationality to the exclusion of right-brain skills, here identified as metaphoric thought.

In early stages of development, according to Piaget, many of the kinds of mindwork best labeled as inventive and integrative in the metaphoric styles are common. Yet inherent in the philosophy of Piaget’s thinking is the developmental thrust to get past those stages into more concrete and formal logical operations. The results are obvious. Schools led by the psychological prejudices of cognitive psychology, by the hierarchies of intellectual development of Piaget, and thus by a dominance of left-hemisphere approaches, systematically wean out the metaphoric strategies. Children, who have a natural tendency to deal with mindwork that includes all four metaphoric styles, are trained to focus comparative and symbolic, the counterparts of Piaget’s concrete operational and formal operational stages (Samples, 1975, p.23).

Of course, Samples ultimately advocates development of both sets of skills in

educational settings. But it serves our research interest here to closely examine the

reason Samples chooses to link reasoning skills with left-hemisphere propositional

aptitudes. The outcome of this examination will suggest that formal operational

reasoning actually has a large component of what Bogen would call right-brain

appositional aptitude and ultimately reflects whole-brain processes. It appears that part

of Samples’ error results from equating “reasoning skills” with the sort of verbal

learning we have already seen criticized by Piaget. Samples ignores the need for a

“structured whole” to underlie any reasoning skills demonstrated verbally.

Other writers also have questioned whether “meaning” in its essential nature is

solely sequential. Evans (1980) cites the dual-process theory of Wason and Evans (1975)

that proposes two different kinds of thinking:

Type 1 processes, which are non-verbal and non-introspectible but control actual selections, and Type 2, verbal processes which underlie the rationalization. It is interesting to note that the Type 2 process corresponds much more closely to the common-sense reasoning....The striking point is, of course, that this Type 2 verbal reasoning process does not operate to control the actual reasoning behavior. (p.235-236).

The Measurable Left Hemisphere

Samples (1975) suggests that propositional (or left-brain) learning predominates

in education because it is easier to measure and evaluate for progress. He says:

Because the cognitive domain, as it has been called, was so rational, so logical and so verifiable, it infatuated those who measured. It is, in fact, far easier to deal with the functions of the left cerebral hemisphere, not necessarily in terms of origins of complexity, but primarily because of the nature of visible cues. Language, linear reasoning, arithmetic and mathematics are much easier to measure and evaluate. The right cerebral hemisphere, on the other hand, obviously capable of handling multiple variables simultaneously, is far more elusive. The result was a detour that took educators’ attention away from intuitive, metaphoric and inventive capacities of the mind. (Ibid. pp. 19-20)

In speaking of “handling multiple variables simultaneously,” Samples ostensibly

refers to the non-linear, time-independent properties of appositional thought. It appears

that Samples does not equate that sort of mental process with the “cognitive domain” of

rational, logical thought. I contend that Samples has confused the process of speaking

about logical thought with the process of doing logical thought. Two reasons

substantiate this contention: 1) Piaget’s theory suggests that formal operational thought

proceeds upon access to a “structured whole,” i.e. multiple variables processed

simultaneously and 2) research using brain-wave recording techniques indicates that,

although the left brain is engaged in speaking about a problem solution during a

Piagetian task, the right brain may be engaged in thinking about the problem. (Kraft,

1976)

The Structured Whole and EEG Coherence

Agreement on Value of “Wholeness”

Various statements by Piaget and Samples indicate that both agree on rational

thought requiring some version of “wholeness.” This joint conclusion by opposing

parties leads to a testable hypotheses regarding whether logical reasoning is a left-brain

15

process, a right-brain process, or a whole-brain process. Each alternative has its

pedagogical implications.

Piaget discusses the transition from the concrete to formal operational stage in

terms of access to the interconnected set of 16 propositional operations (the structured

whole). “Henceforth,” says Piaget, “[formal] thought proceeds from a combination of

possibility, hypothesis, and deductive reasoning, instead of being limited to deductions

from the actual immediate situation” (Inhelder and Piaget, 1958, p. 16).

In comparison to Samples’ passage on right-brain aptitudes, it appears that

Piaget’s concept of the structured whole is no different than the capacity of “handling

multiple variables simultaneously,” as Samples puts it. In fact, Piaget uses terminology

similar to Samples’ own phrases. For example, in a discussion of conservation of motion

in a horizontal plane, Piaget explains the cause of failure in the concrete operational

subject. He writes, “Time after time he fails to determine all the relevant variables

simultaneously. Thus, CHAP discovers the factor of air resistance but fails to think of

the friction for the heavy balls” (Ibid., p. 129) (My italics). In this sense, Piaget indicates

logical thought seems to have a necessary (but perhaps not sufficient) component of

right-brain aptitude. Piaget uses the same line of reasoning about reasoning as Samples.

But interestingly, Samples still feels Piaget’s theory only covers half the brain.

Additional evidence of right-brain involvement in logic comes from experimental

findings by Unruh (1978). Utilizing a psychomotor “torque test” for hemispheric

dominance, Unruh concluded that the Piagetian model does not refer to development of

the analytical hemisphere alone. He suggests that right-hemisphere learning activities

may aid understanding in courses such as physics and astronomy.

EEG Studies of Piagetian Theory

From a neurological point of view, at least three studies have sought

electroencephalographic (EEG) evidence of “whole brain” correlates to performance on

Piagetian tasks.

In a study by Dilling, Wheatley and Mitchell (1976), formal operational

university students showed greater left hemispheric activity during a series of cognitive

tasks than concrete operational students. The EEG measure was log Left/Right alpha

power ratio. The findings seem to support Samples’ contention that formal operational

thought requires greater left-hemisphere activity than other modes of thought. However,

the findings must be considered in light of the restricted number of subjects (six concrete

operational and seven formal operational) and the fact that the findings held only for

alpha readings over the temporal region and not the central region. Readings were taken

during the problem-solving events and no information was presented regarding the

amount of verbal activity relative to thinking activity given during the EEG trials.

(Greater verbal activity will necessarily cause greater left-hemisphere activity, whereas

thought alone may not.) The influence of verbal activity was controlled in another study

done in Wheatley’s laboratory by Kraft (1976, published in Kraft, Mitchell, Languis and

Wheatley, 1980). This second study, however, dealt with concrete operations.

In Kraft’s (1976) study the subjects were six to eight years old and the measure

was also a computer analyzed log Left/Right alpha power ratio. However, measures

were taken during the thinking phase as well as the speaking phase of problem solving.

During the spatial-visual period of the problem solving tasks, subjects demonstrated

right-brain activity. During the subsequent verbal response period, the tasks were

accompanied by left-brain activity. High performers tended, however, to show less left-

brain specialization than low performers during the verbal response period. The author

concluded that:

17

even while high performers gave verbal responses, they utilized greater ability to tap the visuo-spatial right hemisphere’s knowledge about the stimulus. Therefore, Piagetian tasks are behavioral measurements of interhemispheric communication and selective inhibition and further, that the ontogeny of Piagetian stages is a behavioral index of maturing neural fibers (between the left and right cerebral hemispheres and from the reticular activating system to the two hemispheres) which facilitate these processes. (Kraft, 1976)

This speculation is inferred on the basis that subjects who performed better had

higher left/right alpha power ratios during solution presentation, implying less

specialization of the left hemisphere under speech conditions. However, there is no

direct evidence of the degree to which either or both hemispheres contribute to

performance For this it is necessary to utilize a different computer analysis of EEG data,

called “coherence.” Also, there is no direct evidence of interhemispheric

“communication” or transmission of any signal between hemispheres. The Kraft (1976)

and Dilling, et al. (1976) studies merely show L/R ratio covariance with task

performance. No causal link between L and R hemisphere activity is shown. Again,

EEG “coherence” can provide such evidence.

The third Piagetian EEG study used measures of formal reasoning and EEG alpha

coherence (Dennen, 1985). It will be covered below.

EEG Coherence as Measure of Whole-Brain Integration

Briefly, coherence is a mathematical function which describes covariation

between two frequency bands. It has the same interpretation as a squared correlation

coefficient. Coherence expresses the electrical activity of one EEG record as a linear

transformation of activity in another EEG record (Walter, 1963).

An EEG record can be a single recording site on the scalp or a combination of

sites. Coherence is typically computed by decomposing the complex EEG wave form

into its component sine waves. The sine waves are grouped by adjacent frequencies

within an experimenter defined bandwidth (2 to 5 Hz, typically). Within each band, one

EEG record is compared with its counterpart in terms of the change in phase angle

between the sine waves over a given period of time. Coherence, then, is an index of the

degree of stability in the phase angle estimated to relate two EEG records.

Coherence is influenced by changes in frequency or phase between two EEG

records and is unaffected by differences in amplitude. One may consider coherence as a

measure of the variance of one record accounted by variance in the other record, much in

the same sense that the Pearson product-moment correlation coefficient squared

expresses the variance shared between two variables.

Coherence was initially used to study vibration in aircraft and geological

structures, and was adopted for monitoring vigilance in the Gemini space program

astronauts. Initial studies of coherence for the space program investigated learning in

cats (Adey, Walter, and Hendrix, 1961). The researchers found that after training, cats

who responded correctly to stimuli showed greater coherence over the 2-10 Hz band than

cats making incorrect responses. This finding indicated that both vigilance and adaptive

advantage were possibly associated with coherence. Additionally, it is the intrinsic

nature of coherence to reflect anatomical integration and information transfer between

brain areas as measured by EEG.

EEG Alpha Coherence and Psychological Measures

Studies on humans have continued over the years, with at least two early studies

advancing the possibility of coherence measured during the practice of Transcendental

Meditation as an index of intellectual advantage. Most of these studies used EEG

measurements identical to those used in the current study. See Figure 1 for the

placements of the various leads mentioned in the following discussion. One study found

that alpha frontal bilateral coherence was significantly (p <.05) correlated with SAT

Math, SAT Verbal, grade point average, verbal IQ and moral reasoning (Orme-Johnson,

19

Wallace, Dillbeck, Lukenbach, and Rosenberg, 1979). Another study found that alpha

bilateral frontal coherence (F3F4) correlated positively with measures of Fluency,

Flexibility, and Originality on the Torrance Test of Creative Thinking, verbal form.

However, alpha coherence correlated negatively with the same test at the O1O2

derivations (Orme-Johnson and Haynes, 1981). This implies that bilateral occipital

coherence has functional significance different from bilateral frontal coherence. In a

third study, performance on a concept-learning task was better for subjects who had

higher measures of alpha frontal coherence (Dillbeck, Orme-Johnson, and Wallace,

1981).

A fourth study used a coherence index which summed alpha coherence values

greater than .95 for Frontal, Left, Right derivations, and subtracted Occipital coherence

(FLR-O). The authors found this index to be positively related to the subjects’ grade

point average of 20 courses and negatively related to neuroticism. Together they

provided a multiple R of .58 (p = .005). They concluded that “the Coherence Index may

be a very general index of CNS maturation” (Orme-Johnson, Wallace, Dillbeck,

Alexander, Ball, 1982). The FLR-O coherence index suggests that a simplistic

acceptance of coherence as interhemispheric “communication” may be unwise because O

coherence is inversely related to “CNS maturation” for these authors.

Dennen (1985), in a Ph.D. thesis for the University of Florida, found no

significant linear relationship between Piagetian cognitive performance and the EEG

alpha coherence index nor individual measures of coherence. I note, however, that

Dennen used a paper and pencil test of formal and concrete reasoning. A purely verbal

approach to examining Piaget’s concepts of intelligence may impose sufficient

limitations on strategies used by the subjects as to eliminate the expected EEG

differences. Dennen used 349 undergraduate students whose EEG measures were taken

during TM at the same university as the previously cited coherence studies. Therefore,

the coherence measures and subject selection are certainly comparable. Dennen did find,

21

F3 F4

C3 C4

O1 O2

F3C3

Left(Homolateral Derivation)

F3F4 Frontal (Bilateral Derivation)

F4C4

Right(Homolateral Derivation)

O1O2

Occipital(Bilateral Derivation)

Front of head

Top View

Figure 1. Placement of the Derivations Used in TM EEG Alpha Coherence Studies

however, that physics majors, compared to other majors, displayed higher left, right, and

frontal coherences during TM.

In summary, neurophysiological evidence from this sample of studies using a

“standard cognitive state” of TM as well as Kraft’s (1976) study implies that the growth

of logical thought (and learning) reflects the activity of both hemispheres and is not

solely the province of left-brain functioning, as proposed by Samples. This may be

termed “whole-brain” functioning. These conclusions are based on studies of left-right

hemisphere alpha power ratios as well as coherence for F, L, R, and O. Increased

hemispheric communication or interaction is suggested by increased bilateral frontal

coherence. The inverse correlation of bilateral occipital coherence with the anterior

derivations (viz. F+L+R minus O) remains to be discussed in the context of an extended

theory presented in Chapter Five.

Statement of the Problem

The present study tests the relationship of formal operational reasoning and EEG

alpha coherence. In order to decrease between groups variance, a composite measure of

alpha coherence will be used: FLR-O. This measure also represents “whole-brain”

functioning acknowledging the as-yet-unexplained negative relationship with occipital

and lateral coherence. The formal structures tested in this project include the

combinatorial operations schema, the INRC group structure (as found in the mechanical

equilibrium schema), the proportionality schema, and the correlation schema. Subjects

will be grouped according to pass or fail for each task. The dependent variable will be

the FLR-O coherence index measured during eyes-closed TM.

EEG coherence is defined for each subject as the mean coherence within the

alpha band, (9-11.95 Hz). Coherence is combined across the four major EEG derivations

as follows:

23

Coherence Index = (F3F4) + (F3C3) + (F4C4) - (O1O2)

I shall abbreviate this as CI = FLR-O. A single index of coherence is computed

as the sum of the frontal bilateral derivation and the two homolateral derivations minus

the occipital coherence. Since prior research indicates a negative correlation between

occipital coherence and creativity, as well as GPA, the occipital coherence is subtracted

from the three preceding coherence values.

To allow comparisons with previous coherence research and to provide a standard

cognitive state suitable for further replications, EEG measures are taken while the

subjects practice a standardized, commonly taught, and readily available closed eyes

meditation technique, Transcendental Meditation. This is also the same cognitive state

used in the previously described research by Orme-Johnson, Dillbeck, Dennen, and other

researchers.

The study evaluates the strength of the relationship between the scores on each of

the formal operational tasks and the Coherence Index. Since gender and possible age

differences are expected to interact with task performance, all EEG measures will first be

tested with no correction for gender and age. Follow-up analysis will also test for

relationships when alpha coherence is normalized with respect to gender and age prior to

applying any statistical tests.

The study will evaluate the relationship between the Coherence Index and

evidence for attainment of the “stage” of formal reasoning. I will assume that subjects

who fail all four tasks lack evidence of the cognitive reorganization characteristic of

formal reasoning.

Statement of Research Hypotheses

Ho1: There is no significant positive relationship between the FLR-O Coherence

Index and pass-fail measures of formation operational reasoning in any of these four

tasks: Communicating Vessels, Shadows, Combinations, and Correlations.

Ho2: There is no significant positive relationship between the FLR-O Coherence

Index and a pass-fail measure of the formal operational stage. The formal operational

stage is defined as passing at least one of these four tasks: Communicating Vessels,

Shadows, Combinations, and Correlations.

25

CHAPTER II

REVIEW OF RELEVANT LITERATURE

Writings of Jean Piaget

This dissertation examines the relationship between some formal operational

structures and physiological measures of EEG coherence, thereby qualifying as an

attempt at an “organicist reduction” explanation of abstract constructivist structures. This

program of research is discussed and advocated in Piaget’s chapter, “Explanation in

psychology and psychophysiological parallelism” in Experimental Psychology: Its Scope

and Method, Volume I History and Method (Piaget, Fraise, and Reuchlin, 1968). Of

particular interest is Piaget’s recognition of neural interconnection as a source of

psychological structure. He endorses Fessard’s idea of an interdependent lattice of

neurons, like the brain’s reticular formation, “whose elements have identical properties”

and which support “the possibility of introducing a certain homeostatic stability” amidst

“new functions being established between already-formed connections” (p. 173). Piaget

agrees with the organicist reduction trend of modern psychology. He then suggests that a

scientific explanation explains at least a complementary relationship between abstract,

deductive models and neurology, if not more.

We can now interpret this complementarity by basing it on deeper reasons: if parallelism between facts of consciousness and physiological processes is isomorphism between the implicative systems of meanings and the causal systems of the material work, it is then evident that this parallelism involves equally, not only a complementarity, but in the final analysis the hope of isomorphism between the organicist schemata and the logico-mathematical schemata used in abstract models (p. 190).

As a biologist, most of Piaget’s work examines in one form or another the

development of the facts of consciousness. But only later writings attempt to explicate in

detail the laws that underlie the increasing capacity of intelligence to describe the

objective world. In The Grasp of Consciousness (Piaget, 1976) Piaget begins exploring

these issues by describing how the child’s actions themselves embody knowledge, albeit

of an unconscious nature. The theme is continued, with reference to conscious processes

in Success and Understanding (Piaget, 1978). Here, Piaget concludes that while success

is “effective utilization,... understanding brings out the reason of things (because)...it

goes on to knowledge that can dispense with action.” As the subject constructs

operations on preceding operations, indefinitely, the “world of possibilities...necessarily

transcend the bounds of action...the world of ‘reason’ spills over into the world of

possibilities and thus surpasses the given reality” (p. 222).

Piaget culminates this line of research in the development of knowledge in The

Development of Thought, Equilibration of Cognitive Structures (Piaget, 1977). Piaget

discusses the types of equilibration processes that give rise to structures, the reasons for

disequilibration, and causal mechanisms of equilibrations and re-equilibrations. (See the

critical review by Pascual-Leone, 1988 that suggests that while the book describes the

varieties of equilibration, it fails to describe a causal mechanism.) This work itself

contains no clinical interviews, but rather builds on the body of prior research to expand

on the mechanics of cognitive development. Piaget acknowledges neurophysiological

mechanisms that influence knowledge of the object. He cites Pribram’s findings that the

cortex exercises selective attention, admitting some stimuli and eliminating other stimuli.

Piaget identifies this phenomenon as an analog of perceptual centration. “In these

(psychological) centrations, which are abstract and no longer perceptual, we again find

distortion caused by the overestimation of the importance of the characteristics of the

27

objects of attention and the devaluation of the others which are not centered” (p. 144).

Piaget suggests that the individual unconsciously perceives all the important

characteristics of the objects (via “subception”, Cf. Eriksen, 1960, not cited by Piaget),

and that normal regulations will ultimately lessen

the repression of the elements which earlier were set aside....(T)he disturbance can be attributed to the nascent power of these elements, which tend to penetrate into the field of recognized observables, and the compensation will then consist in modifying the disturbance until it becomes acceptable (p. 144).

Of importance to our study of left and right hemisphere differences, Piaget notes

that subception is probably not “unconscious” perception, but rather “perception of

which our consciousness is simply short and evanescent for lack of integration into the

conceptualized consciousness” (p. 146). Because this characterizes non-verbal, right-

hemisphere activity (but not mentioned by Piaget), I give Piaget’s explanation in full:

For example, I often take out my watch and look at the hands without verbal translation. Since it is not before me I take out my watch again a few minutes later and then remember having previously looked at it. My visual perception therefore was not unconscious, since there was memory with delay, but suggests a primary state of consciousness without conceptualized “awareness,” and therefore without the integration which would make it knowledge (as opposed to a mere perception). (p. 146).

Further discussion sheds light on the constructive mechanisms used to overcome

disturbances in equilibrium. For our purposes, these mechanisms indicate the necessity

for neurophysiological mechanisms of inhibition to overcome habits or impulses that

otherwise erroneously represent an object or its status. An erroneous conceptualization

creates a “disturbance” by virtue of rejecting or repressing the true state of the object. To

ameliorate such disturbance, the subject invokes a compensation: “the action in the

opposite direction which will conquer this rejection.” Reinforcement of such

compensation is accomplished via regulations that become more operational over the

period of dissolving the disturbance. Piaget acknowledges the power of such regulations

as being formative, “since conquering the repression involves a modification of the

opposing conceptualization, and on a restricted terrain, it imposes a reorganization,

which is a construction” (p. 153).

Piaget explores similar themes of cognitive growth in Adaptation and

Intelligence, Organic Selection and Phenocopy (Piaget, 1980), originally published in

French in 1974, the year prior to the French publication of The Development of Thought.

However, Adaptation and Intelligence pursues the analogical parallels between the laws

of cognitive development and development of non-human organisms, with particular

regard to the processes of phenotypic adaptation representing equilibration processes

between the organization and its environmental niche. The volume attempts to clarify

the adaptive, constructive processes of intelligence through analogy to the processes of

phenotypic exploration of opportunities for survival in any new environment. While not

using organic reduction per se with regard to intelligence, Piaget provides many

illuminating insights into issues a biological model should address.

Guidance in the definitions of equilibration, formal reasoning, and in the

construction of the four tasks was found in The Growth of Logical Thinking, From

Childhood to Adolescence (Inhelder and Piaget, 1958). Design of the tasks was taken

from chapters 7, 9, 13, and 15, respectively titled, “Combinations of Colored and

Colorless Chemical Bodies,” “Communicating Vessels,” “The Projection of Shadows,”

and “Random Variations and Correlations.” Details on formal reasoning and

equilibration processes were given in the Introduction section, Chapter 1, of this

dissertation. Details on the tasks will be given in the Methods section, Chapter 3, of this

dissertation.

29

Other sources of Piaget’s discussion of equilibrium and equilibration include

Piaget’s (1977) article Problems of Equilibration in which he indicates that “self-

regulation is the important idea for us to take from biology” (p. 9). and Piaget‘s (1972)

book The Principles of Genetic Epistemology. The latter book provides insight into limits

that Piaget would put on a “reductionist” course of explanation. The problem with

reductionism is that on face value, it suggests that higher level structures are “explained”

by lower level structures or regulations.

In the biological field there have been attempts to reduce living processes to known physico-chemical phenomenon, attempts that failed to note the possibility of change in a discipline which is continually being modified; and the reaction was an anti-reductionist vitalism, whose sole merit was the entirely negative one of denoucing the illusions engendered by such premature reductions....

From both these views every ‘new’ structure should be preformed: either within the simplest element or within a complex one; and novelty would only consist in a successful explication of preexisting relationships. Reciprocally, the refutation of reductionism provides a basis for constructivism.

In cases where it has been possible to resolve the problem, the end result has been a situation surprisingly in agreement with constructivist hypostheses: between two structures of different levels there can be no one-way reduction, but rather there is reciprocal assimilation such that the higher can be derived from the lower by means of transformation, while the higher enriches the lower by integrating it. In this way electro-magnetism has enriched classical mechanics, given rise to a new mechanics...In short, the construction of new structures seems to characterize a general process which is constitutive in character and not reducible to a method for achieving a predetermined end. The failures of causal reductionism in the field of the natural sciences; those of deductive reductionism with respect to the limits of formalization and the relationships between mathematics and logic: these all spell the failure of the ideal of a complete deduction implying preformation, and the success of constructivism, which is becoming increasingly vindicated (pp 92-93).

For additional discussion on the the question of the origin of “novel” Piagetian

structures, see Campbell and Bickhard (1987), Bereiter (1985). The relationship of

equilibration and the development of novel structure is covered in a dialog between

several writers: Juckes (1991), Boom (1991), Bereiter (1991) and Pascual-Leone (1991).

Reviews of Piaget’s Equilibration Model

The issues of equilibration are made more palpable in several tutorial articles.

Lawson (1982) applies Piaget’s concepts of equilibration to biology instruction and

evolution. Renner, Abraham, and Birnie (1986) analyzed student teaching dialogs

from a 12th grade physics class to illustrate a cycle of learning. The learning begins

with assimilation that leads to disequilibration, and continues with accommodation

leading to a new organization and a more stable form of equilibration. Parkins

(1987) outlines the concept of equilibration in control system terms alluding to

left/right hemisphere differences. He makes his points in the form of several

cybernetic control flow charts that illustrate a self-correcting, self-regulating adaptive

system. Moessinger (1978) provides a concise tutorial on Piaget’s key ideas from the

book Development of Thought. It is particularly helpful in explaining notions

surrounding the types of equilibrium, including the relationship between the subject

and the object. It addresses the history of Piaget’s model and some criticisms levied

against it. Furth (1977) suggests that Piaget’s account of equilibration is

“biologically and humanly relevant” to students of psychology (p. 18). Gallagher

(1977) gives a tutorial relating the concept of equilibration to its conceptual roots in

biology, logic and cybernetics. Brent (1978) summarizes the implications of Piaget’s

equilibration in the context of Prigoine’s model of “dissipative structures” as a means

by which complex non-equilibrium systems paradoxically manifest self-organization.

Reviews of Research on Formal Operational Tasks

Haley and Good (1976) point out the discrepancy between demands for formal

reasoning in introductory college biology textbooks and the lack of formal reasoning

among many students. They cite results from seven studies using subjects of college

age or above and six studies using high school students. Acknowledging variation in

31

tasks and procedures, they point out that between 11-61% of the tested college subjects

and an average of only 44.5% of the tested 11th and 12th graders used formal

reasoning. Similar passing rates are presented in a review by Blash and Hoeffel (1974)

who thoughtfully lists studies by task, age groups, and the proportion of subjects

passing the task.

Modgil and Modgil (1976) have the distinction of compiling the most complete

review of Piagetian studies and monographs to date, using several volumes to present

their monumental work. It is a cornucopia of research abstracts and short monographs

classified by categories for easy access. The section on formal operations is

informative.

Chiappetta (1977) reviewed ten studies of high school and college students and

concluded that in addition to the overall low percentage of formal reasoning among

students, those who demonstrated formal reasoning on tests in many cases failed to do

so on course work. In light of this, Chiappetta cites Piaget’s (1972) extension of

developmental period of formal reasoning from 11 - 15 years to 15 - 20 years. He

emphasizes Piaget’s qualification that young adults use formal structures in relation to

their area of specialization. Implying, Chiappetta suggests, that science educators must

“build” such structures in their students by introducing concepts in concrete operational

form.

More recently, Nagy and Griffiths (1982) reviewed a large number of Piagetian

formal reasoning studies, paying particular attention to their (many) methodological

flaws. Ranging over many significant topics, the authors conclude: 1) the interview

method determines reasoning levels more effectively than group-administered tests, 2)

even interview methods have pitfalls, such as inconsistent scoring criteria across tasks

by the same investigator or cumulative scoring across several tasks 3) the unity of

formal schema cannot be easily determined with factor analysis, but probably demands

a method based on “consistency of classification” (p. 535), 4) level of development is

clearly, but weakly related to achievement in the science classroom, 5) the jury is still

out on the efficacy of training students in formal reasoning skills.

Meehan (1984) examined the literature between 1972 and 1982 and found 53

studies of formal operational reasoning for her meta-analysis of sex differences. Twenty-

seven studies dealt with propositional logic, 16 dealt with proportional reasoning-type

tasks and 10 dealt with combinatorial-type tasks. Taken together, she found performance

advantages for males with one to five percent of the variance explained by gender. There

was no difference between the 17-year-old and under group compared with over 17-year-

olds. The most reliable finding of sex differences was for the proportional reasoning

problems, with a percent non-overlap of the male and female distributions falling

between 22.2 percent and 31.6 percent. (This group of tasks included three of the tasks

in the current research: Communicating Vessels, Projection of Shadows, and

Correlations.) Meehan did not present an overall pass rate for any of the tasks or groups

of tasks. Note that 34 cases used paper-and-pencil measures of formal operations and

108 cases used manipulative measures.

Lawson (1985) reviews a large number of studies of formal reasoning and

concludes that: 1) lack of formal reasoning is a probable cause for lack of ability in “the

sciences, mathematics, history, social studies, English, and in everyday contexts such as

comparative shopping” (p. 609), 2) formal reasoning is hindered by “intellectually

restrictive social environments, field dependence, low mental capacity, and perhaps by an

impulsive cognitive style” (p. 609), 3) lack of lateralization or hemisphere specialization

may be related to lower developmental levels.

33

Dennen (1985) lists some Piagetian studies in which young and middle-aged

adults outperform older adults in a variety of problem-solving tasks.

Halford (1989) reviews research that questions whether Piaget’s models of

cognitive development are as explanatory as more recent “neo-Piagetian” theories.

Halford’s review is unique in mentioning neurophysiological evidence of brain and

hemisphere maturation that appear to support Piaget’s idea that certain structures can be

attained at lower age limits. This evidence suggests that “attempts to dismiss Piaget’s

theory may be premature, and furthermore, that the development of processing capacity

is overdue for intensive investigation” (p. 348).

While not a review, per se, Martorano’s (1977) interview-based research deserves

some mention for its attempt to determine (“review”) relationships between a large

number of formal schemas. She used interview protocols to study females in grades 6, 8,

10, and 12. She administered ten tasks to each subject, over two meetings, to study these

five schema: combinations, proportionality, multiplicative compensation, mechanical

equilibrium, and correlations. She focused on females to overcome issues of

inconsistency in findings due to gender differences. She concluded that a given subject

did not score similarly across all the tasks. Thirty-three percent of the subjects showed

differences by two substages and 61% demonstrated differences by three substages.

Martorano ordered the proportion of passing performance of the ten tasks and found that

tasks that tapped the same schema appear adjacent to one another. Bart and Mertens

(1979) used her data for an “ordering theoretic” analysis and confirmed that the tasks

within schemes were empirically equivalent and that some common structure underlies

all the tasks. Relative to the schemas examined in the current research, Bart and Mertens

found that combinations was a prerequisite to the proportions and mechanical

equilibrium schemas. The correlation schema was also prerequisite to mechanical

equilibrium. In another analysis, proportions was shown to precede the schema of

mechanical equilibrium, the last schema to be attained.

Replication vs. Group Tests

Nagy and Griffiths (1982) indicate in their review that written tests fail to give

the same details on cognitive function as clinical interviews. This makes for difficult

comparison between Piaget’s work and structural relationships between tasks. Meehan

(1984) compared the percentage of studies that demonstrated male performance

advantages in manipulative versus paper-and-pencil formats. She concluded that females

have more difficulty with manipulative tasks of formal operations than males,

p < .08. Phillips (1980) indicates that a multiple choice question allows subjects to get

“correct” answers by chance. Given these issues and owing to the differences in purpose,

construction, and scoring procedures between group and interview formal reasoning

tests, this review only includes results of interview studies that replicate the original tasks

found in Inhelder and Piaget (1958).

Projection of Shadows Task, Gender, Spatial Skills, and Achievement

Research with the University of Iowa Grouping Model

The Shadows task has attracted a “complex” of issues. Research from a variety

of institutions has linked this measure of proportional reasoning with differences between

males and females and with associated gender differences in spatial and mathematical

reasoning. Obviously, investigators attempt to make sense of this “complex” through

discussion of gender-roles, patterns of science achievement, hemisphere or training

differences between genders, and unequal acquisition of prerequisite concrete spatial

structures (the “genetic-epistemological” hypothesis). This review gives an insight into

35

the relatedness of these issues as discussed by the various authors. The Science

Education Center at the University of Iowa (UI) has been particularly active in pursuing

these issues from the genetic-epistemological point of view.

Several studies at the UI or by former students have used the Shadows task to

study the formal operational schema of proportional reasoning. These studies explored

the contingent relationships between specific concrete and formal structures guided by

Phillip’s (1992) grouping model (see Figure 2) as well as by Inhelder and Piaget’s (1958)

description of formal reasoning schema and associated tasks. The UI research gained

strength by using a reasonably consistent set of task protocols and scoring criteria across

the studies (Phillips, 1981). The proportional schema of the Shadows task and its

structural prerequisites or correlates are studied in Poduska (1983), Poduska and Phillips

(1986), Wavering, Perry, Kelsey, and Birdd (1986), Ibe (1985), Wavering (1984),

Morgan (1979), Treagust (1980, 1982), and Doyle (1980).

College and 12th Grade Subjects

Poduska (1983) (also see Poduska and Phillips, 1986) examined the order of

acquisition of structures that contributed to the concept of “speed” among freshmen and

sophomore community college students from five math and non-math oriented science

courses. The Shadows task was included because it uses the formal operations schema of

proportions (as required for “miles per hour”).

Only eight of the 67 male subjects (12%) and none of the 33 females passed the

Shadows task, indicating that the proportional schema is passed late, if at all.

Statistically significant gender differences were found in three of the other tasks:

Symmetric Speeds, Asymmetric Speeds, and One-to-many (Circular) Speeds. Two other

tasks, Distance, and Time showed no gender differences. The authors found that students

who had previously completed one or more physics courses passed more tasks than those

who hadn’t. This was attributed to “self-selection” of science courses by subjects who

possessed the mental structures enabling them to understand it. The authors found it

notable that a large percentage of subjects did not pass the tests. They felt the gender-

related effects on the

37

Figure 2. Chart of Concrete Operational Structures ( From Phillips, 1992).

speed tasks lacked ready explanation and pointed to the need for more research.

Wavering, Perry, Kelsey, and Birdd (1986) investigated the spatial and logical

prerequisites to the formal schema of proportional reasoning (used in the Shadows task)

and the schema for control of variables (used in the flexible rods task). They

investigated 101 students from grades 6, 9, and 12 (half were female in each grade).

Only the 12th grade results are of interest in the current discussion. 68% of the 12th

graders demonstrated the concrete logical structure of seriation (LG8). The two concrete

spatial structures were passed by less than half as many: PRO8, tilt of a cone (32%) and

EU8, location of a point (32%). Very few 12th graders passed the formal tasks: Shadows

(6%) and Flexible Rods (6%). The authors note that these rates of formal reasoning are

much lower than reported elsewhere “and may be due in part to the individual interview

format which permits greater exploration of reasons in contrast to the written instrument

format” (p. 330). Only one of the projective structures, tested with the tilt of a cone task,

demonstrated significant gender differences across all the grades, although the Shadows

task approached significance. The authors conclude that spatial reasoning skills must be

encouraged in the classroom. For example, the Shadows task measures reasoning needed

to graph data and the two concrete spatial structures are needed for using perspective,

such as in “stereochemistry, phases of the moon, and other concepts that require

reasoning about the orientation of objects in space” (p. 330). Student activities should

include building models and then making drawings of systems being taught. Student

involvement as well as discussion would support development of these important mental

structures.

Wavering (1979, 1984) studied the interrelationships among three formal

schemas: probability, proportions, and correlations in grades 8, 10, and 12. Only the

grade 12 results are of interest here, consisting of data constructed out of raw scores from

39

the dissertation. Out of 29 seniors (14 females and 15 males); 15% (three females and

one male) passed the Shadows task, 10% (one female and two males) passed the

correlations task, and 24% (two females and five males) passed the quantification of

probabilities task. Wavering compared the scores of the Shadows task from all three

grades with Hensley’s (1974) results on the same task and found a near-significant

difference. The near difference may be related to the 12th grade passing rates. Of the 30

students in Hensley’s 12th grade group (50% female), 11 passed (37%), a considerably

larger pass rate than Wavering’s 15% pass rate. Last, neither Hensley nor Wavering

found gender differences in Shadows task performance when considering the three

grades together. Wavering concluded that among his subjects, the schema of probability

was acquired before the schemata of proportions and correlations. This is contrary, he

notes, to Piaget’s theory, in which correlation derives from probability and proportions

structures. Wavering writes that his results suggest that the higher levels of proportional

reasoning, requiring both direct and inverse reasoning, develop after the correlations

structure because the latter only requires direct proportional reasoning. The Farrell and

Farmer (1985) study discussed below indicates that indeed, direct proportions, as

demonstrated in the Mr. Tall and Mr. Short task, is attained earlier than the combination

of direct and inverse proportions required by the Shadows task. In any event, Wavering

indicates that Inhelder and Piaget’s (1958, p. 324) statement about the sequence of these

schemata is “very vague and open to interpretation” (p. 90). I believe the interpretation

should hinge on subsequent statements by Inhelder and Piaget which suggest that the

notion of proportions has a qualitative form as well as a later, quantitative form. In the

former case, the subject

acts in conformity with a sort of schema of expectations, consisting of operations which he could perform to demonstrate the compensation, which is taken for granted. In other words, the compensation is in this way

recognized as possible and often as necessary before the operational procedures which could justify it are made explicit (p. 328).

Therefore, correlations may be attained after the qualitative sense of proportions,

but prior to the quantitative sense of proportional reasoning. This is probably

demonstrated by Wavering’s subjects in that the scoring procedure for the Shadows task

requires a metric, quantitative approach for its solution. In fact, this qualification is

suggested by the sentence Wavering referred to: “Correlation is a notion which derives

simultaneously from that of probability and from a structure close to the one governing

proportions” (Inhelder and Piaget, 1958, p. 324) (italics mine).

Ibe (1985) studied the prerequisite schema to proportional reasoning in a search

for relationships between spatial reasoning and proportionality (a relationship suggested

in Inhelder and Piaget, 1958). Ibe studied 8th, 10th, and 12th grade students. Of the 12th

graders (13 males and 18 females), one (male) out of 31 (3%) passed the Shadows task.

No females passed.

Ibe cites Piaget and Inhelder’s (1967) opening to Chapter 13 of The Child’s

Conception of Space which indicates the close relationship of Euclidean and projective

structures. Ibe develops an argument to show they are both closely related to the concept

of proportionality:

If the projective and Euclidean structures enable a subject to judge the shape, position, and size of an object, then they must be closely related to proportionality which, in its general logical form, is the equivalence of the relations connecting two terms A and B to the relations connecting two other terms X and Y (Ibe, 1985, p. 79).

Ibe studied two projective groupings: PRO4, One-to-One Multiplication of

Projective Elements (Mountains task) and PRO8, One-to-One Multiplication of

Projective Relations (Tilting Straw task). He also included two Euclidean groupings:

EU4, One-to-One Multiplication of Euclidean Elements (Conservation of Interior

Volume) and EU8, Multiplication of Placement and Displacement Relations (Location of

41

a Point in Two or Three Dimensions). Using ordering analysis among the five tasks, Ibe

found that both the projective and Euclidean structures were logical prerequisites to

proportional reasoning in the Shadows Task. The study found no gender differences

across grades 8, 10, and 12. Ibe comments: “The finding of no gender difference

contradicts as many previous findings as it agrees with” (p. 82).

In a similar vein and as part of the UI research program, Treagust (1980, 1982)

studied gender-related differences in three projective and three Euclidean concrete

structures, in follow-up to various findings of male dominance in science attainment

(National Assessment of Educational Progress, 1977, 1978). Using 108 subjects across

grades 8, 10, and 12 (50% of each grade were female), he found males scored higher in

all six structures, with significantly higher scores for males on two of the projective

groupings PRO5 and PRO8 and two of the Euclidean groupings EU5 and EU7. Treagust

concludes from the pattern of results across grades, and results of other UI grouping

research, that the “personal-historical” explanation of male spatial superiority may be

inadequate. Rather, the lack of gender differences in elementary school subjects coupled

with the consistency of gender differences on the six tasks of his research suggests that a

“genetic epistemological” account serves better. Treagust writes: “It is possible that the

apparently slower development in spatial conceptualization by females is a contributing

factor to their reported lower attainment of skills than that of males in handling science

information at the senior high school level and in later years” (1985, p. 95). Treagust

recommends that female students be taught more like male students to reduce differences

in spatial abilities and insure future employment parity with males in areas like science,

engineering, and architecture. In his dissertation, Treagust (1978) cites authors that

suggest a sex-linked gene favorable for spatial abilities in about 50% of males and 25%

of females. He also indicates that Piaget explicitly suggested that spatial structures,

Euclidean or not, did not seem hereditary (pp. 150-151).

Elementary and Middle School Subjects

Given the low rate of success in finding evidence of proportional reasoning in the

Shadows task, and some evidence of females falling behind male performance, it is

reasonable to investigate whether prerequisite concrete spatial structures can be found at

earlier ages, such as between 7 and 12-14, when Piaget found them to develop. We may

also ask, do gender differences begin at ages earlier than adolescence? Much research at

the UI Science Education Center has focused on clarifying and evaluating the presence of

concrete structures that comprise the “grouping model” (Phillips, 1992) that stimulated

both the above research on older students and following research on younger students.

Doyle (1980) reports a study of spatial skills that focuses on the eight concrete

projective grouping using 100 students in grades 3, 6, and 9. By grade nine, five of the

structures had been “completed” (over 75% of the subjects had attained the mental

structure). These included Additional and Subtraction of Projective Elements (PRO1),

Complementary Perspective Relations (PRO2), One-to-Many Multiplication of Elements

(PRO3), Rectilinear Order (PRO5), and Symmetrical Interval Relations (PRO6). The

incomplete structures were One-to-One Multiplication of Projective Elements (PRO4),

One-to-Many Multiplication of Relations (LG7) , and One-to-one Multiplication of

Relations (LG8). The only structure to exhibit significant gender differences was

Rectilinear order (PRO5), with boys performing better. Doyle suggests that the lack of

overall gender differences fails to support the notion of greater mathematical and spatial

abilities reported in Maccoby and Jacklin’s (1974) book The Psychology of Sex

Differences. However, Maccoby and Jacklin also suggest that gender differences in

spatial skills do not become pronounced until later adolescence.

43

Other findings of the “grouping model” research are described and summarized

by Morgan (1979) who conducted an analysis similar to Doyle’s but across all eight

Euclidean groupings. Morgan concluded that although there were some differences

between studies in the proportions of students attaining the various concrete projective

and Euclidean operations, it is obvious that subjects in these studies develop much more

slowly than expected when compared with Piaget’s pass criterion of 75% for subjects at a

given age. Morgan suggests that “the lack of such structures could be a result of formal

schooling practices, nature of subject’s hobbies, and the large amount of time devoted to

watching television” (p. 147). Morgan suggests that student passivity in modern society

conflicts with Piaget’s premise that

knowledge is derived from action, not in the sense of simple associative responses, but in the much deeper sense of the assimilation of reality into the necessary and general coordinations of action (Piaget, 1969, p. 29, cited in Morgan, p., 146).

Morgan (1979) also reviews the findings of gender differences across several

studies at the UI and concludes, “The relationship between task performance and sex

differences is not clear” (p. 151). This is less strong than Treagust’s (1978) view after

reviewing the same research, in which he concluded that there were few results

indicating significant relationships between gender and task performance. However,

Morgan notes a confounding element, namely that a large percentage of all subjects

(male and female) failed to develop the structures, and that females may be “caught in

the middle” between passive activities given both genders in school, as well as

encouragement toward passive activities by sex-role stereotypes. Thus, females in

general may appear to perform more poorly than males, with exceptions he observed

among females who conduct hands-on hobbies such as “woodworking, farming, auto

repair, and carpentry” (p. 150).

Summary

The above findings indicate that proportional reasoning is a high-level structure

that follows development of correlations and probability, probably because it requires a

quantitative approach. It also requires acquisition of both projective and Euclidean

concrete spatial structures, which are only partially attained among even high school

students. Among high school seniors and college underclasspersons, the pass rate ranged

from 3% to 37%, in which roughly 50% of the subjects were female. Among college

males the passrate was 12%. Gender differences are difficult to detect statistically,

owing, in many cases, to the lack of subjects passing the tasks. However, among the

college students studied by Poduska (1983) none of the 33 females passed the Shadows

task. High school students demonstrated some gender differences, at least with higher

pass rates for males, and with statistical significance in enough structures to support other

findings in the psychometric literature on male superiority in spatial tasks. Among

elementary and middle school students, gender differences are less pronounced, although

occasionally found. Again, this supports the psychometric literature that indicate spatial

skills are not differentiated by gender among early adolescents and younger (Maccoby

and Jacklin, 1974).

Other Research Using the Shadows Task

The following studies using the Shadows task are not part of the University of

Iowa research program. Therefore, the task protocols and passing rates will be less

comparable than in the preceding studies.

Dulit (1972) used the Shadows task with 96 subjects, 14-55 years old. Of the 12

adults, 33% passed; of the 23 gifted 16-17 year-olds, 57% passed; of the 40 16-17 year-

olds, regular students who had not failed science or math, 35% passed; of the remaining

21 average 14 year-old students (who had not failed science or math), none passed.

45

Males scored better than females by a factor of four for the 16-17 year-old groups, and

by a factor of three among the adult group. It is possible that Dulit used easier criteria

for scoring than the UI experiments since he makes no mention of requiring subjects to

physically measure the diameter of the rings. They only needed “to make some verbal

statement equivalent to the proportionality principle, and to be able to show some

understanding of the connection between the principle and the correct placement” (p.

293).

Martorano (1977) gave the projection of Shadows task to middle class 6, 8, 10,

and 12th grade females. Of the 20 in grade twelve, 55% passed at level IIIA or better.

She doesn’t give a task protocol but does mention that passing the Shadows task required

use of a metric system of calculating proportions.

Piburn (1980) reviewed the evidence that spatial and visual imagination are

important for science studies. He examined the relationship between spatial reasoning

and proportional reasoning in 6th form (11th grade) New Zealand students certified for

university entrance. 34 S’s took the Card Rotation Test and Surface Development Test

for spatial reasoning as well as Piaget’s Balance and Shadows tasks. All tests except the

Card Rotations Test correlated significantly with the science portion of the university

certification examination and with a composite score of the Balance plus Shadows tasks,

both tests of proportional reasoning. Males scored significantly better on the science

examination and Shadows task. There were no significant gender differences on the

Balance task or on either measure of spatial ability. Piburn suggests these results support

the notion that proportionality measures involve an element of spatial reasoning different

from other schemas of formal thought. However, he was not sure of the mechanism

because the science examination “is nonmathematical, and does not contain items which

are obviously either spatial or require proportionality concepts” (p. 446). Piburn

suggests that the Surface Development test (r =.42 with total score for Balance plus

Shadows tasks) involves transformations of perspective central to the development of

logical thought on through to formal reasoning. Piburn notes that females can have

spatial skill equivalent to males: equal numbers of male and females scored in the upper

quartile of the Surface Development Test. And yet none of these females scored formal

on the composite balance plus Shadows tasks measure. This merits more research, he

writes, but in any event, curriculum design for the sciences must include more work to

develop spatial reasoning.

Bady (1978) attempted to validate the notion that several tasks can test for the

same schema, which resulted in scores being similar. He used five tasks for the schema

of proportions, including the Balance and Shadows tasks. He used three age groups, 9th

and 10th graders, 11th and 12th graders, and early college students. Among the early

college students, he found that 81% scored formal on the Shadows task (as well, 81%

passed the Balance task). In comparing each of the five tasks to the total score for the

schema across all age groups, the Shadows task was the most correlated, r =.84. The

other four correlated with the total score between r =.52 and .74 (Balance task r =.55).

Bady acknowledges the high correlations to be a function of including the target score in

the total score.

Farrell and Farmer (1985) performed an “in-depth” study of proportional

reasoning in 901 college-bound math and science students from 10, 11, and 12th grade

classes across five upstate New York school districts. They investigated the relationship

between gender and course experience on the development of proportional reasoning.

First, a general test for direct proportions using the Mr. Tall and Mr. Short puzzle

identified 53% of the students who used direct proportional reasoning. Of a subsample

of 128 students, administration of the Shadows task identified 24.2% as early or late

47

formal. While no gender differences were found on the Shadows task (21.3% males and

11.3% of females passed) a significant difference favoring males was found on the first

test for direct proportions (58.2% males and 47.5% females passed). However,

calculating the percentages passing for each gender across both tests (not done by the

authors) indicates that 12.4% of the original sample of males passed and only 5.4% of

females passed, a difference of more than a factor of two. Among students who passed

the test for direct proportions, the authors also found no differences between genders in

the number of science or mathematics courses. However, students passing the test of

direct proportions were shown to have taken more science and math courses than those

not passing. The authors conclude that learning and development are related—more

courses in science and math accompany greater cognitive development. However, the

absence of this relationship among the students passing the more advanced Shadows test

indicates that learning fails to promote development after a point. More intensive

developmental instruction is required even in advanced courses. Regarding gender

differences, the authors acknowledge the oft-noted male superiority in spatial tasks.

However, this superiority vanished when subjects equally proficient at direct proportions

were compared again with the Shadows task. Therefore, they suggest, the Shadows task

itself, as a task with definite spatial components, may, in fact, indicate that gender

differences are not spatial in origin, but stem from some other source, perhaps related to

direct proportions, or not. For collaborating evidence, the authors cite Linn and Pulos

(1983) who used several proportional reasoning measures, including the Shadows task,

and found that although males performed better, the superiority could not be accounted

for by various measures of aptitude, including spatial ability.

In conclusion, the literature suggests that males acquire the schema of proportions

earlier than females. However, the exact nature of the influence of psychometrically-

defined spatial skills upon proportional reasoning is not clear and remains to be

investigated.

Other Research on Spatial Reasoning and Gender

Halpern (1992) reviews studies of gender-related cognitive differences (spatial,

verbal and quantitative) and concludes that, indeed, they are substantive. Her self-

defined objective is to review evidence, hoping to reach some conclusion about the origin

of gender differences: whether they arose from biological or psychosocial causes. She

concludes that the two sources of gender differences are sufficiently intertwined to make

it impossible to assign a percentage of the variance that each contributes. However, the

main sources include psychosocial influences such as sex-differentiated life experiences

and their concomitant beliefs, expectations, stereotypes, and self-concepts and such

biological influences as cerebral lateralization, including preference for verbal or spatial

modes of thought. Of course, both sources arise out of the ontogenetic unfolding of

genetic and hormonal influences.

Halpern finds research to indicate that sex differences are diminishing in effect

size over the years. She suggests that the composition of college-age experimental

subjects is changing as women engage themselves in traditionally male-oriented

occupationals. She qualifies this, however, suggesting that there will always be an

interaction with biological tendencies for or against spatial skills. Three spatial tests

appear to display differences that may be “immune” to any currently known psychosocial

moderation. 1) Piaget’s water level test using a drawing of a tipped empty glass.

Females fail to draw the water level line horizontally and tend to draw it in the direction

in which the glass is tipped. 2) Novel tests that require spatial visualization. E.g., males

score considerable higher on mental rotation tests of a three-dimensional object

(illustrated in a two-dimensional drawing). 3) The rod and frame test in which males

49

more accurately position a rod vertically within a distant tilted frame. Halpern mentions

that a “popular hypothesis” suggests that visual-spatial differences underlie sex

differences in quantitative ability. However, her review suggests that empirical evidence

is sometimes, but not always, found. Meanwhile, Halpern also concludes that the verbal

superiorities of young females is probably biological in origin. She indicates that “verbal

ability differences are small, visual-spatial ability differences are large, and quantitative

ability differences are intermediate” (p. 66).

Golbeck (1986) investigated development of a Euclidean system of coordinates

among college undergraduates (32 males and 32 females) using the water level task to

test for concepts of horizontality and the van-on-the-hill task to test for complementary

concepts of verticality. Subjects were asked to draw how a light bulb and cord would

appear in a drawing of a van going up a hill at differing degrees of tilt. Golbeck created

“non-physical” versions of both tasks in an attempt to determine if females suffer a

performance deficit on the tasks (owing to lack of familiarity with the situation) or a

competence deficit (lack of the underlying Euclidean structure). Females scored as well

as males on the non-physical task and significantly worse than males in the physical task.

Golbeck claims this indicates that females indeed possess the necessary Euclidean

structure, but that they may be delayed in its acquisition. Several educational

implications are given: educators must not succumb to lower expectations for females

which in turn could result in lower achievement (several studies are cited). Also, female

elementary teachers must understand that spatial performance in themselves (and

students) may lag their competencies and compensatory measures should be invoked in

the classroom. Finally, spatially-oriented, hands-on science experiences are important to

spatial development. The premise of the study, however, appears flawed by Golbeck’s

design of the non-physical version of the tasks. Essentially, she used tilted rectangles

instead of drawings of the physical objects, and included a sample response with a

correctly drawn line illustrated in the example. At best, this tested for competency to

imitate an example rather than competency in the Euclidean structure.

In a metastudy of sex differences in formal reasoning, Meehan (1984) found that

males performed significantly better than males across all types of tasks, but especially

on tasks using propositional reasoning: Shadows, Vessels, and Correlations. She

examines whether the advantage is due to differences in underlying “competence” in the

domain, or differences in “activation/utilization” such as lack of familiarity with

traditionally male-oriented “scientific” apparatus. Meehan cites research on the topic and

concludes that competencies may indeed underly differences in performance in

proportional reasoning. She cites Piaget and Inhelder’s (1967) suggestion that a

relationship exists between spatial imagery and formal reasoning on the Shadows task.

Meehan cites additional evidence for this claim.

Strauss and Kinsbourne (1981) found that age of menarche, a measure of

maturation, was not related to spatial skills as measured by the water-level test among

171 right-handed females aged 17 - 58, (mean age 26.6). This contradicted earlier

findings by Waber (1977) who used a block design test, a standard spatial abilities test,

and a version of the embedded figures test.

Pallrand and Seeber (1984) found that 11 hours of training for 81 students (11.1%

female) in a calculus-based 10-week introductory physics class for college

undergraduates improved perception, orientation, and visualization skills. The training

consisted of “drawing outside scenes by viewing through a small square cut in a piece of

cardboard. They were encouraged to draw the dominant lines of the scenery and to

reduce the scene to its proper perspective” (p. 510). Other activities included a short

course in geometry and the “Relative Position and Motion” module from SCIS. The

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authors also found that the 10 weeks of physics training in control classes also improved

the tested skills, although not so much. Students who had equivalent math skills, but

who dropped out of the physics class scored less on the pre-test than those who stayed,

implying “cognitive abilities other than those associated with mathematical ability are

utilized in an introductory physics course” (p. 512). The experimental intervention also

was associated with significantly higher course grades. Physics class test items that

demonstrated the enhanced visual-spatial skills were lab work and multiple-choice items

requiring graphical analysis.

Martin (1967-1968) evaluated 530 math teachers and college students in teacher

preparatory courses. Those with mathematics background had greater spatial

visualization skills than those without based on the differential “Aptitude Test of Space

Relations.” Students in different fields, (science or art/industrial arts vs. groups of

prospective secondary and elementary math teachers) but who had several courses in

math did not differ in spatial ability. Prospective teachers at the secondary level, with

more math training, scored higher on spatial visualization than prospective elementary

math teachers. These differences did not extend to scholastic aptitude, which showed no

relation to spatial visualization ability.

Correlations Task

University of Iowa Studies

Rubley (1972) studied four tasks of formal reasoning and their relationship with

dogmatic attitudes among 60 11th and 12th grade chemistry students (50% female). She

found that the Correlations task was the easiest of four formal tasks, passed by 57%.

43% passed the Conservation of Displacement Volume, 42% passed the Flexibility of

Rods task, and 17% passed the Floating Bodies task. More males passed each of the

tasks than females, but the only difference to reach significance was the Floating Bodies

task. Using other evidence from the study, Rubley suggests the higher male performance

may be due to greater science knowledge, perhaps memorized from prior reading,

compared with females.

Wavering (1979) also studied Correlations in addition to the Shadows task,

discussed above. Wavering found that the proportion of subjects passing Correlations

was not statistically different than for the Shadows tasks, and, again there were no gender

difference. Out of the 29 12th grade subjects, 3 (10%) were level IIIB or IIIC. Note that

Wavering decided to classify level IIIA subjects as non-pass because IIIA only indicates

possession of proportional reasoning, not correlational. This strategy allowed greater

fidelity in establishing contingent relationships between target schemas, and is adopted in

my present research reported here. Wavering also compared scores from his 12th grade

subjects with Rubley’s (1972) correlation scores for 11th and 12th grade science

students. No significant difference was found comparing the two score sets across the

levels 0 to 4. However, Rubley identified 27% of her 60 subjects as pass compared with

Waverings 10%. (The lack of statistical difference is probably due to Wavering’s use of

five levels for his Chi-square test rather than comparing pass vs. fail.) Wavering notes

that Rubley’s subjects were taken from chemistry classes, a selected sample, while his

subjects represented all levels of ability, thus resulting in a lower pass rate.

Other Research Using the Correlations Task

Lovell (1961) replicated the Correlations task of Inhelder and Piaget (1958). Of

20 least able 15-18 year-old secondary school students, only five (25%) passed, and of

the 26 ablest students, 20 (77%) passed.

Ross (1973) studied correlational reasoning (among three other formal tasks) in

65 university undergraduates, 35 females, 30 males, average age 20.3 years. 9.2%

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passed at formal level two, which is equivalent to Waverings criteria (and mine) for

passing the Correlations task. When Ross included subjects who scored level IIIA,

displaying only direct proportions on the Correlations task, a total of 98.4% of subjects

“passed.”

Martorano (1977) found 55% of the 20 12th grade females passed the

Correlations task at III or better. No clear definition of the scoring criteria was given.

Dulit (1972) studied correlational reasoning (as well as proportional reasoning,

reviewed above). Of the 12 adults, 25% passed, of 21 gifted 16-17 year-olds, 62%

passed; of 36 16-17 year-old regular students who had not failed science or math, 17%

passed; of the 21 average 14 year-old students (who had not failed science or math), 10%

passed. Males performed better by a factor of two or more in each group except among

the average 14 year-olds, where only females passed. In addition to the scoring liberties

mentioned above for the Shadows task, Dulit mentions that some subjects were

“inspirational” and would leap at a solution, “saying very little by way of explanation.”

If their answer was right, “I scored them as formal, since the Piagetian criteria do not

require awareness of the underlying formal mechanisms” (p. 299). Dulit’s scoring,

however, ignores Piaget’s requirement that subjects explain their rationale which in turn

indicates possession of the schema being evaluated. Of additional interest is Dulit’s

concern regarding the failure of his subjects to pass the tests of formal reasoning with the

same ease as Inhelder’s and Piaget’s original subjects. Dulit reports a personal

communication with Dr. Inhelder who confirmed that “indeed not all cases were

reported” (italics are Dulit’s) thus, invalidating any attempt to compare pass rates with

Piaget and Inhelder’s original research! In other words, the rule used by Doyle (1980)

above, to define “completion” of a mental structure for an age group cannot be applied to

tests of formal reasoning. Doyle defined “completion” as occurring when 75% of the

subjects passed the task. According to Inhelder,

There was no intention to speak to the question of “frequency” or “incidence.” Protocols were used simply as illustrations. Adolescents who failed to function at the formal stage were simply not reported (Dulit, p. 297).

Combinations of Colored and Colorless Chemical Bodies Task

Ross (1973), in the same study described above for the Correlations task, found

75% of his 65 undergraduate subjects passed the Chemical Combinations task. When

comparing males and females on five tests of formal reasoning together, Ross found a

significant difference, favoring males, in spite of the fact there was no significant

difference in their ACT scores and in spite of the fact that females had significantly

higher GPAs. Ross invokes Elkind’s (1962) suggestion that gender differences appear in

the science-oriented tasks due to female aversion to taking on the masculine roles

associated with science activities. Since females did well on the ACT and GPA scores,

Ross feels that females would score much better if tested for formal reasoning within

their vocational or profession specialty, as suggested by Piaget (1972). Of interest, Ross

gave his subjects the Torrance Tests of Creative Thinking to evaluate correlations of the

subfactors with scores on the formal reasoning tasks. Five factors were generated from

the 14 variables (many for only 65 subjects!), and none of the formal tests appeared in

either of the two factors that loaded the Torrance subscales. Ross concluded that formal

reasoning does not include a creative “divergent component.” (See also, Ross, 1976).

Martorano (1977) found 85% of the 20 12th grade females passed the

Combinations task at level III A or better. Bart and Mertens (1979), in an order theoretic

re-analysis of Martorano’s data found that pass scores on the Chemical Combinations

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task were not contingent upon passing any other task except the Colored Tokens task,

also a combinatorial schema.

Kolodiy (1975, 1977) studied the growth of reasoning by comparing formal

reasoning skills of motivated science students and science majors in the 10th grade and in

freshman and senior years of college. No gender breakdown was given. Performance on

the Chemicals task was significantly correlated to scores representing student’s

cumulative grade point average (r =.7781), SAT verbal (r =.3366) and SAT math ( r

=.3292). The other task, Hauling Weight on an Inclined Plane, demonstrated no

significant correlations on those variables. Kolodiy combined the scores of the two tasks

and found that high school sophomores (35% “passing”) and college freshmen (32%

“passing”) were similar in level of development, and both were significantly lower in

development than college seniors (64% “passing”).

Joyce (1977) studied 66 upper-class college students in a science education

curriculum, using five tasks including Chemical Combinations. 95.5% of the subjects

were classified formal, based on “certain criteria” which appear to be “the formulation of

a systematic approach to isolating the proper combination of liquids” (p.155). There is

reason to be suspicious of Joyce’s findings, however, in that he comments that the

“chemicals and simple balance tasks lend themselves to solution by trial and error” (p.

157).

Bady (1978) applied the same approach to combinatorial reasoning as described

above for proportional reasoning. He used five tasks for the combinatorial schema,

including the Chemicals and Tokens tasks. He used three age groups, 9th and 10th

graders, 11th and 12th graders, and early college students. Among the early college

students, he found that 76% scored formal on the Chemicals task (as well, 95% passed

the Tokens task). In comparing each of the five tasks to the total score for the schema

across all age groups, the Chemicals task was the most correlated, r = .70, not

significantly different than a “travel routes” analog, r =.72. The other three ranged from

r =.50 to .55 (Tokens task r =.53.) Bady concluded that the nature of the task can indeed

influence the “pass” classification of a subject; and that tasks that appear similar may

actually tap different schematic requirements.

De Hernandez, Marek, and Renner (1984) evaluated the influence of age and

gender on development of four formal operational schema including combinatorial

reasoning. They compared two age groups of 70 subjects each (both 50% female) with

mean ages of 16.49 and 17.05 years. Slightly fewer passed the Chemicals task in the

lower age group: 20% females and 34% males versus the higher age group: 34% females

and 36% males passing. There was no significant difference between age groups for

either gender, nor was there any significant difference between genders within either of

the groups. Based on evidence including the other tasks (Conservation of Volume,

Bending Rods, Equilibrium in the Balance), the authors conclude that 90% of females

and 70% of males are functioning below formal operations, matching other’s

observations. They also conclude that lack of improvement in scores with age, especially

in combinatorial reasoning, indicates a failure in “providing adequate experiences to help

students develop the use of a systematic general procedure for generating all possible

combinations...an essential tool for learning many science concepts” (p. 369) They also

suggest, in light of their own and other studies of gender differences, that males mature

intellectually earlier than females.

Communicating Vessels Task

Martorano (1977) found 45% of the 20 12th grade females passed the Vessels

task at level III or better. She determined that the Vessels task was passed by

significantly fewer subjects than any other task (including the Shadows, Combinations,

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and Correlations tasks), except for the Hydraulic Press (also a test for the schema of

equilibrium). Bart and Mertens (1979), in an order theoretic re-analysis of Martorano’s

data found that pass scores on the Communicating Vessels task were contingent upon

pass performance of both Correlations and the Combinations tasks.

Brain Localization and Piagetian Studies

Over the last twenty years, most educators interested in brain research have

focused on lateralization as the source of educational implications for curriculum design

(E.g., Tomlinson-Keasey and Kelly, 1979; Yeap, 1989; Rennels, 1976; Hart, 1978;

Galin, 1976; Samples, 1980; Rekdal, 1979; Gray, 1980).

A variety of studies have looked at Piagetian cognitive development in light of

lateralization or brain localization. Wheatley, Frankland, Mitchell and Kraft (1978)

provide a review of issues related to mathematics education. They suggest maturation

moves toward left-hemisphere superiority in task performance and that problem solving

probably requires both hemisphere functions. Lawson and Wollman (1975) found that

students who demonstrated conservation (number, substance, continuous quantity, and

weight) reflected greater left-hemisphere specialization than non-conserving students.

Eye dominance was the independent variable. They conclude that left-hemisphere verbal

and linear functioning characterized intellectual development in the Piagetian sense.

The EEG study by Kraft (1976) (and published in Kraft, Mitchell, Languis, and

Wheatley, 1980), has been covered in the introduction, as well as the study by Dilling,

Wheatley and Mitchell (1976). Additional research from this group (Willis, Wheatley,

and Mitchell, 1979) indicates that purported visuo-spatial task processing demands were

more readily reflected in alpha power ratios than the perceptually obvious requirements.

The tasks, however, were not Piagetian.

Somewhat related, Butters, Barton and Brody (1970) found that successful

performance on tasks involving mental rotation (including the Piagetian “Village scene

task”) required intact parietal lobe functioning not only in the left hemisphere, but also in

the right hemisphere.

It is important to note that studies of laterality are beset by issues of

interpretation. What are the influences on a change in left/right EEG alpha amplitude

ratios? Is the left greater, the right hemisphere lesser, or do both hemispheres vary in

their measurement? McManus (1983) discusses pitfalls of this research and suggests

alternative analytic methods. Note that coherence measures avoid these pitfalls.

Several studies have noted frontal involvement in a Piagetian developmental

paradigm. Molfese, Molfese, Buhrke, Shute, and Wang (1983) used visual-evoked

responses to study “conservation of quantity” in adults. Initial judgments were

associated with frontal activity over both hemispheres. Later judgments elicited only

left-hemisphere responses, indicated an interaction between habituation and hemisphere

processing. Note, however, that these authors failed to use a task that would reasonably

meet strict criteria of a “Piagetian task,” their own claims notwithstanding. Diamond and

Doar (1989) and Diamond (1985) used Piaget’s “Object Permanence task” to study

frontal development in infants. They concluded that indeed, frontal lobe development

was measured in this Piagetian task the same as with the similar but more commonly-

used tool for frontal research: the delayed response task.

Case (1981, 1985) outlines a neurophysiological approach to answering many

questions associated with Piaget’s developmental psychology, and appends specific

suggestions for instructional design based on his findings. Other psychophysiological

studies using Piagetian theory will be discussed in Chapter Five, Discussion and

Conclusion.

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EEG Coherence Studies

The reader is directed to these references for a basic introduction to EEG

coherence: tutorials are provided in Shaw (1981 and 1984). Normative findings for male

adults are presented in Tucker, Roth, and Bair (1986), Tucker and Roth (1984), Wieneke,

Deinema, Spoelstra, Storm Van Leeuwen and Versteeg (1980), Adey (1967, 1969),

Walter, Kado, Rhodes, and Adey (1967), Walter, Rhodes, and Adey (1967). Studies

with substantive reviews include Gasser, Jennen-Steinmetz and Verleger (1987), Ford,

Goethe and Dekker (1986), Hinrichs and Machleidt (1992), Berkhout, Walter and Adey

(1969), French and Beaumont (1984) and Beaumont and Rugg (1979). Of particular

interest is a study by Corsi-Cabrera, Herrera, and Malvido (1989) that reports literature

indicating that EEG alpha power measures fail to correlate with measures of EEG alpha

coherence.

The current study utilizes subjects engaged in maintaining a “standard cognitive

state” while having their EEG alpha coherence measures taken. The following sections

review the literature that reports results of studies into the relationship between cognitive

skills and EEG alpha coherence measured during the practice of a standard cognitive

state, in this case, Transcendental Meditation.

Standard Cognitive State (Transcendental Meditation) and EEG Coherence Studies

Specific experiences of “transcending” during TM appear related to increased

cognitive skills. The experience of transcending can be characterized a “going beyond”

thought, resulting in the experience of awareness without an object of thought. Reports

indicate that his may occur very briefly, and be hardly noticed, or it may occur for

longer, more noticable periods. It is also called the experience of “pure consciousness”.

Jedrczak, Beresford, and Clements (1985) measured subjective reports of transcending in

TM and vividness of imagery during practice of the TM-Sidhis (advanced TM practices)

in relation to fluency scores from the unusual uses subtest of the Torrance Tests of

Creative Thinking and scores on the WAIS digit symbol test among 152 subjects, 66 of

whom were female. The frequency of transcending and the clear experience of imagery

were significantly positively correlated with the Torrance tests. Clear experience of

imagery was also significantly correlated with the digit symbol test. The number of

months of practice of the TM-Sidhis program correlated significantly with both digit

span scores and fluency scores when the major confound, age, was partialled out.

Orme-Johnson and Haynes (1981) studied the combination of subjective

experience, EEG alpha coherence, and a measure of cognitive aptitude. They compared

two groups of males, both with a mean age of 25+ years. One group consisted of

subjects with self-reported clear experiences (CE) of inner awareness without thoughts

(clear transcending) and the other group without CE. The CE group showed significantly

higher measures of alpha coherence and creativity (ideational fluency on the Unusual

Uses subtest from the Verbal form of the Torrance Test of Creative Thinking). F, L, R,

and Central (C3C4) alpha coherences were significantly greater for the CE group in a

MANCOVA with all four measures, with the mean of these four coherences significantly

correlated with ideational fluency, r = .66. Similarly, the CE group also had

significantly greater R alpha coherence and “dominant” alpha coherence (using the

largest coherence measure from the four possible pairs). Both measures significantly

correlated with ideational fluency, r = .5, and r = .64 respectively. In addition, bilateral

F alpha correlated significantly with creativity, r = .65. As implied above, the CE group

scored significantly higher on the creativity test than the unclear experience group.

The current research utilizes a “Coherence Index” that reflects an inverse

relationship between anterior coherences and bilateral occipital coherence (FLR-O). The

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following studies explore this anterior-posterior difference in relation to measures of

cognitive aptitude.

Studies Related to EEG Alpha Coherence and Intelligence

In addition to their findings for FLR-O index of alpha coherence index greater

than .95, Orme-Johnson et al., (1982) also examined effects related to individual

derivations. Among other findings, they found significant inverse correlations between

alpha O coherence and verbal IQ (WAIS), principled moral reasoning, and 4 of 6 scales

from the Torrance Test of Creative Thinking: Verbal fluency, Verbal flexibility, Verbal

originality, and Figural fluency. Correlations with anterior derivations, where found,

were positive. To explain the differential activity of the anterior and posterior cortex, the

authors hypothesize an “anterior-posterior axis” in which coherence is higher or lower in

different attentional processes, meeting specific brain processing needs. Specifically...

We propose that when a cortical area is involved in a generalized, integrative function that coherence is high in that area, whereas when the area is performing its specialized motor or perceptual function that coherence will be low (Orme-Johnson et al., 1982).

Posterior Coherence Inversely Related to Intelligence

It is important to examine in some detail the above claim since the functional

significance of coherence has been difficult to identify by many if not all researchers

using coherence. Some researchers suggest that low coherence fulfills the need for

functional differentiation among cortical locations, which essentially reflects the notion

of “concrete, specialized functions” given above. For example, Thatcher, McAlaster,

Lester, Horst, and Cantor (1983) correlated WAIS-R IQ scores with measures of

coherence across many derivations in a study of 191 normal children during eyes closed,

rest condition. Frequency bands included delta, theta, alpha, and beta. Of the

correlations that were statistically significant, all were negatively related to IQ. Most of

the correlations were in the posterior regions of the scalp, although some appeared

anteriorally as well.

For alpha, the posterior bilateral derivations included O1O2, P3P4, and T5T6; the

anterior bilateral derivations included C3C4, F3F4, and F7F8. Only the posterior T3T4

and anterior C3C4 were not significantly correlated with full scale IQ. Among the five

homolateral derivations, only the posterior P3O1 and P4O2 were significantly correlated

with full scale IQ. Thatcher, et al. speculated that for “local distance” electrodes (7 cm

or less apart), high coherence represents “neural redundancy,” or low functional neural

differentiation. They interpret this to reflect reduced capacity for information coding

capability and therefore, lower intelligence. “In other words, when the underlying

generators that contribute to the EEG seen at the two sites are coherent with one another,

there is less capacity for coding the information that may become available from the

outside world or from other groups of cells” (p. 143).

Thatcher, et al. also found that IQ was correlated with increased amplitude

asymmetry for all frequency bands (regardless of which side of the head displayed

greater amplitude). Differences in amplitude were interpreted to support the theory that

enhanced differentiation represented increased coding capacity. (In the alpha band,

however, only F7F8 demonstrated a significant linear amplitude ratio correlation with

IQ.)

Other coherence researchers relate similar theories. Clusin and Giannitrapani

(1970) presaged Thatcher’s findings and interpretation with their study of 11–13 year-old

right-handed males. They found an inverse relationship between the Weschsler Digit

Span and resting EEG coherence between 2–34 Hertz. The relationship was present

across the entire frequency range, although strongest between 25 and 33 Hertz; it held for

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both bilateral and homolateral measures in the occipital, lateral-parietal, and prefrontal

areas. They concluded that short-term digit retention scores

may be associated with a general differentiation [i.e., less coherence] of on-going neural activity in certain cortical regions. These findings are compatible with clinical evidence on the effects of lesions in these areas, and with Luria’s observations that the evolution of higher cognitive functions parallels histological differentiation of the cortex (p. 418).

Similarly, Gasser, Jennen-Steinmetz and Verleger (1987) independently suggest

that the greater the maturation and intelligence among their child subjects (10-13 years)

the lower the coherences—“assuming that progressing differentiation of brain regions

went along with an EEG at rest” (p. 151). This theory received statistically significant

confirmation in the alpha band for bilateral coherence between occipital O1O2 (7.5–9.5

Hz), as well as between O2 Pz (7.5–12.5 Hz). The experimental group of mildly

mentally retarded children demonstrated higher coherences during rest than the normal

IQ children, supporting (but not mentioned by Gasser et al.) the findings of both Clusin

and Giannitrapani (1970) and Thatcher, et al. (1983). All the above research used

monopolar electrodes with linked ear lobes (where reported) in contrast to bipolar

electrodes, which have been shown to reflect different coherence responses to task

conditions (Merrin, Floyd, and Fein, 1989).

Corsi-Cabrera, Herrera, and Mavido (1989) studied the relationship of verbal,

spatial, and reasoning subtest scores from the Differential Aptitude Test (DAT) with

EEG alpha interhemispheric correlation at C, T, P, and O bilateral derivations during

eyes closed rest (referenced to “ipsilateral earlobe”). Note that EEG interhemispheric

correlation (Pearson product-moment correlation coefficients) is an analog to coherence,

but not an identical measure. They used nine males and nine females with mean ages of

23 and 27 respectively.

The authors found significant negative correlations (p < .05) in the alpha band

EEG for males at C3C4, T3T4, and P3P4 on the abstract reasoning subtest, at C3C4 and

T3T4 for the verbal subtest, and at C3C4 for the spatial subtest. This is in line with the

above research findings. For females, however, the authors report the alpha correlations

were mostly positive, with statistical significance only at C3C4 for both the abstract and

spatial subtests. The authors point out that the differences in signs for the correlations

mitigated against finding a significant DAT-IQ correlation for the group as a whole.

They conclude that sex indeed impacts the relationship between the EEG measure and

cognitive ability, in addition to individual differences, during rest. They point to similar

findings under task conditions reported by Beaumont, Mayes, and Rugg (1978) who

located higher coherences among females while performing cognitive tasks. No theory

regarding the cause of the differences was offered, except to point out that hemispheric

differentiation may play a different role for each sex. High intercorrelation (low

hemispheric differentiation) appears related to failure in information processing in men

and vice versa in women. They point out that their data also show higher intercorrelation

for the four derivation pairs for the female group (less hemispheric differentiation),

significant for C, P, and O derivations. They suggest this is consistent with reports in the

literature of lower hemispheric asymmetry in women (e.g., McGlone, 1980).

Hernandez (1985) replicated the work of Thatcher, et al. (1983) in a sample of 48

school children ages 10–16 (50% females) who practiced the TM technique while EEG

coherence measures were taken. WAIS-R performance and verbal tests were

administered about four weeks prior to the EEG. Hernandez used three conditions for

the coherence measures: TM, eyes closed rest (EC), and eyes closed mental arithmetic

(MA). All three conditions revealed significantly greater anterior alpha coherences than

posterior alpha coherences. Looking at the correlation between alpha coherence and IQ

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with seven anterior and posterior bilateral coherences pooled, the TM condition

demonstrated statistically greater correlations (p < .05) than the EC or the MA

conditions. This indicates the advantage of using TM as a “standard cognitive state” for

such studies.

Despite this overall advantage for the TM condition, tests of the posterior and

anterior derivations in the TM condition revealed only one bilaterally significant alpha

coherence-IQ correlation (C3-C4, negative, p < .05) and one homolaterally significant

correlation (T3-T5, positive, p < .05). In comparing pooled anterior bilateral derivations

with pooled posterior derivations, there were no statistical differences in the coherence-

IQ correlations for the alpha band. However, delta and theta bands demonstrated

statistical differences with positive correlations in the anterior and negative correlations

in the posterior measures. Hernandez indicates the patterns were similar in alpha and

beta bands, but without significance. (When pooled, the homolateral alpha coherences-

IQ correlations of left versus right derivations failed to indicate any hemisphere

advantage.)

In conclusion, when taking all three states into account, (TM, EC, and MA)

Hernandez found the patterns of negative coherence-IQ correlations within the posterior

regions to uphold Thatcher et al.’s findings. This caused her to conclude that “COH is a

relatively stable, state-independent characteristic of the subjects under the conditions

measured. These results are therefore consistent with the neural redundancy

interpretation of local-distance COH” (p. 59).

Anterior Coherence Positively Related to Intelligence

Regarding the anterior findings, however, Hernandez suggests two implications:

1) the children practicing TM may differ from those in the Thatcher et al. study, and 2)

the frontal, anterior areas, support different functions than the occipital, posterior, areas.

“Because of the highly integrative function of these (frontal) areas of the cortex, high

frontal COH may be more reflective of the potential for integrated function, in contrast to

high posterior COH which may be reflective of neural redundancy” (p. 66). Following

the second point, Hernandez suggests that the functional significance of coherence may

vary with scalp location. The integrative functions of the frontal lobes include

integration of multimodal sensory information, abstract conscious processing such as comprehension, judgment, and social responsibility (Luria, 1980), and selective attention (Yingling, 1980). Anatomically, the frontal cortex has extensive interhemispheric connections as well as other cortical, limbic, and subcortical connections. This structure allows for more integrated, synthetic functioning (p. 66).

This reflects the “integrative functions” suggested by Orme-Johnson et al. (1982)

and presumably holds for the current research using Piagetian tests of formal reasoning.

(A neurophysiological definition of “integration” will be offered in Chapter Vunder

Directions for Future Research, in the context of the functional significance of alpha

coherence.)

TM-Related Anterior Coherence Changes

Following the first point given by Hernandez, the difference in subjects may

prove a key parameter related to “integrative functions.” First, note that the Thatcher et

al. research measured EEG during rest, eyes closed. The TM subjects, although sitting

with eyes closed and experiencing restful relaxation (Wallace & Benson, 1972),

additionally engage in following a set of simple instructions, i.e., the subjects engage in a

task. The results of the task have been characterized by Wallace (1970; 1986) as “restful

alertness” with an EEG “signature” different than either wakefulness, eyes closed rest,

drowsiness, or sleep (Also, see Levine et al., 1976).

Evidence that this task alters the subject’s coherence measures occurs in several

studies. All studies indicate increases in anterior coherence with TM .

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First, Levine (1976) found that subjects practicing TM tend to increase alpha

coherence in the frontal and central areas at the beginning of the TM period, but without

marked decrease at the end of the period. He found that coherence also tends to spread to

other frequencies. Control subjects practicing “mock” meditation using repetitive

backwards counting in a non-taxing fashion usually demonstrated decreases in any alpha

coherence that may have been present upon closing the eyes.

Second, coherence is related to TM and not just rest. Dillbeck and Bronson

(1981) compared pre-tests during non-TM rest periods for 15 subjects in a longitudinal

study, with post-tests taken during TM two weeks after instruction and found

significantly greater alpha frontal coherence above the .95 threshold. (No significant

increases in alpha power were detected, indicating that alpha coherence is not necessarily

correlated with alpha power.) Furthermore, the twice-daily 20-minute rest period (i.e.,

rest without TM) was not the cause of the change because prior to the TM instruction,

coherence for the same subjects was compared under other experimental conditions.

Prior to the TM instruction, half of the subjects performed twice daily relaxation (without

TM) and half followed their normal schedules for 2 weeks. There were no group

differences in alpha coherence or alpha power, indicating that the regular discipline of

eyes-closed “relaxation” was not the source of change in coherence.

A third indication demonstrates that coherence has positive characteristics in TM

subjects. Anterior increases in coherence between eyes-open, to eyes-closed, and then to

TM, show a positive relation with cognitive skills. For example, Orme-Johnson et al.

(1982) report evaluation of a “second order coherence factor” (SOF) that consisted of

positive anterior and negative posterior measures of alpha and theta bands. The SOF

measure also correlated significantly with GPA, verbal IQ, and principled moral

reasoning. Among their 47 subjects, highly significant increases in the SOF factor

occurred in the transition from eyes-open to eyes-closed (p < .0001), and from eyes

closed to TM (p < .002). This indicates that increases in this coherence index from rest

to TM represent neurophysiological changes almost as great as from eyes-open to eyes-

closed (simple rest). And moreover, the magnitude of the SOF (with positive anterior

coherence) indicates emergent cognitive skills unrelated to any particular cognitive

training.

The fourth and perhaps the most compelling evidence supporting the positive

over the negative relationship between anterior coherence and IQ in TM subjects is

offered by Gaylord, Orme-Johnson, and Travis (1989). In this longitudinal study, 83

black adults (aged 17-44, median age 21) were measured prior to random assignment to

one of three treatments: TM, progressive relaxation (PR), or a cognitive program for

stress management. During the pretests, the authors found that bilateral frontal (F3F4)

alpha 1 (8-10 Hz) coherence was negatively correlated with IQ (Otis Lennon Mental

Abilities Test) r = -.31, p < . 05. (Unfortunately, occipital measures were lost during the

study.) The coherence measures also included F3C3, F4C3, F4C3, F3C4, and C3C4,

using for analysis the clearest minute of EEG near the end of the TM/PR/rest period.

Note that initially, all subjects were nonmeditators during the pretests. After two and a

half months, in the posttest of all subjects (in which one third (25) of the subjects

practiced TM) analysis showed a positive correlation between left hemisphere (F3C3)

alpha 1 (8-10 Hz) coherence and IQ, r = .33, p < .05. The authors note there were

insufficient subjects to study posttest correlation patterns for each group separately, and

therefore interpretation of the finding is difficult. But they conclude from their own and

prior studies (such as given above) that frontal coherence may be different in meditators

and non-meditators.

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Note that these findings by Gaylord, Orme-Johnson, and Travis (1989) are

conservative in light of the fact that no overall longitudinal changes were found in any

group. That is, the lack of longitudinal changes indicate that the observed switch in

correlation sign between anterior alpha coherence and IQ is based on minimal

neurophysiological “conditioning” and that the locus of the switch may well be the nature

of the task instructions given for TM practice as much as any longitudinal changes that

occur with the practice. The authors note that subjects reported at posttest a failure to

practice any treatment program with regularity and that this may explain the lack of

longitudinal changes. But this does not explain the switch in valence between anterior

alpha and IQ. In speculation for other causes for the switch, it can be said that the

subjects in the other two techniques may have responded differently during the posttest

eyes-closed rest EEG session, as well, such as reduced orientation, etc., thereby

contributing to the difference across the three groups. However, in defense of the

position that the TM condition was primarily responsible for the switch, it can be pointed

out that the authors also report that the TM subjects were unique among the three groups

in producing increases in EEG coherence from eyes-open to eyes-closed during the

posttest. Significant increases were found taking all coherence pairs and all frequency

bands (4-25 Hz) into account, and also for right-hemisphere (F4C4) coherences in theta

(6-8 Hz), alpha 1 (8-10 Hz), and alpha 2 (10-12 Hz) bands. Given the reports of Orme-

Johnson et al. (1982) of longitudinal increases in the SOF factor for eyes-open to eyes-

closed, as well as eyes closed to TM, we can reasonably speculate that a similar

phenomenon occurs in the Gaylord, et al. study.

In summary, an anterior-posterior coherence axis appears related to the cognitive

changes associated with the practice of TM. One author has suggested the mechanism of

the “transcending reflex” (Arenander, 1986) that is hypothesized to increase the EEG

coherence in a fashion that enhances the adaptive functions of the brain (also see

Wallace, 1986). Arendander associates this phenomenon with mechanisms imputed by

the orienting response (OR) of Sokolov (1963). Various authors have indicated that

voluntary ORs are associated with frontal lobe activity (Cf. Hernandez’s, 1985 discussion

of the “integrating” influence of anterior coherence above). What additional support can

be given for this model? Let us examine evidence regarding orientation and habituation

in relation to cognitive aptitudes. Brain activation during problem solving can be

associated with the orientation response.

EEG Alpha Coherence and Frontal Lobe Activation

Several studies have evaluated the contribution of EEG alpha coherence to

cognitive success during decision making. The research task using the dependent

variable occurs outside of the practice of TM, however, subjects are experienced in the

practice of TM. These studies shed light on the significance of alpha coherence relative

to improvements in cognitive skills and intelligence. For example, Sheppard and Boyer

(1990) examined the influence of EEG alpha coherence on a decision task among male

and female adults. The study specifically tests whether coherence is related to brain

“semantic activation” as it is understood in the context of “priming” (or alerting) the

subject about a concept prior to exposing the subject to a target stimulus that may or may

not be associated with the concept. The study examines reaction times required for the

subject to determine if a target stimulus is a word or a nonword. In each trial, the

stimulus is preceded by a “prime” that could take one of three values: a related word, a

non-related word, or a neutral letter string “xxxxx.”

The authors found evidence that, compared with trials preceded by low

coherence, trials with the greater coherence were associated with faster reaction times

when the target stimulus was related to the prime. In other words, under conditions of

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high coherence the prime “activated” the brain to respond more effectively. (Their

findings apply only to right hemisphere coherence (10 pairs summed across both anterior

and posterior regions) and left hemisphere posterior-parietal (5 pairs summed)).

Similarly, when the target stimulus was not related to the prime, the activation associated

with coherence slowed the subject’s reaction time. The second finding suggests that

coherence can serve to inhibit reactions, as well as facilitate reactions.

The authors agree that this does not allow a clear-cut generalization that

coherence speeds information processing. However, I suggest an amended interpretation:

that the delayed reaction time in the non-related prime condition actually results from an

orientation response (OR) that typically gives rise to momentary inhibition of motor

activity. This OR would result from the lack of relationship between the prime and the

target—a mismatch with the neuronal model. Greater coherence may support a stronger

OR, increasing the subjective salience of the mismatch, and thus slowing RT in the

context of providing adaptive cognitive value.

Sheppard (1989) concludes in his dissertation version of the above research that

the coherence results refute the “redundancy theory” of Thatcher et al. (1983) and other

authors mentioned above. Instead, he suggests his results support a notion of

“information flow” as suggested by Galbraith (1967) and Livanov (1977). Redundancy

theory suggests that coherence reflects the amount of coherent (redundant) activity in a

neural system and is inversely related to the system’s capacity to encode and process

information (e.g., WAIS IQ).

A possible reinterpretation of the redundancy theory arises, given Arenander’s

(1986) transcending reflex model. We specifically note that during the Thatcher, et al.

study, subjects experienced eyes closed rest during their coherence measurements. It is

reasonable to assume that the youngsters of lesser IQ were more susceptible to

distraction, anxiety, and other, internally generated, stimuli that increased frontal and

posterior (voluntary and involuntary) OR activity. Conversely, higher IQ youngsters

would habituate more rapidly to the setting and events, and when told to “rest” would

indeed follow the instructions better, both mentally as well as physically, resulting in

little or no frontal or posterior OR activity. If EEG coherence is in fact related to brain

activation (and much evidence can be given to indicate this is so), then the lower IQ

subjects, engaging in various voluntary and involuntary orienting activities should indeed

display higher anterior as well as posterior coherence values since they would find it

more difficult to maintain attentional contol.

Note that several EEG derivations in the Sheppard and Boyer (1990) study

indicated higher posterior coherences associated with information processing. I suggest

that the interactive nature of the experiment could require automatized, posterior

functions, as well as anterior functions. Based on the above reasoning, I suggest that

higher anterior coherence during the practice of the set of instructions that constitute the

TM technique may reflect greater attentiveness to the task at hand (i.e., volition, paying

attention, anticipation) and lower bilateral posterior coherence may reflect greater ability

to habituate to distraction (i.e., to resist non-adaptive automatization, to decentrate). For

example, Berkhout and Walter (1980) report a biofeedback study in which “volitional

control” of interhemispheric coherence changed levels of occipital and parietal

coherence. They found that behavior tending to increase arousal (i.e. enhance focusing)

also decreased coherence at 10 Hz, clearly for occipital areas, and less clearly for parietal

areas. This may explain the efficacy of the FLR minus O coherence index to

discriminate pass and fail scores in the tests indicated above by Orme-Johnson et al

(1982). The notion of “paying attention” in this context provides empirical and

theoretical support to Orme-Johnson et al.’s (1982) suggestion that FLR-O reflects an

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index of CNS maturation. In an earlier exposition of the longitudinal study of the effects

of the TM and TM-Sidhi program, Orme-Johnson, Wallace and Dillbeck (1982) suggest

that the “shift towards relatively greater coherence in the frontal regions produced by the

TM-Sidhi program is developmentally beneficial, perhaps reflecting a change in

developmental emphasis from primary perceptual areas to higher association areas

involved with planning and sustaining intentionality” (p. 1685).

CHAPTER III

METHODS AND PROCEDURES

Pilot Study

A pilot study was accomplished to determine any difficulties which could arise in

the main study. The pilot study utilized 6 individuals associated with programs at

Maharishi International University. The pilot study served to:

1. Ascertain the efficacy of the protocols in determining the specific formal operational structures for which they were designed.

2. Ascertain the adequacy and validity of the scoring criteria.

3. Test the equipment used for the tasks.

4. Provide experience with administering the tasks.

Four interviews were audio taped for subsequent review by the experimenter and

an independent evaluator. After review, the protocols were adjusted to permit more

clear-cut evaluation of performance.

Sample Selection

Students from Maharishi International University were participants in a routinely-

scheduled yearly EEG battery. Recruitment of students tended to be on a class-by-class

basis, although no strict criteria were levied or met. Females were requested to schedule

EEG evaluation outside of three days on either side of their menstrual period (Becker,

Creutzfeldt, Schwibbe, and Wuttke, 1982; Little and Zahn, 1974; and Hampson and

Kimura, 1988). Both undergraduate, graduate, and some staff members were included in

the routine evaluations. The subjects were considered a random sample from the MIU

student population of individuals who regularly practice the Transcendental Meditation

technique.

EEG Measurement

Equipment

The electroencephalographic measurements were taken with a 17-channel Grass

model 780 EEG and polygraph with a Megatek Laboratory Interface connected to a Data

General Nova 32K word Nova 3 minicomputer. The 7P511H amplifiers were set at 0.3

Hz, 0.1 Hz, and 5 µv/mm for EEG with a 60 Hz notch filter in. The output from the J6

of each of the Grass amplifiers was digitized on-line to 12 bits at 60 samples per second

per channel. The pen filters were set at 90 Hz with the pen’s 60 Hz filter out, and the

chart speed was 15 mm/sec. Records of four seconds (240 samples per channel) were

recorded on a nine-track, 75 inch per second, 800 bytes per inch Data General (Model

6030) magnetic tape subsystem. The coherence spectrum, a measure of the correlation

between two signals, was computed for the following pairs of electrodes: F3F4, F4C4,

F3C3, and O1O2. All recording was monopolar with linked ears for the reference

electrode. The Fast Fourier Transform, with epochs of four seconds was used according

to the methods of Levine (1976). Coherence was computed using the average of seven

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overlapping frames of 128 samples each, incremented with 18 samples between frames.

Coherence was analyzed to .468 Hz resolution and averaged for the alpha band, 8.2 to

11.95 Hz. Mean coherence scores were computed for ten .53 minute periods during

which all subjects practiced the TM technique. The 10 scores were averaged for an

overall average for each pair of derivations. All amplifiers were calibrated at the

beginning and end of each session. Measurements were taken in an electrically shielded,

sound attenuated room.

Procedures

Maharishi International University routinely administers EEG measures as part of

their student evaluation procedures. Two to three subjects were evaluated each half day.

When subjects came in they were shown the laboratory in order to familiarize them with

the environment, and then they filled out consent forms and background questionnaires.

Subjects had no recent history of neurological problems or drug use. No females were

scheduled within three days before or after menstruation. The International 10-20 system

was used to place electrodes at F3, F4, C3, C4, and O1, O2, referenced to linked ears.

The head was cleaned with alcohol and Grass EEG 10mm gold plated cup electrodes

were attached with electrode cream (Grass type EC-2). Electrode impedances were

below 10K ohms. After application of the electrodes, the subjects were encouraged to

walk around for a few minutes to restore circulation and alertness prior to the EEG

session. The test session used instructions played from a tape recorder and received

through loud speakers set at low volume. Subjects sat for 5 minutes with eyes open then

5 minutes with eyes closed, 15 minutes of the TM technique, then 5 minutes with eyes

closed resting. The 5.3 minutes of EEG was taken towards the end of the 15-minute TM

period. The above procedures and equipment were standard procedure for evaluating

students yearly at MIU. Other published research from MIU used essentially the same

protocol (e.g., Orme-Johnson et al., 1982; Dillbeck and Araas-Vesely, 1986).

Task Measurement

The protocols for formal operational reasoning were developed from guidelines

set out in Inhelder and Piaget (1958). The protocols assessed the presence of four formal

operational structures: the combinatorial operations schema, the INRC group (as found in

the mechanical equilibrium schema), the proportionality schema, and the correlation

schema. Sufficient test time was allowed to prevent distortion of performance due to real

or imagined pressure for speeded problem solving. The tasks were administered by the

male experimenter (the author) immediately after the EEG measurement, or in some

cases, immediately before the EEG. Subjects took about an hour for the four tasks total.

The order of tasks was counterbalanced across subjects.

Task Selection Criteria

Since we seek to verify whether or not a direct relationship exists between a

neurophysiological measure (coherence) and measures of formal operations, it serves our

purpose to select measures which are most likely to result in a spread of achievement

scores. This is a standard approach in correlation studies, for instance, in which there is

greater chance for locating correlations if the spread between high and low scores has

roughly the same distributions as the independent variable.

Thus, on the one hand, we could if we wished, include measures confined to

concrete operations in addition to measures of formal operations in order to achieve a

spread of levels of cognitive development. On the other hand, we are particularly

interested in the neurophysiological conditions which support the “structured whole”—

Piaget’s term for the system which permits operations on operations. Since formal

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operations express a qualitatively different mode of cognition than concrete operations,

this study focuses only on structures which Piaget has uniquely associated with the

structured whole, i.e., formal operations and operational schemata. Fortunately, it turns

out that these tasks can be scored for concrete operational as well as formal operational

performance, thus providing the range of performance needed for a correlational study.

Given this approach, it is possible to consider two choices:

1. The study can concentrate on the properties of formal operations per se which support the formation of propositional operations, as in the case of the 16 binary operations. Or,

2. The study can focus on the resultant “operational schemata” which Piaget characterizes as operations and concepts which are new to the formal operational stage yet which:

emerge in close linkage with the establishment of propositional logic; they require intellectual capacities greater than those of the concrete level and derive from the operational transformations entailed by the total structures... inherent in propositional logic rather than the propositional operations themselves (Inhelder and Piaget, 1958, p. 105)

It appears useful to select measures from the second set of options, the set of

“operational schemata” for the following two reasons:

1. We will be testing for the “structured whole” in its most general form in all the tasks we select. That is, we will be dealing with general structures characterizing the structured whole of propositional logic and the INRC group, as opposed to only dealing with the more specific 16 binary propositional operations themselves. The selected tasks not only represent logical structures of their own, but also give evidence of “certain characteristic logical relations” (Piaget and Garcia, 1991, p. 130) that constitute the stage of formal reasoning.

This differs from using individual tasks to evaluate the presence of absence of a particular logic structure. Rather, failure to pass any of a reasonable sample of tasks indicates an epistemological condition of the subject. It reflects the lack of any reorganization of the “whole of the instruments already used by the subject” (Ibid, p. 136, italics by the original authors).

Thus, we can test for the failure of subjects to attain the “stage” of formal reasoning by locating subjects who fail to pass any of the tasks that test for formal logical structures. This approach follows the assertion of Garcia: “to say that there are characteristic structures in action at each stage is very different from saying that the stage is defined by a logical structure. Piaget’s formulation of stages involves the first assertion, not the second.” (Ibid, p. 130)

2. Each task will not only speak for the structured whole, but will emphasize a particular aspect of it. Certain of the operational schemata, as Piaget analyses them, require a more explicit application of either or both the component structures which contribute to the structured whole, viz., the group INRC and/or the lattice structure of propositional logic. Other of the operational schemata seem to emphasize the important utilitarian or intellectually practical applications of the group INRC or lattice structures, namely, proportional and correlation reasoning.

Thus I will seek evidence of formal operational thought in four tasks. The first

two tasks will focus on the combinatorial system "presupposes the elaboration of a

'structured whole’ and consequently of a lattice structure with the general laws of

reciprocity which characterize it” (Inhelder and Piaget, 1958, p. 307). Study of the

combinatorial system is, in essence, study of the structure of propositional logic (as

opposed to study of the propositional operations themselves). Piaget writes:

The new system which results from this combinatorial operation... is a generalized classification of a set of all possible classifications compatible with the given base associations. But this is exactly the same as the lattice structure, based on the “structured whole” of n-by-n combinations, in contrast to the structure of elementary groupings [of concrete operations] (Ibid., p. 291).

Later in his exposition, Piaget explicitly links the combinatorial system with the

structured whole of propositional logic (i.e. the lattice structure):

The combinatorial composition deals with propositions (in formal operational thinking).... As soon as the proposition states simple possibilities and its composition consists of bringing together or separating out these possibilities as such, this composition deals no longer with objects but rather with the truth values of the combinations. The result is a transition from the logic of classes or relations [of concrete operations] to propositional logic [of formal operations] (Inhelder and Piaget, 1958, p. 292).

Chemicals Task

The specific task used to evaluate presence of the combinatorial structure will be

the Combination of Colored and Colorless Chemical Bodies tasks. Piaget suggests that

this task represents two aspects of combinatorial structure: the mathematical

combinatorial system (which relates to units) and the propositional combinatorial system

(which relates to qualities). Thus, the Chemicals task serves to elicit the “deliberate and

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reasoned use of combinations” (Ibid., p. 310) in a mathematical sense, while still

requiring the functions of the lattice (the structured whole) in a more general sense. This

task will test for both of these structures simultaneously, providing evidence of whether

the propositional combinatory structure (lattice) is present as well as providing evidence

whether the mathematical combinatory structure is also present. The former is used

spontaneously, without “conscious or explicit decision” and the latter is used

“intentionally when the subject is faced with problems whose solution requires a

systematic table of combinations” (Ibid., p. 313).

Piaget suggests that both of these combinatorial structures arise simultaneously,

but the nascent, maturing combinatorial system seems to deal first with qualities and then

numbers. This feature should allow us to observe a greater “spread” of formal

operational reasoning skill than if I were to test only for the combinatorial system of

propositional logic alone. The equipment, protocol and scoring for the Chemicals task

follows. The scoring form appears in the Appendix.

Colored and Colorless Chemical Bodies Protocol

Equipment

Four identical eye-dropper bottles containing colorless solutions and identified as

follows:

“1” - Dilute sulfuric acid

“2” - Water

“3” - Hydrogen peroxide solution

“4” - Sodium thiosulphate

One eye-dropper bottle of distinctly different shape with a

colorless solution and identified as follows:

“g” - Sodium iodide

Fifty small transparent plastic cups to hold combinations of

liquids.

Only seven are made available on the work surface. The remainder are stationed

visibly in reserve until requested. (E may ask, “Do you need more?”)

One paper pad and pencil.

Instructions

1. Prior to S’s appearance, E mixes a solution of one and three in a small plastic cup. When S is present, E says:

“This set-up gives you a chance to do an experiment to produce a color from these colorless chemicals. I prepared this solution earlier to show you the color we want.”

E hands the bottle of “g” to S.

“Use this to add a squirt to the cup and you’ll see the color we are looking for.” (S responds.)

“There are several ways to get the yellow color. I want you to work with these chemicals and make as many different combinations as you can to get the yellow color. You may use anything on the table if you think you need it. Here is paper and pencil. The “g” solution is necessary to test your combination. Any questions?”

E answers any questions.

“Go ahead.”

When S stops, E asks:

“How did you decide what to test?” (S responds.)

2. If S has not stated that all possible ways were tried, E asks:

“Have you tried all of the possible ways of mixing the chemicals?” (S responds.)

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E permits S to continue or suggests S go on if additional ways are noticed.

3. When S is done, and S has not already volunteered answers to the following, E asks:

“Can you tell me what each chemical does and how you can prove it?” (S responds.)

If S is unclear, E says:

“With reference to creating the yellow color, what does chemical one do? What does two do? What do three and four do?”

4. If S concludes with several ways of making yellow without clearly identifying the role of each chemical, E asks:

“Which chemicals are necessary to create the color? How do you know?” (S responds.)

Terminate.

Narrative Scoring Criteria for Colored and Colorless Chemical Bodies Task

Scoring Level Criteria

5. S exhibits in speech and action a methodologically complete approach from the beginning of the task. The approach allows for referral to the data, mentally or in written form, at any time. S tries all combinations with no unnecessary repetitions. This score is possible even if S makes additional combinations after E asks whether all possible combinations have been made. S correctly identifies the roles of each chemical and the two conditions of the yellow color. S utilizes propositional logic to make these identifications. 1x1 combinations not required if S’s plan excludes them. This level is scored formal (late).

4. S ultimately performs the same as in level 5. However, S may begin with some initial trial and error and may omit one or more combinations in an otherwise apparently methodological system. This level is scored formal (early).

3. S exhibits a methodologically complete approach as in levels 4 or 5. However, one or more of the following failures is evident:

a) S fails to identify the role of chemical 4, and no others;

b) S utilizes evidence, impression or guesswork in identifying the role(s) of the chemicals and the conditions of the yellow color. (Viz., S merely relates what has been empirically demonstrated to prove the roles held by each chemical).

2. S never exhibits in speech or action complete command of a methodological approach to the data which permits its recovery and use for analysis. S does at least some 2x2 and some 3x3 combinations. The method may be replete with repetitions due to forgetting what had been done. The level applies regardless of whether the S utilizes propositions, empirical evidence or guesswork in proving the roles of the chemicals. Likewise, it applies regardless of how well the S identifies the roles of the chemicals and conditions of the yellow color.

1. S is methodologically incomplete to the extent of only dealing with 1x1 or 2x2 combinations. No regard need be taken of S’s logical rigor.

Communicating Vessels Task

The second task evaluates the presence of the INRC group structure (see Easley,

1964 for additional description of the INRC group structure). This task will evaluate the

INRC group structure in the sense of both a general operational structure and a specific

operational schemata (belonging to the schema of mechanical equilibrium). Piaget

remarks on this dual presence of the group INRC. He suggests that the mechanical

equilibrium model,

which happens to be that of any equilibrium, corresponds to the internal equilibrium of his own logical operations without his being aware of it. This occurs in such a way that, in the explanation of a mechanical system in the equilibrium, the group of inversions and reciprocities (INRC group) comes into play on two completely different levels at the same time. First, it governs the propositional operations which the subject uses to describe and explain reality; as such it constitutes an integrated structure at the interior of his thought, a structure of which he is naturally not aware. But second, as a direct phenomenon under analysis (since, in the given data, these consist of a physical system whose equilibrium represents the very problem to be resolved). Thus, the group gives rise to the operational schemata which the subject uses in this and similar situations to account for the physical modifications he finds and their coordination. (Ibid., p. 321)

The task for evaluating the presence of the group INRC structure is the

Communicating Vessels task. Of the four tasks Piaget uses to evaluate the INRC group

structure (that supports the schema of mechanical equilibrium) this task is easiest to

administer while simultaneously most suitable for avoiding the possibilities of facile and

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rote responses by the subject. The equipment, protocol, and scoring for the

Communicating Vessels task follows. The scoring form appears in the Appendix.

Communicating Vessels Protocol

Equipment

1 glass titration tube, 20 x 400 mm, held in burette clamp and stand

1 glass titration tube, 40 x 600 mm, held in burette clamp and stand

2 moveable rubber bands (one placed on each tube)

1 piece plastic tubing connecting bottom outlets of the tubes

1 pinch clamp on the plastic tubing

1 stand with 80 x 600 mm cardboard rectangle attached to permit concealment of the large titration tube

1 pencil

1 meter stick

red colored water to fill the connected tubes to the 200 mm level

1 flask shaped titration tube

Instructions

1. E explains the apparatus and indicates by pointing:

“Here we have two glass containers connected by a plastic tube. Water can flow between the containers. The tube is not blocked off. Here is pencil and paper and a measuring stick if you need them.”

E points to the movable tube and says:

“We can adjust the height of this tube by loosening the clamp and moving it up or down. We can mark the current water level with this rubber band.” (E does this.)

2. E then asks:

“Compared to the rubber band mark would anything happen to the water level in this tube if we raised the tube? Will the water level go up, down or stay where it is compared to the rubber band? ” (S responds.)

“Why do you think so?” (S responds.)

After S responds, E covers the non-movable tube (B) with the screen (blank side to the S), raises the movable tube a predetermined distance (previously set so the water will lower from M to S on diagram A), and sets the clamp. If S has not predicted the outcome correctly, E terminates. If S has been wrong and wishes to see the result, E shows the result and asks:

“Why do you think this outcome occurred? Tell me what happened.” (S responds.)

3. E turns the screen around to reveal diagram A. E lowers the rubber band on the movable tube all the way to the bottom.

“Look at the drawing of the narrow tube. It shows the tube behind it. The line at M represents a rubber band marking the level of water in this tube." (E indicates tube B). “Is the line even with the water level?”

If the line is not even, E suggests:

“You can adjust the picture with the clamp to make it even.”

E continues:

“Now we’ll cover the tube with the screen.” (E does this.) “I am going to lower the movable tube. Can you tell me the letter which matches the water level of the hidden tube? ” (E lowers tube A the amount it had been raised in item 2 above.) (S responds.)

“Is this as close as you can possibly determine? ”(S responds.)

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“Why do you think the water level is there?” (S responds.)

If S predicts the water levels are the same, then continue. Note that due to parallax error, S may respond with letter R even though E has set the apparatus for the level to be a letter S. If S fails to indicate the proper level, terminate.

4. E continues and points as appropriate to tube A:

“Now look at the picture with the V shaped, conical tube. Pretend that it is connected to this movable tube at the bottom. The water level remains the same for this movable tube, here.” (E points.) “The conical tube has letters down the center. Can you tell me the letter which indicates the water level in the conical tube? ” (S responds.)

“How did you decide that?” (S responds.)

5. E brings out drawing B and hands it to S.

“You can see the conical tube and the movable tube in this drawing. Use your pen to draw in the estimated levels as they are now. Imagine I block off the connecting tube under the conical tube and that the bubble tube is empty. Now we pour this water into the bubble tube and open up the connection. Make a drawing of what you think will happen. Use this pencil. You can estimate.” (S responds.)

“Why do you think the water levels are there? ”(S responds.)

Terminate.

Narrative Scoring Criteria for the Communicating Vessels Task

Scoring Level Criteria

5. S completely understands the system of inversions and reciprocities which relates the water levels of the two containers. The system is understood in its most general case, including containers of unequal volume and shape. Equality of water levels is described in terms of mechanical equilibrium based on action and reaction of the quantities of liquid in each of the containers. The terms need not be precise; however, the description must convey that S appreciates the notion of equilibrium in a system. This level is scored formal (late).

4. S seeks to explain the equality of levels in mechanical terms of action and reaction. The explanation is incomplete, however, due to confusion regarding the role of

volume in maintaining equilibrium. Thus, S does not expect equality of levels to hold for unequal forms and volumes. This level is scored formal (early).

3. S can predict that the levels will be equal based on past experience or current observations. S cannot use terms of compensatory actions and reactions to give an explanation for the equilibrium observed. S may or may not correctly identify conditions of equal levels when presented with containers of unequal shape and volume.

2. S fails to predict the reciprocal equality of level in a hidden tube based on what is seen in the connected tube. S may or may not invoke a rationale based on a system of action and reaction. Usually, if such a system is described it consists of compensations required in the hidden tube to offset changes in the movable tube, but which do not result in equality of the water level.

1. S fails to predict the inverse relation between the lifting of the movable tube and the lowering of the water level compared to a reference mark on the tube. If S does correctly predict such an inverse relationship, the reasoning is based on guessing or great uncertainty, admitted by the S.

The third and fourth tasks of this study represent those formal operational

schemata which have greatest utilitarian value in nearly any college science curriculum:

the proportional schema and the correlation schema. Proportions are the foundation of

reasoning with fractions and ratios. Correlations presuppose the presence of the notion

of probability and both the concepts of probability and correlation are the foundation of

statistical reasoning. All of these mathematical functions are of obviously crucial

importance to the qualitative and quantitative comprehension of social and physical

science topics.

Projection of Shadows Task

The proportionality schema will be evaluated using the Projection of Shadows

task, whose properties permit testing for geometrical/spatial operations in contrast to the

preceding two tasks which predominantly tested for mathematical skills. Piaget links

proportional reasoning to the structured whole by suggesting that “the notion of logical

proportions is inherent in the integrated structure which seems to dominate the

acquisitions specific to the level of formal operations” (Ibid., p. 314).

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Logical proportions apparently precede mathematical proportions, which is a

distinction that the Shadows task can assess. Also, the schema of proportionality seems

to reflect a more general function of the INRC group structure than is found in the

schema of mechanical equilibrium. This expanded role derives from the fact the task is

more spatially organized than physically organized. This requires the subject to

simultaneously consider two distinct reference systems and coordinate them utilizing the

principle of inverse and reciprocal relationships between the variables (Ibid., p. 208).

Also, ratio is a concept that derives more from the INRC group structure than the lattice,

in contrast to the combinatorial schema (evaluated by the Chemicals task) which strongly

reflects presence of the lattice structure.

The proportional schema effects the transition between the schemata originating

in the lattice and those which are integral with the group structure, more particularly, the

group of inversions and reciprocities (INRC) (Ibid., p. 314).

Of special interest in a neurological sense is Piaget’s analysis that the concept of

ratio between time and distance (in the case of proportions of distance per time, or

“speed”) depends on an “intellectual decentration.” That is, when faced with unequal

times and spaces traversed by moving objects, the subject “is unsuccessful at the very

onset of the new construction, because he thinks either of the times, or of the distances,

in a kind of alternating intellectual centration, without being able to unite them in a

single ratio” (Piaget, 1948, p. 214). Thus, it appears meaningful to seek neurological

evidence to aid our understanding of the process of decentration, or in other terms, see

the neurological correlates to the span of temporal and spatial attention. The equipment

protocol, and scoring for the Shadows task follow. The scoring form appears in the

Appendix.

Projection of Shadows Protocol

Equipment

1 Slide projector situated with the lens centered at 18.2 cm above the working surface. The lens is covered by posterboard pierced in the center with a light hole.

1 45 cm square screen constructed of rigid white cardboard located 120 cm from the light hole.

1 Wooden beam, 5 x 5 x 100 cm, placed lengthwise between the screen and light source. The beam contains holes 1 cm apart along the top. Every 10 cm is marked with a letter beginning with 0 at 10 cm, then B, A, F, G, K, M, R and N at 90 cm.

1 Wire ring, 5 cm in diameter with white indicator tape.

1 Wire ring, 10 cm in diameter with red indicator tape.

1 Wire ring, 15 cm in diameter with green indicator tape.

Each ring also has a support wire of such length that the center of each ring is 20 cm above the bottom of the support wire. The support wires fit the holes of the wooden beam.

1 Meter stick.

1 Paper pad and pencil.

Instructions

1. E begins with the light off and with the rings lying on the work surface. E turns on the light as he speaks:

“Here is a light source, some rings and a screen. We also have pencil and paper and a measuring tape if you need them. When I place a ring on this board the shadow appears on the screen.”

E places the red ring at the G position and removes the card blocking the light.

“Do you see the shadow? ” (S responds.)

Terminate if S doesn’t see a shadow.

2. E blocks the light with a card and picks up the green ring.

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“If I use this ring at the same place on the board as the red ring, will the shadow size be larger, smaller, or remain the same as the one for the red ring? ” (S responds.)

“Why do you think so?” (S responds.)

“Let’s check your answer.”

E uncovers the light so S can inspect the shadows. If S’s answer was wrong, E asks:

“What happened?”

3. E covers the light, removes the red ring and places the green ring at G.

“If I move this green ring closer to the screen, will the shadow size become larger, smaller or remain the same? ” (S responds.)

“Why do you think so?” (S responds.)

“Let’s check your answer.”

E first uncovers the light while the green ring is at G to see the current size, then recovers the light, moves the ring to the N mark, and uncovers the light again. If S was wrong, E asks:

“What do you think happened?”

If S seems not to understand the change in shadow size, terminate.

4a. E removes the green ring and holds it with the red ring. E asks:

“Can you make a single shadow with these two rings? ” (S responds.)

“Show me.” (S responds.)

If S says a single shadow is impossible, terminate.

After S has placed the rings, E asks:

“Why do you think this will create one shadow?” (S responds.)

“Let’s see what you have.”

E uncovers the light. If S is wrong or has indicated uncertainty, E allows further trial and error with the light on by suggesting:

“You can move the rings.”

4b. After S has experimented making a single shadow, E covers the light and asks:

“Are there any other positions where the two rings will make just one shadow? ” (S Responds.)

If S says there are none, terminate. Otherwise, E says:

“Show me.” (S responds.)

“Is this as accurate as you can get?” (S responds.)

“How did you determine this?” (S responds.)

4c. If E finds that S makes some attempt at analyzing the problem in some way other than pure trial and error, E should permit a third attempt with two rings and a single shadow. Repeat item 4.

5. If S attains accurate performance after 3 attempts with two rings, yet E feels proportional reasoning is not totally comprehended, or wishes to check S’s reasoning, E can introduce the white ring and ask:

“Can you make a single shadow using three rings?” (S responds.)

5a. If S answers “no,” terminate. Otherwise ask:

“Can you show me?” (S responds.)

“How did you determine this?” (S responds.)

5b. After S has experimented making a single shadow, and if E wishes to check S’s reasoning, E covers the light and asks:

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“Are there any other positions where the three rings will make just one shadow?” (S responds.)

“How did you determine this?” (S responds.)

Terminate.

Narrative Scoring Criteria for the Projection of Shadows Task

Scoring Level Criteria

4. Whether from the beginning or after some trial and error S ultimately succeeds in stating a metrical formulation of the inverse proportional relationship between the rings and the light source. S can successfully place two or three rings to form a single shadow. The distances have the same relation to each other as the size of the ring to the smallest ring. Only this level requires that the subject utilize a metric approach. Therefore, only this level is scored formal.

3. After some trial and error, S concludes by stating a non-metrical formulation of the inverse geometrically proportional relationship between the rings and the light source. S asserts that the closer to the light the rings are placed, the closer together they should be arranged to create a single shadow.

2. S never formulates a geometrically inverse proportional relationship, however, S makes attempts to invoke metrical or perceptual strategies in solving the problem, or may just place the rings in the correct order, with the largest nearest the screen.

1. S knows that shadow size depends on the ring size, but fails to understand the inverse relation between the distance from the light source and shadow size. If S asserts that the shadow does get smaller as the ring gets farther from the light, S can only base the response on past experience or intuition and not on analysis of this inverse relationship.

Correlations Task

The last task utilized in the study involves assessment of the degree of correlation

between two variables. Piaget suggests that while the notion of correlations appears later

than the qualitative notion of proportions, it appears before the quantitative sense of

proportions reasoning as discussed in the literature review. Thus, the proportions schema

serves as the topmost level of achievement in the range of tasks assembled for the study.

A balance of emphasis is obtained by using the correlation structure for evaluation in that

it utilizes the lattice structure (propositional logic) for its solution. Thus, two tasks

emphasize the propositional logic of the lattice structure (Chemicals task and

Correlations task) and two others emphasize the group INRC system of inverse and

reciprocal relationships (the Communicating Vessels and Shadows task). This balance of

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structural emphasis should prove useful in post-hoc analysis of the data. The equipment,

protocol, and scoring for the correlations task follow. The scoring form appears in the

Appendix.

Correlations Protocol

Equipment

Two sets of 12 cards each, all of which carry the same line drawing of a child’s

face. Each card is 11 x 14 cm and each set is colored as listed below.

Each set has four groups of color schemes. The groups are referenced as A, B, C

and D and the set of groups is notated (A,B,C,D). Thus, if group A contains 4 cards, B

contains 2 cards, C contains 3 cards and D contains 5 cards, we will read (4,2,3,5). If

one group is absent in the set, zero is used to indicate this in the protocol.

Instructions

1. E presents set 1 randomly ordered. E says:

“Here are some pictures of children with differently colored hair and eyes. Can you sort these cards into groups?”

If S sorts them into three or less groups, E asks:

“Is there any other way to group these cards? Show me.”

If S fails to locate four groups, terminate. Otherwise, S asks:

“Do you think there is a relationship between eye color and hair color in these cards or not?” (S responds.)

If S says “no” then ask:

“Why do you think so?”

If S does not understand the question, E says:

“Let’s go to the next question to clear it up.”

2. E removes groups C and D of set 1 and puts them aside, leaving (4,2,0,0). E says:

“Let’s look at just these cards for a moment. Pretend I cover my eyes and pick one at random. What are the chances the card will show brown eyes with blonde hair?” (S responds.)

“How did you determine that?” (S responds.)

3. E repeats 2 but utilizes groups C and D:

“If I pick one at random, what are the chances the card will show brown eyes with blonde hair? ” (S responds.)

“How did you determine that?”(S responds.)

4. E removes groups B and C leaving (4,0,0,4) and asks:

“If I pick one of these cards at random, and tell you the hair color, what are your chances of telling me the correct eye color?” (S responds.)

E desires S to notice that the set illustrates full relationship. If S correctly notes the chances are 100%:

“Since you can predict hair color all the time, we call this a ‘perfect’ relationship, right?”

5. E replaces groups C and D of set one and says:

“Using any or all of the cards on the table, can you construct a set of cards in which the hair color has no relationship with the eye color? You can take away any cards you want.” (S responds.)

“How did you determine that?”(S responds.)

6. E rearranges set one in S’s original pattern (4,2,2,4) and says:

“Now judging from all of these cards, pretend I cover my eyes and pick one at random. I look at it and tell you the color of hair. What are your chances of telling me the correct eye color?” ( S responds.)

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“How did you determine that?” (S responds.)

If by this time, S has not utilized some type of probability to accurately relate at least A to A+B and C to C+D in the full set of cards, then terminate.

7. E pushes the set to the side, saying:

“We’ll return to this set in a moment.”

E brings out set 2 which has been pre-ordered.

“Here is another set of cards already sorted. You can set them out.” (S responds.)

“Just considering this new set by itself, can you find a relationship between hair color and eye color?” (S responds.)

“What are your chances of telling me the correct eye color if I pick a card and tell you the hair color?” (S responds.)

Table 1. Description of Color Schemes for Correlation Task

_____________________________________________________________________The four color-schemes Number of cards in each group

Group Set 1 Set 2_____ Blue-eyed blondes (A) 4 3Brown-eyed blondes (B) 2 3Blue-eyed brunettes (C) 2 1Brown-eyed brunettes (D) 4 5

______________________________________________________________________

“How did you determine that?” (S responds).

8. E returns attention to set 1.

“Now let’s compare set 1 with set 2. Look at the hair color and eye color relationships in each set. Can you tell me if the relationship in set one is more, less or the same than for the second set?” (S responds.)

“How did you determine that?” (S responds.)

9. E points to groups A, B, C and D in turn in the second set, asking:

“What about this group? How does it influence your judgment?”(S responds.)

10. Making reference to both sets, E asks:

“Using any or all of the cards on the table, form two sets of your own. Can you make them so one set gives you a greater relationship between hair color and eye color than the other?” (S responds.)

“How did you determine that?” (S responds.)

Terminate.

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Narrative Scoring Criteria for the Correlations Task

Scoring Level Criteria

6. At one of three points in the protocol, S establishes a relationship between confirming cases of a relationship and either 1) the whole of cases or 2) the disconfirming cases. Thus, S invokes either of the following ratios: 1) (a+b)/(a+b+c+d) or 2) (a+d)/(b+c). This is evaluated during questions about the relationship of hair color to eye color in set I, set II, and during the comparison of set I with set II. This level is scored formal (late).

5. S invokes a simple ratio of hair/eye color for each color of hair at the points of evaluation listed for level 6. Thus, S makes comparisons in terms of a/(a+b) and d/(c+d). This level is scored formal (early).

4. S is able to establish ratios between hair and eye color for a given hair color, as in level 5. But when called upon to form two sets, one set with a greater relationship between hair and eye color than the other set, S cannot do so. S may or may not be able to construct a single set with a relationship which demonstrates zero correlation between hair and eye color. Although Piaget scores this level as early formal, it only indicates possession of direct proportions. Therefore, I do not score it as formal (see discussion in Chapter II, Review of Relevant Literature.)

3. S is unable to correctly identify the probabilistic ratio of hair color to eye color described in levels four and five. However, S is able to construct a relationship with zero correlation and identify a relationship which exhibits a perfect correlation.

2. S performs as in level three but fails to either 1) construct a relationship with zero correlation, or 2) identify a relationship which exhibits a perfect correlation.

1. S fails to correctly identify two simple probabilistic relationships in quantitative terms: b/(a+b) and d/(c+d).

Analysis of Data

The responses to the Piagetian tasks were scored according to Inhelder and Piaget

(1958). Each subject’s name, sex, coherence, and task scores were recorded. Subjects

were additionally classified along a “Formal Stage Criterion” dimension. Subjects who

passed at least one of the four tasks were considered to have “passed” the formal stage

criterion. Subjects who failed to pass any of the four tasks were considered to lack

evidence of any cognitive “reorganization” that supports formal operational reasoning.

These subjects were classified as “fail” on the formal stage criterion.

Scores were recorded that reflect the subject’s preference for Science, Math,

Verbal, and Art activities. (See background questionnaire in the Appendix.)

The EEG alpha coherence scores were combined to create a single number, the

“Coherence Index” (FLR-O). The 4 basic coherence measures (F, L, R, O) for each

subject consist of eighty four-second coherence measures taken over 5.3 minutes of

meditation. The number of samples during the 5.3 minutes is sufficient that we can

invoke the assumption of normality for the initial data. The resulting means for each

subject can also then be assumed to represent a stable measure of coherence.

Since the task data is ordinal (pass or fail), non-parametric analysis will be used

when the task score is the dependent variable.

Where coherence is used as the dependent variable, parametric analyses will be

used.

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CHAPTER IV

RESULTS

Results of Subject Selection

The population for this investigation is undergraduate and graduate students

attending a small liberal arts college, Maharishi International University (MIU), located

in Fairfield, Iowa. Fairfield is a rural town of about 7,000 persons supported mainly by

agriculture and light industry. Another 2,000 faculty, staff, and students are associated

with M.I.U. Most of the students live on campus. At the time of the research, all of the

students were from outside of Fairfield, with origins ranging from the U.S. west coast to

the east coast and Europe.

M.I.U. students can be considered “average” in many ways, since it has an open

admission policy. Many of the students receive financial aid and/or scholarships.

Therefore, family economic wealth is not a particular criterion for admission. The

students all participate in the school-sponsored “Maharishi Technology of the Unified

Field,” otherwise known as Transcendental Meditation. The avowed goal of TM is to

culture the nervous system to support a state of “restful alertness” (M.I.U. Bulletin,

1992-1993) in which stress is minimized and expression of individual potential is

maximized. The students reputedly do not use alcohol or drugs, probably owing to peer

pressure, school policy, and the pro-self-development attitudes of the students

themselves. Given that the students participate in a specific program of self-

development, the sample does not represent any “average” university population. They

are self-selected to join the rather unique collection of students. This qualification limits

the findings to similar populations of students practicing TM. However, since the study

is correlational, and the practice of TM is claimed to result in “naturally” occurring

outcomes, it is not unreasonable to generalize at least to others with similar age and

education who practice TM.

As part of an ongoing research program into longitudinal physiological changes

in students, M.I.U. required an annual electroencephalographic evaluation of each

student. I arranged to “piggyback” additional tests of formal operational reasoning onto

the EEG research program. EEG data was freely made available. Students attending

more than one year most likely had received a previous EEG evaluation. Therefore, it

was not an entirely new or unusual experience. This fact, plus the fact that students

received the measures during the practice of TM, suggests that no undue arousal effects

would bias the EEG data. The students were quite experienced in the practice of TM and

would therefore habituate rapidly to the situation and not feel “pressured” or otherwise

distracted during the EEG session.

Sample

The 58 subjects who participated in this study were taken as needed and at

random from the stream of students taking their required annual EEG readings at the

International Center for Scientific Research located at MIU. Only about 10% of the

sample are international students. They are European and sufficiently acclimated to

American culture that no obvious linguistic or cognitive differences seemed to set them

apart from their American peers.

Although students were contacted class-by-class, students in any selected class

could accept or reject the opportunity to have their EEG scheduled within a given week.

Females were not scheduled for EEG within three days before or after their menstrual

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period. All subjects were advised to eat lightly the meal before their appointment. The

research was conducted between mid-January and mid-March of 1981.

Participation in the present study was voluntary and no one refused. Typically,

two to four subjects were scheduled for each of the morning and afternoon examination

periods. The EEG usually took approximately 60-90 minutes including time to apply the

electrodes. Prior to removing the electrodes, subjects typically went immediately after

their EEG examination into a near-by room where they received the Piagetian protocols.

The presence of the leads was never mentioned as a hindrance to performance nor did

they appear to cause distraction or discomfort. Protocol administration required an

average of 60-70 minutes for the set of four tasks. Two randomly selected subjects were

videotaped.

A total of seventy-eight subjects were tested on each of the four tasks:

Correlations, Shadows, Vessels, and Combinations. The first ten subjects served in the

pilot study. Based on the pilot experience, the experimenter revised and standardized

both the written protocol and experimenter behavior. Of the remaining 68 subjects, eight

were not scored because the subject indicated some degree of left-handedness to the

question: “Do you consider yourself left-handed or ambidextrous in any regular activity

such as writing, eating or sports? (list).” Two other subjects were rejected due to possible

confounding variables: one subject stuttered, and another subject’s data set displayed

excessive EEG artifacts. This left a total of 58 subjects for the current data analysis. The

mean age was 26.7 years ranging from 17.8 to 35.8, with a S.D. of 4.3 years.

Thirty-nine subjects were male and 19 were female. Male mean age was 26.9 and

female mean age was 24.6. Males were significantly older, t (56) = 2.002, p = .0502.

The mean year in college was 4.0 with a minimum of 2 years and a maximum of

8 years. The S.D. was 1.6 years. There was no significant difference in mean years of

college between males and females, t (55) = .437, NS.

Since the students were contacted on a class-by-class basis for their EEG

evaluation, an interest inventory was given to detect any bias in favor of science and

math in the subject group. Subjects marked their level of “fulfillment and success” on a

scale of 1 (lowest level)–7 (highest level) for Art, Science, Verbal disciplines, and

Mathematics (see Participant Questionnaire, Appendix A). Math and Science were not

preferred over the other disciplines. Thereby implying that the subjects were not biased

toward those disciplines. In order of preference, means were Art: 5.228, Verbal: 5.035,

Science: 4.772, and Math: 4.351. Differences in means were tested with a Friedman test

for matched groups (Hays, 1973, p. 785) resulting in a between-measure chi-square

approximation of 7.5105, N = 57, 3 df, marginally significant at p = .0573. In a post-

hoc comparison using the Wilcoxon matched-pairs test (Hays, 1973, p. 780), Art and

Verbal were preferred significantly higher than Math, Z = -2.8203, p = .0048, and Z = -

2.0276, p = .0426, respectively. Science was preferred over Math with marginal

significance:

Z =-1.9040, p = .0569. All tests are two-tailed.

Measurement Reliability

Measurement reliability involves the possibility of scorer bias in evaluating

subject’s performance on each of the four tasks. Also, EEG data may be subject to

artifacts. Checks were made to evaluate both issues.

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Task Scoring Reliability

To validate the reliability of the scoring criteria used in each of the four tasks, fourteen

randomly-selected subjects were independently evaluated by a second independent judge.

For each subject, the judge was provided with audio tape recordings of the protocols and

the experimenter’s scoring sheets. The judge had prior experience in Piagetian task

scoring, as well as task design and theory. Table 2 presents the percentage of agreement

between the investigator and the judge on pass/fail evaluations for each task.

EEG Artifact Analysis

Eighteen EEG records were set aside after inspection revealed eye or muscle

tension artifact in more than five of the eighty 4-second sampling epochs. In subsequent

reprocessing of the digitized data, an artifact rejection program deleted all epochs that

exceeded a criterion voltage. Seventeen of the records were returned to the subject pool

after removing artifactual epochs. One record could not be used at all.

Summary of Data

Summary of Task Scores

The number of subjects scoring at each level of each task and the task index is

given in Table 3. The number and proportion of subjects passing each task and the

formal stage criteria are given in Table 4, together with the levels of attainment needed to

pass each task.

Passing achievement is defined on the basis of Piaget’s criteria for formal

operational reasoning, as given in the methods chapter. Generally, subjects are

considered passing (early formal) if they took a systematic approach to the task and if

they formulated the issues qualitatively correctly without guessing. The one exception to

this generalization is the Shadows task. Early formal, according to Inhelder and Piaget

(1958) requires that a metric approach be taken in addition to application of a qualitative

sense of positioning the rings with respect to their diameter and distance from the light.

For all the tasks, subjects are scored on a higher level of formal reasoning (late formal) if

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Table 2. Percentage Agreement on Pass/Fail Ratings By Two Independent Judges (N=14)

_________________________________________________________________________Task Scored* Agree Percentage Agreement

______________________________________________________________________________________

Vessels 13 12 92%Shadows 13 11 85%Combination 13 12 92%Correlations 13 12 92%

________________________________________________________________________*Certain protocols could not be scored due to inability to hear portions of the audio tape, therefore only 13 data points were obtained across the 14 subjects.

Table 3. Data Summary: Number of Subjects Scoring Each Level For Each of the Four Tasks and the Formal Stage Criterion

____________________________________________________________________________________ Scoring Level

Number ofTask Subjects 0 1 2 3 4 5 6

____________________________________________________________________________________Vessels

Male 39 6 7 11 10 14Female 18 9 2 2 3 2Total 57 15 7 11 10 14

ShadowsMale 37 4 9 13 11Female 19 10 4 4 1Total 56 14 13 17 12

CombinationsMale 39 4 12 4 13 6Female 19 5 6 0 7 1Total 58 9 18 4 20 7

CorrelationsMale 38 8 5 7 4 9 5Female 19 5 4 4 1 4 1Total 57 13 9 11 5 13 6

Formal Stage Criterion*Male 36 8 8 9 7 4Female 18 7 5 4 2Total 54** 15 13 13 9 4

______________________________________________________________________________________* The Formal Stage Criterion gives a summary measure of the number of tasks passed by each subject. Subjects who fail all four tasks are considered to lack evidence of developing the stage of formal operational reasoning. Subjects who pass one or more tasks are considered to have developed the characteristic structures in action at the formal operational stage, acknowledging that the subject may not have developed more logical structures than indicated by passing the particular given task. Here, 15 subjects, 8 males and 7 females, fail to meet the formal stage criterion.

** 4 subjects (3 male, 1 female) are not accounted in the Formal Stage Criterion because one of their 4 tasks lacked clear audio recording and thus prohibited proper scoring. Note that for each of these 4 subjects, none of the other tasks were passed. Therefore, the best they could have done would be a scoring level of “1.” Using the observed probabilities (15 S’s scored “0” and 13 S’s scored “1”) as a guide to the expected distribution, roughly half would then have scored “1” and the other half “0.”

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Table 4. Data Summary: Number and Proportion of Subjects Passing Each Task, the Combination of Tasks, and the Formal Stage Criterion

______________________________________________________________________________________

Levels Number of Constituting Subjects

Task Subjects Passing Passing Proportion (%)______________________________________________________________________________________

Formal Stage Criterion 54 1 or greater 39 72.2Vessels 57 4 and 5 24 42.1Shadows 56 4 12 21.4Correlations 57 5 and 6 19 33.3Combinations 58 4 and 5 27 46.6

V,S,Corr,Comb 54* 4 7.4

V,S,Corr 54 0 0V,S,Comb 54 1 1.8V,Corr,Comb 54 5 9.3S,Corr,Comb 54 3 5.6

V,S 54 3 5.6V,Corr 54 1 1.8V,Comb 54 4 7.4S,Corr 54 1 1.8S,Comb 54 0 0Corr,Comb 54 4 7.4

V 54 6 11.1S 54 0 0Corr 54 1 1.8Comb 54 6 11.1None 54 15 27.8

______________________________________________________________________________________*Only subjects who were scored on all four tasks were included in this analysis.

they produced quantitative rationale for their explanations. In either case, whether early

formal or late formal, they receive a pass on the task.

Subjects who fail all four of the tasks are considered to lack evidence of

characteristic structures associated with formal operational reasoning. Therefore, these

subjects are scored “fail” on the Formal Stage Criterion (15 out of 54). Subjects passing

one or more tasks are scored “pass” on the formal stage criterion acknowledging that the

subject may not have developed more logical structures than indicated by passing the

particular task (39 out of 54). Note that 37 of the subjects who passed the formal stage

criterion passed either the Vessels task or the Combinations task or both. Conversely,

only two subjects failed both Vessels and Combinations tasks among those who passed

the formal stage criterion. (One passed the Correlations task and one passed both the

Correlations and the Shadows task.) This data suggests that the “Formal Stage Criterion”

is defined primarily by the structures associated with the Vessels and Combinations tasks,

namely, the INRC group and the combinatorial lattice, respectively.

According to Inhelder and Piaget (1958), a subject can score early formal (IIIA)

on the correlations task without actually demonstrating possession of the schema of

correlations. As pointed out by Wavering (1979), the first level indicates proportional

reasoning, a formal operation ability, but unrepresentative of the correlational schema.

Wavering excluded this level of performance from receiving a “pass” score with the

justification that correlational reasoning (IIIB and IIIC) must be demonstrated to justify

receiving a “pass” score for a correlational task that is comparable to a “pass” score in the

other formal schemata being tested and compared. I concur with this reasoning, and

adopt the same convention in this research.

109

Summary of EEG Alpha Coherence Measures

Descriptive statistics for the EEG alpha coherence measures and Coherence Index

are presented in Table 5 The measures are broken down by gender in Table 6. Since the

kurtosis values are less than 3.0 corresponding to the normal distribution, the

distributions are slightly platykurtic, or more flat. The skewness values also depart from

the value of 0.0 corresponding to the normal distribution. However, visual inspection of

the standardized form of the distributions indicates that none of the departures from

normality are extreme.

Analysis 1 - Unitary Composition of Task Index

Although the formal stage criteria suggests that 72 percent of those subject

possess the characteristic structures in action at the formal stage, inspection of the rate of

passing the tasks suggested an obvious difference in difficulty between the tasks. Only

21% of the subjects passed the Shadows task compared with 42% passing the Vessels

task. To evaluate the degree and impact of this apparent non-homogeneity of the formal

reasoning tasks, all possible pairs were tested using the McNemar chi-square test for the

equality of two correlated proportions (Hays, 1973, p. 740). See Table 7 for the

calculated chi-square values and the percentage of subjects that received the same score

(confirming cases) in a given pair of tasks. Figure 3 presents the contingency

relationships for subjects scored pass and fail on the pairs of tasks.

The ordered diagram of the statistically significant pairwise tests is presented in

Figure 4. It includes the percentage of subjects who passed one of the tasks more

frequently compared with all subjects who had a pass score on only one of the two tasks.

The more frequently passed task is assumed to be easier. Subjects gave evidence of

attaining the INRC group schema (Vessels task)and the combinatorial schema more

easily than the proportions schema (Shadows task). Although not statistically significant,

Table 5. Data Summary: EEG Data By Total Subjects

______________________________________________________________________________________

Alpha CoherenceCoherence Index F3F4 F3C3 F4C4 O1O2

______________________________________________________________________________________Number of Subjects 58 58 58 58 58Mean 1.513 .785 .714 .687 .674SD .251 .077 .085 .102 .082Kurtosis .251 -.267 .128 2.181 .034Skewness -.592 -.784 -.463 -1.111 .457____________________________________________________________________________________

Correlations with...Coherence Index 1.000*

(.000)F3F4 .545 1.000

(.000) (.000)F3C3 .922 .419 1.000

(.000) (.001) (.000)F4C4 .85 .328 .787 1.000

(.000) (.012) (.000) (.000)0102 -.502 .136 -.381 -.208 1.000

(.000) (.307) (.003) (.116) (.000)______________________________________________________________________________________*Pearson correlation coefficient. Numbers in parentheses give the p value. Significance cut-off is p ≤ .05

111

Table 6. Data Summary: EEG Data By Gender

______________________________________________________________________________________ Alpha Coherence

Gender Coherence Index F3F4 F3C3 F4C4 O1O2______________________________________________________________________________________ FNumber of Subjects: 19______________________________________________________________________________________

Mean 1.52171 .77955 .72371 .67726 .65397

SD .24227 .06291 .09358 .10071 .06735Kurtosis 2.07886 -.27102 1.15003 2.06954 1.27294Skewness -.52907 .05237 -.35221 -.94447 .93540

______________________________________________________________________________________M Number of Subjects: 39______________________________________________________________________________________

Mean 1.50651 .78912 .70961 .69214 .68437SD .25896 .08476 .08270 .10422 .08812Kurtosis -.14627 -.24502 -.39490 2.73066 -.12699Skewness -.62486 -.99174 -.60749 -1.24315 .24908

______________________________________________________________________________________Test for Differences Between the Means

t .291 -.436 .584 -.500 -1.33df 56 56 56 56 56p value .772 .665 .562 .619 .188

_____________________________________________________________________________________

Table 7. Analysis of Relative Difficulty of Task Pairs: McNemar Chi-Square Test for the Equality of Two Correlated Proportions (with Bonferroni Correction)

______________________________________________________________________________________

Confirming Cases Disconfirming CasesPair* Pass Fail (% of Total N) X2 (df=1) p N % of Both**______________________________________________________________________________________

Shadows 12 43 35 7.200 .007*** 4Vessels 24 31 (63.6%) 16 80.0%

Shadows 12 43 40 3.267 .071 4Correlations 19 36 (72.7%) 11 73.3%

Shadows 12 44 33 9.787 .002*** 4Combinations 27 29 (58.9%) 19 82.6%

Vessels 24 32 33 1.087 .297 14 60.9%Correlations 37 19 (58.9%) 9

Vessels 24 33 34 .391 .532 10Combinations 27 30 (59.65%) 13 56.5%

Correlations 19 38 43 4.571 .032 3Combinations 27 30 (75.4%) 11 78.6%______________________________________________________________________________________*Missing task scores cause the total N to vary from pair to pair.

**This statistic represents the proportion of subjects that pass the particular task but fail the other task compared with the total number of subjects that pass either task but fail the other task (a disconfirming relationship between the tasks). It gives a sense of the magnitude by which subjects as a group acquire the underlying schema prior to acquiring the other schema with which it is compared. Note that this statistic is inversely related to the p values.

***Significant at p ≤ .0083 (This criterion reflects a significance cut-off of p ≤ .05 corrected for multiple tests (6) as recommended by Bonferroni. Note that the Bonferroni correction assumes independence among the tests. However, in this case, we can reasonably expect correlated data, which would raise the alpha level. Here, we divide the .05 alpha level by six, the number of tests, making the outcome a conservative, over-corrected estimate of the probability that the proportions are correlated.)

113

Shadows Vessels Combinations Pass Fail Pass Fail Pass Fail

Pass 8 11 10 9 16 3 Correlations Fail 4 32 14 23 11 27 Pass 8 19 14 13 Combinations Fail 4 25 10 20 Pass 8 16 Vessels Fail 4 27

Figure 3. Contingency Relationships for Subjects With Scores on Both Tasks

Most difficult task: Shadows (proportions schema) Correlations Easiest tasks: Combinations Vessels (equilibration schema)

73.3%*

78.6%

82.6%** 80%**

_______________________________________________________________________________

*The percentage of subjects who pass the easier task compared with subjects who pass only one of the two tasks

**Significant at p ≤ .0083, reflecting a Bonferroni correction for multiple tests

115

Figure 4. Ordering Diagram for Four Tests of Formal Reasoning: Arrow Indicates Direction of Logical Prerequisite

the combinations schema is passed more easily than the proportions aations schemata.

There is no statistically significant relationship in the order of acquisition between

combinations and equilibrations schemata (Vessels task), or correlations and

equilibration schemata. There is a modest, but non-significant nd correlrelationship that

indicates the correlations may appear prior to the proportions schema.

As mentioned above, the Formal Stage Criterion is passed primarily by subjects

who pass either the Vessels task and/or the Combinations task. They may or may not

have passed the Shadows or the Correlations tasks. Only two subjects who passed the

Formal Stage Criterion failed to pass either the Vessels or the Combinations tasks. It is

difficult, if not impossible, to explain how both subjects passed the Correlations task

without giving evidence of either the INRC group or the lattice structure, and likewise

for the one subject that also passed the Shadows task. Presumably this is evidence of the

notion that formal reasoning “stage” is not bounded by possession of any particular

structure. However, given the pre-eminent “status” of the INRC group and lattice

structure among the ten structures Piaget has identified, the findings remain to be

explained. It may be that the contexts of these two tests were sufficiently unfamiliar to

these particular subjects that they could not extrapolate the structures to the situation.

Analysis 2 - Relationship Between Gender and Task Performance

A two-tailed Fisher exact test of independence (Hays, 1973, p. 736) was

performed to test the null hypothesis that there were no significant differences between

male and female performance in each task. The Fisher exact test of independence was

used because some of the cells have expected minimum frequencies of less than 10 and

the test uses a df = 1. The chi square test of independence may not be conservative

enough. The test result for the Shadows task was significant at the 0.05 level, two-tailed.

117

Only 5.3% of females passed compared with 29.7% of males. No other tests showed

significant differences. The results are summarized in Table 8. The Vessels task

appeared to result in similarly lopsided results with 27.8% of females passing versus

48.7% of males. However, the difference was not significant, p = .161, two-tailed. The

lower passing rates of females on the Shadows and Vessels tasks may reflect EEG

differences reported by other EEG coherence researchers in which females scored lower

on tasks with spatial components (Beaumont, Mayes, and Rugg, 1978). Normally, such

gender differences would dictate that further analyses would be done for each gender

separately. However, owing to reported gender differences in the Shadows task, it is

expected that the EEG may reflect gender differences that are task related. Therefore,

the Analysis 2 following, will not covary for gender or age. Note that females are

significantly younger than males in this study. Age is not covaried since age can also

reasonably be expected to be reflected in both EEG coherence and task performance.

Analysis 2 - Relationship Between Coherence Index and Task Performance

Student's t test was used to test the null hypothesis that there was no significant

difference in the mean Coherence Index of subjects who passed a task and those who

failed the test.

The results given in Table 9 indicate that subjects who passed the Vessels task

measured significantly higher on the Coherence Index than subjects who failed the

Vessels task, t (55) = -1.676, p = .0495 (one-tailed). Passing subjects had a mean

Coherence Index score of 1.577 compared with failing subjects who had a mean of

1.465.

Means associated with the other tasks were in the predicted direction, with higher

mean coherence for subjects in the pass group. Interestingly, the test for the formal stage

Table 8. Analysis of Differences in Male and Female Performance on the Four Tasks

______________________________________________________________________________________Performance N Number of Subjects Passing Fisher Exact TestMeasure Males Females Males Females of Independence (df=1)______________________________________________________________________________________ Formal Stage Criterion 18 36 28 11 .216

(77.8%)** (61.1)Vessels 39 18 19 5 .161

(48.7%) (27.8%)Shadows 37 19 11 1 .043*

(29.7%) (5.3%)Correlations 38 19 14 5 .555

(36.8%) (26.3%)Combinations 39 19 19 8 .781

(48.7%) (42.1%)______________________________________________________________________________________*Significant at p ≤ .05 (two-tailed)

*Percentage of males and females passing

119

Table 9. Results of Unpaired T-Test of Differences in Coherence Index Means between Pass and Fail Groups

______________________________________________________________________________________

Group N Mean S.D. t df p *______________________________________________________________________________________Formal Stage CriterionPass 39 1.542 .234 1.618 52 .0558***Fail 15 1.418 .298______________________________________________________________________________________VesselsPass 24 1.577 .248 -1.676 55 .0495**Fail 33 1.465 .248______________________________________________________________________________________ShadowsPass 12 1.596 .289 -.938 54 .176Fail 44 1.492 .242______________________________________________________________________________________CorrelationsPass 19 1.538 .196 -.498 55 .310Fail 38 1.503 .278______________________________________________________________________________________CombinationsPass 27 1.549 .236 -1.021 56 .156Fail 31 1.482 .261______________________________________________________________________________________*All significance tests are one-tailed.

**Significant at p ≤ .05

*** Trend at p ≤ .06

criterion was nearly significant at p = .0558. This suggests that the alpha coherence index

may indeed reflect a developmental function relative to stages of epistemological growth.

Analysis 3 - Relationship between Coherence Index and Task Performance Controlling for Age and Gender

In light of the Beaumont, Mayes, and Rugg’s (1978) findings of task and gender

interaction on coherence measures, it is surprising that Analysis 2 showed Coherence

Index differences between pass and fail subjects on the Vessels task whereas Analysis 1

indicated gender differences on the Shadows task. In other words, the anticipated

influence of gender on both coherence index and task did not appear. (Albeit, both

Vessels and Shadows used the INRC group schema.)

Therefore, to further examine the possible relationships between age, gender,

EEG alpha coherence, and task performance, we should also test to see if any interactions

are present between gender and task and also see if the relationship between task and

EEG alpha coherence strengthens, weakens, or remains the same when the influence of

gender and age are controlled. First, however, we must insure there is no significant

interaction between the continuous covariant, age, and the grouping variables. This is a

test of the assumption of homogeneity of slopes, and is accomplished by testing for

significant interactions with an ANCOVA (analysis of covariance) using a general linear

model that adjusts for unequal numbers of subjects in the various group cells (Wilkinson,

1989).

The results given in Table 10 indicate that assumption of homogeneity of slopes

holds. There are no significant interactions between the continuous covariant, age, and

any of the grouping variables, gender and task performance. Further analysis evaluated

the interaction between the grouping variables of gender and task performance. (See

Table 11). The model included task, gender, age, and taskXgender interaction.

121

Table 10. Results of Tests of the Assumption of Homogeneity of Slopes for Age as a Covariant with Task and Gender

______________________________________________________________________________________ (N)Group Effect SS df MS F-Ratio Probability *______________________________________________________________________________________Formal Stage Criterion (54) Formal Stage 0.0256 1 0.0256 0.3786 0.5413 Gender 0.0060 1 0.0060 0.0889 0.7669 Age 0.0278 1 0.0278 0.4119 0.5241 Formal StageXAge 0.0142 1 0.0142 0.2100 0.6489 GenderXAge 0.0195 1 0.0195 0.2893 0.5932 Formal StageXGenderXAge 0.1159 1 0.1159 .7173 0.1964 Error 3.1724 47 0.0675______________________________________________________________________________________Vessels (57)

Vessels .0194 1 .0194 .2932 .5906Gender .0244 1 .0244 .3691 .5462Age .0011 1 .0011 .0166 .8980VesselsXAge .0068 1 .0068 .1029 .7497GenderXAge .0320 1 .0320 .4838 .7497VesselsXGenderXAge .0063 1 .0063 .0956 .7585Error 3.3088 50 .0662

______________________________________________________________________________________Shadows (56)

Shadows .0017 1 .0017 .0253 .8744Gender .03800 1 .0380 .5537 .4604Age .0240 1 .0240 .3509 .5563ShadowsXAge .0089 1 .0089 .1295 .7205GenderXAge .0537 1 .0537 .7832 .3805ShadowsXGenderXAge .0157 1 .0157 .2296 .6339Error 3.3583 49 .0665

______________________________________________________________________________________Correlation (57)

Correlation .0000 1 .0000 .0002 .9892Gender .0528 1 .0528 .7640 .3863Age .0008 1 .0008 .0115 .9149CorrelationsXAge .0001 1 .0001 .0008 .9780GenderXAge .0536 1 .0536 .7754 .3828CorrelationsXGenderXAge .0077 1 .0077 .1110 .7404Error 3.4543 50 .0691

______________________________________________________________________________________Combination (58)

Combination .0524 1 .0524 .8180 .3700Gender .0547 1 .0547 .8543 .3597Age .0412 1 .0412 ..6436 .4261

CombinationsXAge .0554 1 .0554 .8650 .3567GenderXAge .0573 1 .0573 .8946 .3487CombinationXGenderXAge .0935 1 .0935 1.4602 .2325Error 3.2650 51 .0640

______________________________________________________________________________________*All significance tests are two-tailed.

123

Table 11. Results of Analysis of Covariance in Coherence Index Between Tasks, Controlling for Age and Gender

______________________________________________________________________________________

(N) ProbabilityTask Effect * SS df MS F-Ratio Two-tailed One-tailed______________________________________________________________________________________Formal Stage Criterion (54) Pass Tasks 0.1849 1 0.1849 2.7980 .050** Gender 0.0223 1 0.0223 0.3374 0.5640 Age 0.0000 1 0.0000 0.0001 0.9939 Error 3.3037 50 0.0661______________________________________________________________________________________Vessels (57)

Vessels .201 1 .201 3.177 .040**Gender .013 1 .013 .200 .654Age .013 1 .013 .204 .656Error 3.350 53 .063

______________________________________________________________________________________Shadows (56)

Shadows .082 1 .082 1.250 .134Gender .036 1 .036 .549 .463Age .005 1 .005 .082 .776Error 3.533 52 .066

______________________________________________________________________________________Correlation (57)

Correlation .017 1 .017 .257 .307Gender .005 1 .005 .067 .797Age .002 1 .002 .024 .876Error 3.533 53 .067

______________________________________________________________________________________Combination (58)

Combination .068 1 .068 1.057 .154Gender .006 1 .006 .086 .770Age .002 1 .002 .032 .858Error 3.486 54 .065

______________________________________________________________________________________*When the GenderXTask interaction is included in the models, the interaction p values are: Formal Stage Criterion, p = .707, Vessels, p = .961, Shadows, p = .828, Correlations, p = .630, Combinations, p =. 287.

**Significant at p = or ≤ .05, one-tailed test

ANCOVA revealed no significant interactions (see footnotes to Table 11). A subsequent

ANCOVA on the same model, but without the interaction, revealed that the Vessels task

demonstrated virtually unchanged results, F = 3.177, df = 1, p = .040, one-tailed. That

is, when holding age and gender constant (a Type III test), the Coherence Index

continued to demonstrate statistically significant differences between the pass and fail

groups for the Vessels task. The test for Formal Stage Criterion indicated significant

results (p = .050) consistent with the hypothesis that the coherence index is a measure of

developmental progress with respect to the stage of formal operational reasoning.

Results of these tests on the other three tasks demonstrated similar resemblance to

their equivalent t -tests. Therefore, it is concluded that overall, the relationship between

the Coherence Index and tasks are independent of age and gender. In other words, the

relationship holds across both genders. What holds for males is expected to hold also for

females, without regard to differences in age, for the given range and distribution of

ages.

Follow-up Analysis 1 - Analysis of Differences in Various Coherence Measures Between Pass and Fail Subjects

The Coherence Index is constructed as the sum of three “anterior” alpha

coherence derivations , F3F4 (frontal or “F”), F3C3 (left or “L”), and F4C4 (right or

“R”), minus the “posterior” derivation O1O2 (occipital or “O”). The Coherence Index

was constructed based on empirical relationships among the derivations (frontal + left+

right - occipital or “FLR-O”) established in previous research on creativity and mental

health (Orme-Johnson, et al., 1982). Do the empirical relations taking each derivation

separately still hold for the formal stage criterion or any of the four tasks for formal

reasoning?

125

Here, follow-up analysis reports additional tests on the derivations and the ratios

between certain of the derivations. Ratios were tested to explore possibilities for greater

discriminatory power between pass and fail groups within each task. The ratios included

typical measures of laterality differences, (R-L)/(R+L), and the analog measures of

anterior/posterior differences, (R-O)/(R+O) and (F-O)/(F+O). Because frontal bilateral

activity may signify different mental processes than left or right homolateral activity, the

ratio of frontal to left coherence, (F-L)/(F+L), was also studied.

The results are presented in Tables 12 - 16. Preliminary texts for taskXgender interaction

revealed only one statistically significant interaction (p ≤ .05): the ratio (L-R)/(L+R)

demonstrated interaction in the Shadows task. However, interpretation is difficult since

only one female passed the Shadows task. Post hoc Sheffé tests of all possible pairs

indicated that the ratio was less for the pass female than the fail male group (p = .0665,

not significant). The lack of other interactions, especially in the (L-R)/(L+R) ratio in the

two INRC group tasks, Vessels and Shadows, was surprising in light of the significant

difference between males and females in the Shadows task (p = .043) and the trend for

differences in the Vessels task (p = .161). Apparently, males and females are

“neurologically equivalent” for the measures used here. Subsequent analyses and

conclusions will, therefore, apply to both genders.

For tests of pass vs. fail, one-tailed tests were made where the direction of effect

was expected (anterior derivations : higher for pass, posterior derivation : higher for fail).

For ratios constructed out of measures within the anterior derivations , no expectations

could be made regarding the relationship between pass and fail groups and the dependent

measures. Therefore, these latter tests used a two-tailed alpha test. Because the tests are

exploratory, no Bonferroni corrections in the alpha level (p ≤ .05) were made to

compensate for the multiple tests in this and subsequent follow-up analyses. Although

results indicate that among the tasks there are no significant differences that

discriminated pass from fail groups, also note that results of the tests indicate no

significant differences

127

Table 12. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Formal Stage Criterion Pass and Fail Groups*

_____________________________________________________________________________________ Probability

Group N Mean S.D. t df Two-tailed One-tailed______________________________________________________________________________________

F = F3F4Pass 39 .789 0.070 0.413 52 .341Fail 15 .780 0.092

L =F3C3Pass 39 0.7236 0.0788 1.3875 52 .086Fail 15 0.6868 0.1068

R = F4C4Pass 39 0.6973 0.0975 1.1372 52 .130Fail 33 .672 .099

O = O1O2Pass 39 0.6683 0.0764 1.7135 52 .046**Fail 15 0.7099 0.0883

F-L ratio = (F3F4-F3C3)/(F3F4+F3C3)Pass 39 0.0447 0.0547 1.0867 52 .282Fail 33 .057 .074

L-R ratio = (F3C3-F4C4)/(F3C3+F4C4)Pass 39 0.0212 0.0526 0.0949 52 .925Fail 33 .021 .042

R-O ratio= (F4C4-O1O2)/(F4C4+O1O2) Pass 39 0.0187 0.1050 1.7433 52 .044**Fail 15 -0.0405 0.1284

F-O ratio= (F3F4-O1O2)/(F3F4+O1O2) Pass 39 0.0841 0.0701 1.6639 52 .051***Fail 15 0.0469 0.0825

______________________________________________________________________________________*ANCOVAs using a full model of gender, task, and genderXtask interaction indicated no significant interaction. Therefore, male and female subjects were pooled for t-tests of pass vs. fail.

**Significant at p ≤ .05

***Near significant at p = .051

Table 13. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Vessels Task Pass and Fail Groups*

_____________________________________________________________________________________ Probability

Group N Mean S.D. t df Two-tailed One-tailed______________________________________________________________________________________

F = F3F4Pass 24 .794 .084 -.595 55 .277Fail 33 .781 .071

L =F3C3Pass 24 .733 .077 -1.507 55 .069Fail 33 .698 .090

R = F4C4Pass 24 .710 .107 -1.393 55 .085Fail 33 .672 .099

O = O1O2Pass 24 .661 .085 1.198 55 .118Fail 33 .687 .079

F-L ratio = (F3F4-F3C3)/(F3F4+F3C3)Pass 24 .041 .043 .959 55 .342Fail 33 .057 .074

L-R ratio = (F3C3-F4C4)/(F3C3+F4C4)Pass 24 .020 .059 .001 55 .928Fail 33 .021 .042

R-O ratio = (F4C4-O1O2)/(F4C4+O1O2)Pass 24 .033 .114 -1.558 55 .063Fail 33 -.013 .109

F-O ratio = (F3F4-O1O2)/(F3F4+O1O2)Pass 24 .093 .076 -1.463 55 .075

Fail 33 .064 .071______________________________________________________________________________________*ANCOVAs using a full model of gender, task, and genderXtask interaction indicated no significant interaction. Therefore, male and female subjects were pooled for t-tests of pass vs. fail.

129

Table 14. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Shadows Task Pass and Fail Groups*

______________________________________________________________________________________

ProbabilityGroup N Mean S.D. t df Two-tailed One-tailed______________________________________________________________________________________F = F3F4

Pass 12 .793 .061 -.442 54 .330Fail 44 .781 .083

L = F3C3Pass 12 .708 .086 -.988 54 .164Fail 44 .736 .092

R = F4C4Pass 12 .684 .098 .087 54 .465Fail 44 .686 .126

O = O1O2Pass 12 .643 .082 1.525 54 .066Fail 44 .684 .082

F-L ratio = (F3F4-F3C3)/(F3F4+F3C3)Pass 12 .039 .065 .494 54. .623Fail 44 .050 .064

L-R ratio = (F3C3-F4C4)/(F3C3+F4C4)Pass 12 .044 .064 -1.626 54 .110Fail 44 .017 .046

R-O ratio = (F4C4-O1O2)/(F4C4+O1O2)Pass 12 .024 .146 -.645 54 .261Fail 44 -.000 .104

F-O ratio = (F3F4-O1O2)/(F3F4+O1O2)Pass 12 .16 .068 -1.650 54 .052**Fail 27 .069 .077

______________________________________________________________________________________*ANCOVAs using a full model of gender, task, and genderXtask interaction indicated only one significant interaction: (F-L)/(F+L) p = .0352. Interpretation is difficult, however, since only one female passed the task. Post hoc Sheffé tests of all possible pairs revealed that the pass female measure was less than the fail male measure, p = .0665, not significant. Given the difficulty of interpretation with only one pass female, male and female subjects were pooled for t-tests of pass vs. fail.

**Near significant at p = .052

Table 15. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Correlations Task Pass and Fail Groups*

______________________________________________________________________________________

ProbabilityGroup N Mean S.D. t df Two-tailed One-tailed_____________________________________________________________________________________

F = F3F4Pass 19 .779 .070 .676 55 .259Fail 38 .794 .079

L = F3C3Pass 19 .722 .070 -.419 55 .338Fail 38 .711 .094

R = F4C4Pass 19 .717 .077 -1.515 55 .068Fail 38 .673 .112

O = O1O2Pass 19 .680 .077 -.165 55 .435Fail 38 .676 .083

F-L ratio = (F3F4-F3C3)/(F3F4+F3C3)Pass 19 .038 .059 1.022 55 .311Fail 38 .056 .064

L-R ratio = (F3C3-F4C4)/(F3C3+F4C4)Pass 19 .004 .043 1.942 55 .057Fail 38 .031 .053

R-O ratio = (F4C4-O1O2)/(F4C4+O1O2)Pass 19 .027 .087 -1.041 55 .151Fail 38 -.006 .122

F-O ratio = (F3F4-O1O2)/(F3F4+O1O2)Pass 19 .069 .070 .549 55 .292Fail 38 .081 .077

______________________________________________________________________________________*ANCOVAs using a full model of gender, task, and genderXtask interaction indicated no significant interaction. Therefore, male and female subjects were pooled for t-tests of pass vs. fail.

131

Table 16. Results of Unpaired T-Test of Differences in Various Coherence Measures Between Combination Task Pass and Fail Groups*

______________________________________________________________________________________

ProbabilityGroup N Mean S.D. t df Two-tailed One-tailed______________________________________________________________________________________

F = F3F4Pass 27 .784 .067 .188 56 .425Fail 31 .788 .088

L = F3C3Pass 27 .721 .077 -.585 56 .280Fail 31 .708 .094

R = F4C4Pass 27 .708 .088 -1.411 56 .082Fail 31 .670 .112

O = O1O2Pass 27 .664 .076 .927 56 .179Fail 31 .684 .087

F-L ratio = (F3F4-F3C3)/(F3F4+F3C3)Pass 27 .042 .053 -1.021 56 .312Fail 31 .054 .071

L-R ratio = (F3C3-F4C4)/(F3C3+F4C4)Pass 27 .011 .041 1.594 56 .117Fail 31 .031 .056

R-O ratio = (F4C4-O1O2)/(F4C4+O1O2)Pass 27 .031 .101 -1.573 56 .125Fail 31 -.014 .117

F-O ratio = (F3F4-O1O2)/(F3F4+O1O2)Pass 27 .084 .077 -.670 56 .253Fail 31 .071 .072

______________________________________________________________________________________*ANCOVAs using a full model of gender, task, and genderXtask interaction indicated no significant interaction. Therefore, male and female subjects were pooled for t-tests of pass vs. fail.

(p ≤ .05) that contradicted the expected directions. Two tests were near-significant at p ≤

.058. More important to our hypothesis, however, the tests on formal stage criterion

indicate two significant results and one near-significant result. These three results are

associated with the O1O2 derivation and suggest the group of subjects who fail the

formal stage criterion exhibit greater alpha coherence in the bilateral occipital

derivation . The three derivations include O1O2 (p = .046), (R-O)/(R+O) (p = .044),

and (F-O)/(F+O) (p = .051). The implications of observing negative relationship

between the bilateral occipital derivation and cognitive development as given by these

results will be explored in Chapter V under “Recommendations for Future Research.” I

suggest that the increase in anterior alpha coherence may, under certain conditions, give

rise to reduced bilateral occipital coherence as a necessary consequence of the lack of

bilateral commissural connections in the occipital lobes.

Of interest is the general pattern of near-significant p values (p ≤ .1) for the right

hemisphere derivation F4C4 in the Vessels, (p = .084) Correlations (p = .068), and

Combinations tasks (p = .082). This suggests that the right hemisphere may play a role

in discriminating pass from fail subjects, albeit, not statistically significant. The Vessels

task also resulted in a low p value (p = .069) in the left hemisphere deriviation and in the

ratios that compare the posterior derivation with anterior derivations (p = .063 and p

= .0745). Furthermore, Shadows task demonstrated near-significant differences (p

= .065) in the O1O2 measure associated with bilateral coherence in the occipital region

and in the ratio comparing bilateral frontal with occipital coherence (p = .052). These

trends were all in the expected directions: anterior derivations were higher for the pass

group and posterior derivations were higher for the fail group. These trends in general

reinforce the previous empirically supported relationship between adaptive functioning

(positive traits) and the individual measures of alpha coherence reported in the

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Introduction. Since left, right, and occipital regions all contribute to the discriminatory

trend, it may be suggested that FLR-O represents a “whole brain” measure.

Overall, in the case of tasks of formal reasoning used here, task success is

indicated across a greater variety of tasks in individual measures of right and occipital

coherences (and associated ratios) than by the Coherence Index alone. The anterior left

and/or right coherence measures appear to play at least a modest role in all four tasks as

well as in the formal stage criterion. The posterior, occipital coherence measures appear

to play an additional role in the Shadows task and significantly so in the case of the

Formal Stage Criterion. Together, these findings imply that the Coherence Index

maintains a relationship to formal operational reasoning through positive correlations

with anterior homolateral coherence and negative correlations with posterior occipital

bilateral coherence. This gives support to the original empirical equation (FLR-O) by

Orme-Johnson et al. (1982).

Follow-up Analysis 2: Tests for Relationships Between Preferences and Task Performance

The Art, Verbal, Science, and Math preference measures previously indicated that

subjects were not selected with a bias towards mathematics or science. Here, a follow-up

investigation examines the relationship between preferences and task performance.

Because the data lack an interval scale and fail the assumptions of normality, non-

parametric tests were conducted using the Mann-Whitney test for two independent

samples (Hays, 1973, p. 778). Where a direction of relationship between pass

performance and a preference could be anticipated, the alpha criterion was made one-

tailed. Specifically, other research indicates that affective and course performance

measures in science and mathematics correlate well with achievement in tests of formal

reasoning (Modgil and Modgil, 1976; also see Rennie and Punch, 1991). No predictions

can be made regarding Art or Verbal activity preferences.

Statistically significant positive relationships (p ≤ .05) were found between

preference for Science and pass performance on the Formal Stage Criterion as well as the

Vessels, Shadows, and Correlations tasks. Similarly, statistically significant relationships

were found between Math preference and pass scores on the Formal Stage Criterion as

well as the Shadows, Correlations, and Combinations tasks. (See Table 17.)

Confirming, and near-significant positive relationships were found between Math

preference and Vessels pass score (p = .055), as well as Science preference and

Combinations pass scores (p = .055).

Conversely, preference for Art was related to fail performance for Combinations

(p = .003). Confirming, but non-significant (p ≤ .1) relationships were indicated in the

same direction for Art preference in the Formal Stage Criterion, and the Correlations and

Shadows tasks.

The overall pattern of test results indicates that self-reported preference for (and

past success in) Science and Math are reasonable positive predictors of performance in

formal stage attainment as well as passing each of the four tasks, while Art, an hitherto

uninvestigated variable, is a negative predictor. In fact, based on the p values

demonstrated in this research, the preference measures were stronger and more consistent

indicators of formal reasoning across the tasks than any of the alpha coherence measures.

Self-selection processes should not be discounted in the search for sophisticated

“diagnostic” procedures of formal reasoning!

Note that “formal operations” have a content-specific component, and may be

unaccounted in areas outside the subject’s domain of familiarity (Piaget, 1972).

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Therefore, preference for Art may ultimately be related to formal reasoning if tasks were

invented that used the context of art activities!

Follow-up Analysis 3: Tests for Relationships Between Preferences and Gender

Given the findings of significantly better male performance on the Shadows (p =

task, and given the success of the preference measure to predict task performance, I

conducted further analyses to see if the preference measures demonstrated similar gender

differences. Because the data is ordinal and lacks normal distribution, it is not

appropriate to use analysis of variance, a procedure that would allow straightforward

tests for interaction between gender and task performance. Instead, separate tests were

conducted on three main effects using the Mann-Whitney test for two independent

samples. One-tailed tests were used with Science and Math preference scores. Tests

evaluated:

• differences in preference by gender without regard to task,

• differences between males and females within each task (pass subjects examined

in tests separately from fail subjects), and

• differences between pass and fail (females examined in tests separately from

males.

Differences in Preference, by Gender, Without Regard to Task

Table 18 indicates that the male group has significantly greater preference scores

for math (p = .013) than the female group. Near-significant differences (p ≤ .08)

included higher scores for Science and lower scores for Art preference among males.

The greater preference for Science and Math among males parallels their tendency for

better performance on the Shadows task.

Table 17. Results of Tests of Differences in Preference Measures Between Task Pass and Fail Groups

______________________________________________________________________________________

Mean Preference Rating Probability Task Preference Pass Fail U* Two-tailed One-tailed______________________________________________________________________________________Formal Stage Criterion N= 39 15

Art 4.974 5.867 206.0 .087Verbal 4.974 5.071 265.5 .875Science 5.077 4.000 419.0 .006***Math 4.641 3.600 392.5 .025**

Vessels N= 24 33Art 4.875 5.455 467.5 .236Verbal 4.917 5.094 412.2 .782Science 5.375 4.303 218.0 .002***Math 4.667 4.030 299.0 .055

Shadows N= 12 44Art 4.417 5.455 356.0 .059Verbal 4.667 5.139 290.0 .496Science 5.417 4.614 167.5 .024**Math 5.167 4.114 170.0 .028*

Correlations N= 19 38Art 4.737 5.526 457.00 .093Verbal 5.263 4.892 291.0 .275Science 5.421 4.421 207.0 .004***Math 4.895 4.053 252.0 .030**

Combinations N= 27 31Art 4.556 5.839 604.0 .003***Verbal 5.555 5.067 430.5 .846Science 5.074 4.484 319.0 .055Math 4.741 3.935 308.0 .039**

______________________________________________________________________________________*Mann-Whitney test for two independent samples

**Significant at p ≤ .05

***Significant at p ≤ .01

137

Table 18. Results of Tests of Differences in Preference Measures Between Male and Females

________________________________________________________________________Mean Preference Rating Probability

Preference Male Female U* Two-tailed One-tailed______________________________________________________________________________________

N= 39 19**Art 4.949 5.842 476.0 .073Verbal 4.923 5.279 387.0 .776Science 4.9284.368 282.0 .066Math 4.6673.579 237.5 .013***

______________________________________________________________________________________*Mann-Whitney test for two independent samples

**For Verbal, female N=18 due to missing data

***Significant at p ≤ .05

It is interesting that Art, a presumed “ spatial” mode of expression, appears to be

a female predilection (p = .073), considering that Shadows and the Vessels tasks are

spatially oriented tasks on which females tend to perform poorly. Apparently, the INRC

group schema for “balance” that both tasks require is not an element exercised in artistic

endeavor, even though visual “balance” can be a significant component in a work of art.

This suggests that the results reflect the separate natures of operational spatial thinking

versus figurative spatial thinking.

Differences Between Males and Females Within Each Task (Pass Groups Tested Separately From Fail Groups)

The next main effect tested was preference differences between males and

females for each task separately looking at pass subjects separately from fail subjects.

See Tables 19 and 20 for the results. Among the 40 tests, only five statistically

significant (p ≤ .05) differences discriminated males and females. Among subjects who

passed a task, preference for Science was greater for males than females in the Shadows

Table 19. Results of Tests of Gender Differences in Preference Measures Taken Separately for Each Task Pass Group

______________________________________________________________________________________

Mean Preference Rating ProbabilityTask Preference Male Female U* Two-tailed One-tailed______________________________________________________________________________________Formal Stage Criterion (Pass) N= 28 11

Art 4.679 5.727 206.5 .094Verbal 4.929 5.091 157.0 .923Science 5.250 4.636 116.5 .115Math 4.964 3.818 96.0 .032**

Vessels (Pass) N= 19 5Art 4.7475.400 56.0 .536Verbal 4.7895.400 57.5 .467Science 5.2635.800 58.5 .208Math 4.9473.600 31.0 .113

Shadows (Pass) N= 11 1Art 4.1807.000 .5 .138Verbal 4.9112.000 10.5 .136Science 5.7312.000 11.0 .050**Math 5.3643.000 9.5 .118

Correlations (Pass) N= 14 5Art 4.5005.400 24.00 .300Verbal 5.4294.800 43.5 .392Science 5.8574.200 54.00 .035**Math 5.5003.200 61.0 .007***

Combinations (Pass) N= 19 8Art 4.2635.250 103.0 .145Verbal 4.8425.375 85. .607Science 5.2114.750 60.0 .192Math 5.0004.125 53.0 .107

______________________________________________________________________________________*Mann-Whitney test for two independent samples

**Significant at p ≤ . 05

***Significant at p ≤ . 01

139

Table 20. Results of Tests of Gender Differences in Preference Measures Taken Separately for Each Task Fail Group

______________________________________________________________________________________

Mean Preference Rating ProbabilityTask Preference Male Female U* Two-tailed One-tailed______________________________________________________________________________________Formal Stage Criterion (Fail) N= 8 7

Art 5.875 5.857 30.5 .76Verbal 4.750 5.500 18.0 .4173Science 4.125 3.857 29.0 .452Math 4.125 3.000 38.0 .121

Shadows (Fail) N= 26 18Art 5.231 5.778 200.0 .402Verbal 4.923 5.471 184.0 .335Science 4.692 4.500 256.0 .294Math 4.462 3.611 296.5 .064

Vessels (Fail) N= 20 13Art 5.150 5.923 99.5 .247Verbal 5.050 5.167 120.5 .983Science 4.650 3.769 171.5 .058Math 4.400 3.462 167.5 .080

Correlations (Fail) N= 24 14Art 5.250 6.000 131.0 .241Verbal 4.583 5.462 106.0 .102Science 4.417 4.429 166.5 .486Math 4.250 3.714 197.0 .184

Combinations (Fail) N= 20 11Art 5.600 6.273 134.5 .280Verbal 5.000 5.200 108.5 .700Science 4.700 4.091 81.5 .111Math 4.350 3.182 65.5 .029**

______________________________________________________________________________________*Mann-Whitney test for two independent samples

**Significant at p ≤ .05

***Significant at p ≤ .01

(p = .05) and Correlations (p = .035) tasks. Preference for Math was greater for males

in the Formal Stage Criterion (p = .032) and the Correlations task (p = .007).

Among subjects who failed a task, males demonstrated a significant preference

only in the case of Math in the Combinations task (p = .029) compared with females.

Note that only one of the five significant tests occurred among the fail group.

Interestingly, Art does not discriminate males and females on any task, implying that its

predictive power was related less to gender and more to pass/fail intermediating variables

on the tasks.

Overall, the evidence suggests that males demonstrate greater preferences for

Math and Science activities than females especially among subjects that pass one or more

tasks.

Differences Between Pass and Fail Groups (Female Groups Tested Separately From Male Groups)

The question now reduces to whether the pass subjects have greater or lesser

preference strength within a single gender group. Among females, Mann-Whitney

tests indicate no significant differences (p ≤ .05) that discriminate pass from fail

groups. (The Shadows task was not examined because only one female passed the task,

obviating any statistical variance.) However, non-significant trend differences were

demonstrated in Art (p = .055) and Math (p = .086) preferences when comparing pass

and fail females on the Combinations task. The pass group measured lower in Art

preference and higher in Math preference than the fail group. Pass means are presented

in Table 19 and fail group means are in Table 20. No table is given for the U statistic

or the p values. In summary, discriminations between pass and fail females only

occurred in the Correlations task, albeit non-significantly, by preference for Math (in

the pass group) and Art (in the fail group).

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Preferences appear a weak indicator among females, perhaps due to an overall

weak preference for Math and Science. However, in tests comparing pass and fail males,

Science was significantly preferred by the pass group in the Correlations task (p = .001),

and the Shadows task (p = .013). Confirming trends occurred in the Vessels task (p

= .061) and weakly so in the Combinations (p = .094) task. Likewise, Math preference

was significantly greater in the Shadows task (p = .013) and confirmed with a weak trend

in the Vessels task (p = .064). Last, pass males exhibited a significantly weaker preference

for Art (p = .020) than fail males in the Combinations task, with a similar trend

demonstrated in the Shadows task (p = .096). In summary, among males, Science

preference was stronger (p ≤ . 1) in the pass group in all four tasks, with Shadows and

Correlations exhibiting statistically significant differences (p ≤ .01). The Shadows task

demonstrated three discriminating preferences (p ≤ .1) of which Science and Math were

significant at p ≤ .02. The third discriminating preference was Art.

Although the evidence does not support a causal relationship, it appears that males

who pass one or more tasks are more apt than females to express a stronger preference for

science or math than their female counterparts. It appears that among females, preferences

may be more homogeneous.

Conclusions Regarding Gender, Task Performance, and Preference Measures

We must remember that the statistical power is much less for these preceding

tests than for the tests including both genders together. (For example, passing females

numbered 1, 5, 5, and 8 across the four tasks). Yet, Science and Math preference still

discriminated males from females, and pass from fail within each gender in several

tasks. Therefore, given the nature of the findings, I suggest that they agree with the

generally acknowledged greater aptitude (and subjective satisfaction) for math among

males (Benbow, 1988). The findings also concur with findings that greater science

achievement is associated with higher performance on tests of formal reasoning (Modgil

and Modgil, 1976).

Follow-up Analysis 4 - Tests for Relationships Between Preferences and Other Variables

Given the tendency of several preference measures to discriminate pass subjects

from fail subjects on the various tasks, and given the association of some of the EEG

coherence measures to the tasks as well, it is reasonable to ask if a direct relationship

holds between any of the coherence measures and the task scores. Table 21 presents the

results of Spearman rank correlations between these variables.

As expected, the tests indicate a moderate and significant positive monotonic

relationship between Science and Math preference (p ≤ .002). Science and Art

preferences are inversely related, as expected, but not quite within statistical significance.

Unexpectedly, rank correlations indicate a complete lack of monotonic or linear

relationship between the physiological variables and the preference variables. Given the

reasonable degree of the previously established relationships between the physiological

measures and the measures of preferences and task performance, the lack of rank

correlations lacks ready explanation. Although speculative, it is suggested that the

attenuation of the rank correlations may be a function of the relatively short range of the

preference measures (1-7), their bunched distribution, and their interaction with the much

wider ranged and more normally distributed EEG coherence measures. In other words,

compared to the coherence measures, the preference measures had too many ties and thus

lacked rank differences needed by the statistic.

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Table 21. Results of Tests for Relationships between Preference Measures and Non-task Variables: EEG Coherence Derivations and Ratios

______________________________________________________________________________________

Preference MeasuresCovariate Art Verbal Science Math

______________________________________________________________________________________

Art 1.0000*Verbal .0945 1.0000Science -.2239** .1902 1.0000Math .0161 -.0357 .4450*** 1.0000

Coherence Index .0379 -.0209 .0252 .1243F = F3F4 .1413 -.0129 .1366 .1342L = F3C3 .0338 -.0210 .0561 .1817R = F4C4 -.0872 .0517 .0040 -.0351O = O1O2 -.0490 .1161 .1059 .0256

F-L ratio = (F3F4-F3C3)/(F3F4+F3C3).0478 .0247 .0084 -.0607

L-R ratio = (F3C3-F4C4)/(F3C3+F4C4).1265 -.0870 .0448 .1211

R-O ratio = (F4C4-O1O2)/(F4C4+O1O2)-.0156 -.0721 -.0545 .0031

F-0 ratio = (F3F4-O1O2)/(F3F4+O1O2).0888 -.0858 -.0163 .0927

______________________________________________________________________________________*Spearman rank correlation coefficient. Critical value for alpha p ≤ .05 is rS = .2582 or more.

**Non-significant but of interest, p >.05 and ≤ .1.

***Significant, p = .002

CHAPTER V

DISCUSSION AND CONCLUSION

Review of Purpose and Procedures

Although much has been said by educators regarding left-right brain approaches

to education in general, relatively little effort has been directed toward integrating

neurological research with the body of Piagetian theory and research. The lack of

research has led to speculations by a popular writer that Piagetian reasoning skills are

“left brain” and ignore student aptitudes for “metaphorical” or “right brain” thought

(Samples, 1975).

The current research attempts to examine the role of left-right hemisphere

involvement in formal operational reasoning. Early attempts to relate these two fields

using direct EEG measures of brain functioning have been illuminating, although

inconclusive. EEG power measures indicated increased left hemisphere activity among

university students during tests of concrete and formal reasoning (Dilling, Wheatley, &

Mitchell, 1976). However, no controls were made to discriminate the presumed right-

hemisphere visual-spatial “thinking” portion of the reasoning task from the left-

hemisphere, speaking portion. A subsequent study from the same laboratory instituted

such controls and found that high performers differed less between the two conditions

than the low performers (Kraft, 1976). Subjects in the second experiment ranged

between six and eight years old and were tested on concrete operational reasoning.

Kraft suggests this implies that the left hemisphere verbal activity may have

simultaneously drawn upon right hemisphere thinking activity which reduced the EEG

hemispheric differences. She posits that this indicates greater left-right hemispheric

information transfer during the task. This indicates “whole brain” function is associated

with higher levels of reasoning.

The findings have limited scope, however. The limitation lies with an intrinsic

problem of using EEG power ratios. The experimenter cannot determine if the

experimental results indicate an increase in the power of one hemisphere, a decrease of

power in the other hemisphere, or a mixture of both. A ratio confounds the two.

Therefore, EEG power ratio measures cannot conclusively fix the locus of hemispheric

change.

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A measure of EEG coherence, however, is free of the variables that confound

power measures, such as variation in skull and scalp thickness among subjects. EEG

coherence measures the degree to which two points on the scalp exhibit the same

frequency within a given short period of time. Coherence is analogous to the square of

Pearson’s correlation coefficient, which represents the percentage of variance in

frequency at one point accounted for by variance in frequency at another point of the

scalp. For example, a coherence measure of .95 indicates that the two EEG signals have

a difference of less than .05 Hz (Levine, 1976).

An additional obstacle in much EEG research has been the lack of a standard

cognitive state against which to evaluate the significance of the EEG measures

(Giannitrapani, 1985; and Webster and Thurber, 1978). Where tasks have been

administered during the EEG, experimenters usually lack knowledge of the subject’s

precise strategy in accomplishing a given task. This makes it difficult to evaluate the

significance of the EEG measures. For this reason, subjects were chosen who were

experienced in a commonly-available mental technique, Transcendental Meditation (TM)

which is claimed to result in restful alertness of the mind. The subjects were students

and staff at a small private university where all the students, faculty, and staff engaged in

the practice of TM as a regular routine. Students were accustomed to yearly EEG

coherence measures taken as part of their annual “EEG report card,” from which data for

this research was taken.

The common notion of right brain thought being “wholistic” supports Piaget’s

claim that formal reasoning consists, in part, of the “structured whole,” a key element of

formal operational reasoning. Piaget says the structured whole is non-verbal and requires

consideration of all the relevant variables simultaneously. Both of these qualities have

been applied to right-hemisphere functions. Piaget suggests that cognitive growth moves

in the direction of greater stability or equilibrium. The structured whole acts like a “field

of force governed by the laws of equilibrium” (Piaget, 1957). In fact, he suggests that

this tendency to master the structured whole must have its reflection in neurology as well

as behavior. I suggest that right-hemisphere functions must be represented as well as

left-hemisphere functions in formal reasoning. The FLR-O index captures data that

reflect L and R hemisphere operation during a standard cognitive state. This

combination of L and R measures reflects a “whole brain” approach to the study of

reasoning skills.

This study seeks to extend the previously mentioned studies of the development

of logical thought by using the Orme-Johnson et al. (1982) FLR-O index of EEG

coherence as a continuous measure and pass-fail performance on clinical versions of four

Piagetian tasks as the classification variables. Fifty-eight university-level subjects (19 F

and 39 M) were studied. The cognitive state is controlled during the measurement period

by the experienced practice of a stress-reduction technique, Transcendental Meditation

(Wallace, 1972). Immediately before or after the EEG session, subjects were tested for

formal operational schemata using clinical versions of tasks patterned after Inhelder and

Piaget (1958): combinatorial reasoning (Chemicals task); INRC group (Communicating

Vessels task); proportionality schema (Projection of Shadows task); and the correlation

schema (Correlations task). A composite measure was constructed in which subjects who

fail at all four tasks were considered to have failed attainment of the Formal Stage

Criterion. These subjects gave no evidence of the cognitive reorganization characteristic

of formal reasoning. Subjects who passed at least one task, however, were considered to

have “passed” the Formal Stage Criterion.

147

Discussion of the Data

Proportion Passing the Tasks

Formal Stage Criterion

In this study, 72.2 percent of the subjects passed one or more of four tasks

purported to evaluate the presence of logical structures associated with formal

operational reasoning. This contrasts with other published reports that only 50 percent or

less of college students exhibit formal operations (Haley and Good, 1975). The

difference arises out of a possible misunderstanding on the part of many researchers who

feel that failure on any one task indicates lack of development of the stage of formal

operations. Piaget, however, has made it clear that although a subject may indeed fail in

exhibiting any particular formal logical structure, the subject may still have undergone

the cognitive reorganization that gives rise to “characteristic structures in actions at the

formal stage (Piaget and Garcia, 1991, p. 130). In my study, I assume that each of such

reorganizations is implied by failure to pass any of the four tasks that test for their

corresponding logical structures. This assumption could be shown wrong if subjects, for

example, were to pass a task associated with any of the six remaining structures not

tested here.

Shadows Task

In the current research, 21.4% of the subjects passed the test of proportional

reasoning (Shadows task). With only 5.3% of females passing versus 29.7% of males

passing, the gender difference was statistically significant. The ratio of 37 male to 19

female subjects make it difficult to directly compare the overall pass rate with other

research. However, similar research at the University of Iowa (UI) suggests the pass rate

is within expectation for the subject age and education.

At the UI, Poduska (1983) and Poduska and Phillips (1986) found 12% of 67

university males passed and none of 33 females passed, also a significant gender

difference. Other UI studies used high school seniors. Wavering, Perry, Kelsey, and

Birdd (1986) found only 6% of their subjects (50% female) passed the Shadows task,

although they acknowledge their passing rate are much lower than reported elsewhere,

probably due to the interview format, they say. Wavering (1979, 1984) reports 15% of

seniors (about 50% females) passed the Shadows task. Hensley reports 37% of seniors

(about 50% female) passed. Neither of the last two studies demonstrated any gender

differences in the rate of pass. Ibe (1985) studied seniors also, among whom only one

(male) of 31 subjects (13 males) passed.

Other research, outside of the UI program, found different passing rates, probably

owing to different test protocols, gender ratios, and scoring criteria. Dulit found 33% of

adults passed, 57% of gifted 16-17 year-olds, 35% of regular 16-17 year-old students,

and no regular 14 year-old students passed. Across the groups, males scored better than

females by a factor of three or four. Martorano (1977) found 55% of her 12th grade girls

passed, a very good percentage considering she explicitly required use of a metric system

of calculating proportions. Piburn (1980) found that 11th grade males scored

significantly better on the Shadows task than females, no pass rates were given. Bady

(1978) found 81% of early college students passed the Shadows task. Farrell and Farmer

(1985) found 12.4% of 10-12th grade males and 5.4% of females passed the Shadows

tasks. These last researchers go on to cite their own work and other’s to suggest that

better male performance may not be accounted for by spatial ability, but rather some

other source, even though the Shadows task has definite spatial components.

Thus, in general, the current study appears within the range of results of other

studies. The significant difference in passing rates between the genders is upheld in

149

several other studies. This suggests that the gender difference should show up in the

alpha coherence measure, perhaps as a right-hemisphere “deficit” for the female group

compared to males. This would appear as a genderXtask statistical interaction.

However, as we shall see, this was not the case.

Correlations Task

The current study found 33.3% of subjects passed (36.8% of males and 26.3% of

females passed). Among University of Iowa studies, Rubley (1972) found 57% of 11-

12th grade chemistry students passing (50% of the subject group were females).

Wavering (1979) found that 10% of 12th grade students (50% females) passed. Neither

researcher found any gender differences. Wavering notes that Rubley’s subjects were a

selected sample, from a chemistry class thus accounting for their rather high pass rate.

Also, Wavering elected to classify III-A subjects as non-pass because IIIA only indicates

direct proportional reasoning, not correlational reasoning. The current research takes the

same position.

Other research elsewhere indicates a range of task and scoring protocols that

make comparisons difficult. Lovell (1961) found 77% of ablest 15-18 year-old students

passed and only 25% of the least-able students passed. Ross (1973) found 9.2% of

university undergraduates passed, not counting level IIIA. With level IIIA included,

98.4% passed. Martorano (1977) found 55% of 12th grade girls passed. Dulit (1972)

found 25% of adults passed, 62% of gifted 16-17 year-olds, 17% of regular 16-17 year-

old students, and 10% of average 14 year-old students passed.

In general, the current study appears to have obtained reasonable results. The

lack of gender differences appears to be the norm.

Combinations of Colored and Colorless Chemical Bodies Task

46.6 percent of subjects passed the task in the current study (48.7 percent males

passed and 42.1 percent of females passed). No University of Iowa research is reported

for this task. Elsewhere, Ross (1973) reports 75 percent of his undergraduate subjects

passed. Martorano (1977) found 85 percent of the 12th grade females passed. Joyce

(1977) found 95.5 percent of the subjects passing, although questionably, since subjects

may have been allowed to use “trial and error.” Bady (1978) found 76 percent of college

students passed. De Hernandez, Marek, and Renner (1984) found 34 percent females and

36 percent males passing (mean age 17 years) with no difference between genders.

When compared with studies done at other institutions, the current study appears to

follow in the conservative trend established by the UI clinical interview method.

Therefore, although the pass rates in my study appear less than reported in other studies,

they are probably acceptable. No published gender differences appear for this task.

Communicating Vessels Task

42.1 percent of subjects in the current study passed (48.7% males and 27.8%

females passed). Martorano (1977) found 45 percent of 12th grade females passed. No

other results could be found. The current results must stand on their own as there’s no

ready explanation for the lower percent age of females passing in my study compared to

Martorano’s study. Both studies used the clinical interview method. Although males

scored better, as a group, the advantage was non-significant (p = .161). Both the Vessels

task and the Shadows task appear to be visuo-spatially oriented, with each drawing upon

the INRC group, albeit to different degrees (see discussion below). The apparent spatial

orientation of the Vessels and Shadows task may contribute to the male advantage in pass

rate. And although the advantage is non-significant for Vessels, it may tap right-

hemisphere skills in the same manner as hypothesized for the Shadows task. Again,

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however, as we shall see, the expected genderXtask interaction, with a right hemisphere

“deficit” for alpha coherence among the females group, did not manifest.

Hierarchical Ordering of Task Difficulty

The current study found statistical significance (p < .05) on three tests when

testing pairs of tasks for differences in passing rates within subjects. Subjects passed

both Combinations and Vessels tasks more frequently than the Shadows task. The

Combinations task was passed more frequently than the Correlations task. Nearly

significant at p = .07, a fourth comparison, Correlations, was passed more frequently

than the Shadows task. These results were based on a sample that had roughly 33%

female subjects. To examine these findings in a more standard fashion, the same tests

were conducted for males only. Only one of the significantly related pairs changed

status, with the males-only group passing the Combinations task only slightly more

frequently (p = .095) than the Correlations task. Also, males passed the Correlations

task about the same frequency as they passed the Shadows task. Based on the reasonable

similarity of the “standard” all-male profile with the mixed gender profile, the following

discussion will use the mixed gender result, thereby reflecting trends evidenced by

gender differences.

In summary, the Shadows task was more difficult than any of the other three

tasks. The Correlations task ranked more difficult than the Combinations task. This

pattern is borne out in the literature with some qualifications as follows.

Poduska (1983) and Poduska and Phillips (1986) studied university students and

concluded that the proportions schema used in the Shadows task is passed late compared

with other schema used in the concept of “speed.” Wavering (1979, 1984) found his

research with the Correlations and Shadows tasks contradicted what he feels to be

Piaget’s claim that the proportion structure precedes correlation. (Wavering found no

significant difference in pass rates between the two tasks among 8th, 10th, and 12th

grade students.) However, Wavering failed to notice that Inhelder and Piaget (1958)

define the proportions schema with an early qualitative form as well as a later,

quantitative form. Therefore, correlations may be attained, in Piaget’s theory, after the

qualitative sense of proportions, but prior to the quantitative notion of proportions. The

quantitative form is tested in the current research. This latter sequence, correlations

preceding the later form of quantitative proportional reasoning, was found in the current

research.

Bart and Mertens (1979) performed an order theoretic analysis of Martorano’s

(1977) data and found that passing the Combinations task was not contingent upon any

other schema. The current study reflects this finding.

Bart and Mertens also found that pass scores on the Vessels task depended upon

pass performance of both the Correlations and Combinations tasks. Furthermore,

Martorano’s original findings included these results with the addition that passing the

Vessels task also depended on passing the Shadows task. None of these findings are

supported in the current study. The difference in results may exist because Martorano

studied only female students. For example, the current study found that females passed

significantly less than males on the Shadows task and marginally less on the Vessels task.

Therefore, a sample of 100% females could possibly reverse Martorano’s ordering within

the confidence interval of the current study.

Inhelder and Piaget

Inhelder and Piaget (1958) suggest the following regarding the ordering of the

four tasks:

The Combinatorial schema is a prerequisite to other elements of formal

reasoning: “The most general property in terms of which we can characterize formal

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thought is that it constitutes a combinatorial system, in the strict sense of the term...this

property implies all the others and thus is more general than they are” (p. 254). The

theorists affirm that even at this initial level, “the main feature of propositional logic is

not that it is verbal logic but that it requires a combinatorial system” (p. 254). This

statement implies, in our current neurophysiological context, that formal reasoning is not

solely a left-brain, verbal enterprise, but rather more. The authors imply they have been

misunderstood on similar points, and reiterate: “...in spite of appearances and current

opinion, the essential characteristic of propositional logic is not that it is verbal logic.

First and foremost, it is a logic of all possible combinations, whether these combinations

arise in relation to experimental problems or purely verbal questions” (p. 253). Given a

characterization of right brain processing as “simultaneous,” Piaget and Inhelder’s

comment can be interpreted to suggest that “all possible combinations” is a right brain

function. The current study found no prerequisite structures to the combinatorial

schema, which is consistent with Piaget’s theory. The current study also found that right

brain coherence contributed to the coherence index which was greater for the pass groups

in all four tasks, significantly so for the Vessels task.

The INRC group structure, as in the Communicating Vessels task, also is a

prerequisite to formal operational reasoning. The INRC group structure is used both as

an internalized formal structure that integrates the transformations of inversions and

reciprocities and also as a means to understanding the transformations that underlie

equilibrium in a mechanical system. In the sense of the “structured whole,” the INRC

group structure complements the combinatorial system. The INRC group structure

provides the set of transformations that permit inferences and implications to be drawn

from propositions that arise from the combinatorial system (Inhelder and Piaget, p. 307).

The current study found no prerequisite schema to the INRC group structure, which is

consistent with Piaget’s theory. The INRC transformations in many ways suggest the

processes of “mental rotation,” which has been shown to utilize right brain functions (see

De Lisi, Locker & Youniss, 1976; Dean, 1978; Kerr, Corbitt, & Jurkovic, 1980; and

Shepard, 1984).

The correlations schema, according to Inhelder and Piaget (1958), appears to

require the combinatory schema. “The search for correlations does in fact require a

combinatorial system, since the subject’s problem is not simply to classify the four

possible cases, but to distinguish the various realized and realizable combinations among

them” (p. 325). The current study found that passing the Correlations task required prior

passage of the Combinations task, which is consistent with Piaget’s theory.

The proportions schema, as found in the Projection of Shadows task, has been

discussed in the context of Wavering’s (1979, 1984) interpretation that the proportions

schema should come before the correlation schema, contrary to Inhelder and Piaget’s

suggestion of a qualitative notion and a quantitative notion of proportional reasoning. I

suggest that several points indicate that the Shadows task has several prerequisites

including not only the quantitative version of proportional reasoning but also a version of

the INRC group that goes beyond mechanical equilibrium. Regarding the first point,

Inhelder and Piaget actually state that the discovery of proportionality in the Projection

of Shadows task “results from an understanding of multiplicative compensations” (p.

207). In explaining multiplicative compensations, Inhelder and Piaget make clear that

the calculations that constitute the schema (e.g., x y = x’ y’) follow the qualitative notion

of proportions in which “the subject has the feeling that a proportionality exists before

calculating it” (p. 328). Regarding the second point, Piaget suggests that solutions to the

Shadows task requires two other operational schemata, in addition to the schema of

Proportions, that involve the INRC group: the already-mentioned Multiplicative

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Compensations, as well as the Coordination of Two Systems of Reference. Therefore,

this broader range of schematic dependencies would certainly imply that the Shadows

task would follow attainment of other single schema tasks, such as Vessels, which use a

simpler manifestation of the INRC group. Likewise, it would follow attainment on

Combinations, which is prerequisite to any manifestation of formal reasoning schema.

The current study found that subjects passing the Shadows task generally had also passed

the Combinations and Vessels tasks. A non-significant trend indicated that the subjects

also had passed the Correlations task.

In summary, the current study demonstrated an ordered hierarchy of task

difficulty that was very similar to the hierarchy implied by Inhelder and Piaget.

EEG Coherence Measures

Several sources allow comparison of the EEG coherence means on other groups

of students as they were practicing the Transcendental Meditation program in the same

university setting. The equipment set-up was the same as the current study. Orme-

Johnson, Wallace, and Dillbeck (1981) published means and standard deviations of F, L,

R, and O alpha coherence measures for two groups of subjects with the following results

(see Table 22).

Nidich, Ryncarz, Abrams, Orme-Johnson, and Wallace (1983) also published

measures of coherence in two groups of subjects practicing TM in a separate study at the

same university using the same EEG setup. They used ten .53 minute periods as in the

current study (see Table 23).

Table 22. Coherence Results for Orme-Johnson, Wallace, and Dillbeck (1982)

_________________________________________________________________________Group A: N = 26, 15 males, 11 females, sophomores, mean age = 20.8

Derivation Alpha Coherence SD

F3F4 Frontal .7087 .1596

F3C3 Left .6497 .1514

F4C4 Right .6671 .1549

O1O2 Occipital .6885 .1533

Group B: N = 21, 11 males, 10 females, sophomores, mean age = 22.1

Derivation Alpha Coherence SD

F3F4 Frontal .7714 .0742

F3C3 Left .7114 .0785

F4C4 Right .6975 .0694

O1O2 Occipital .6782 .0764_________________________________________________________________________

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Table 23. Coherence Results for Nidich, Ryncarz, Abrams, Orme-Johnson, and Wallace (1983)

_________________________________________________________________________

Group C: N = 13, 6 males, 7 females, mean age = 28.7

Derivation Alpha Coherence SD

F3F4 Frontal .8220 .046

F3C3 Left .7343 .093

F4C4 Right .7127 .084

Group D: N = 13, 8 males, 5 females, mean age = 28.5

Derivation Alpha Coherence SD

F3F4 Frontal .7670 .051

F3C3 Left .7198 .065

F4C4 Right .7135 .071_________________________________________________________________________

Of these four groups, group B is most similar to the profile obtained in the current

study (Frontal = .78, Left = .71, Right = .69, Occipital = .67). The variability across

the groups encompasses the range of findings and subject ages in the current study

indicating the reliability of the coherence findings of this study relative to other studies

involving similar subjects and the practice of TM.

Task and EEG Alpha Coherence Index Relationships

The current study sought evidence of a relationship between a whole-brain index

of EEG alpha coherence measures and task performance. Prior research (Beaumont,

Mayes, and Rugg, 1979) suggests that gender and age contribute to differences in the

proportion of subjects performing well on spatially oriented tasks as well as contribute to

differences in their EEG coherence measures when taken under task conditions.

Therefore my initial analysis did not control for gender or age because gender and age

are reasonable causal influences on both task performance and coherence measures.

Student’s t-tests indicate that an index of four EEG alpha coherence measures (Frontal +

Left + Right- Occipital: FLR-O) was significantly greater for the group of pass subjects

than the group of fail subjects in the Communicating Vessels task (p = .0495, one-

tailed). The other three tasks demonstrated non-significant differences in the same

direction. The Formal Stage Criterion test indicated near-significant differences between

pass and fail groups (p = .0558), in the expected direction. To validate these results in a

way that could be compared with future research with different ratios of gender and ages,

subsequent ANCOVA’s were performed that controlled for gender and age. Essentially

the same results appeared, with the Vessels task reflecting slightly stronger differences

between pass and fail subjects (p = .040) in the FLR-O index. The Formal Stage

Criterion also reflected stronger differences in the expected direction (p = .050).

Two of the tests, then, appear to reflect differences between pass and fail

subjects, based on a “whole-brain” measure, FLR-O alpha coherence. How do these two

tests relate to the other three tests? The Vessels task uses the schema of proportionality

and the INRC group structure. The INRC group structure, at face value, appears to tap

visuo-spatial cognitive skills. Apparently the metric requirements for passing the

Shadows task pose an extra cognitive burden in addition to the visuo-spatial skills and

therefore the Shadows task is more weakly related to the FLR-O index than the Vessels

task. The Combinations task draws on the combinations schema, which is fundamental

to formal reasoning, and therefore, it is theoretically required for the Vessels task.

However, failure of the FLR-O index to significantly discriminate pass and fail groups in

the Combinations task suggests that the INRC group visuo-spatial skills used for the

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Vessels task remain the “unique” element that is detected by the FLR-O index. In

summary, while these three tasks Vessels, Shadows and Combinations, have some

theoretical relationship with each other, only the Vessels task clearly demonstrates the

INRC group schema. Therefore, the significant difference between pass and fail groups

with respect to the dependent measure, the FLR-O index, may reflect possession or

absence of that schema. The FLR-O index failed to detect even marginal differences

between pass and fail groups in the Correlations task. This may result from the relative

absence of the INRC group structure in the Correlations schema.

The Formal Stage Criterion is met when at least one of the tasks is passed.

Therefore, subjects who pass the Vessels task will necessarily pass the Formal Stage

Criterion. It is speculated that the Formal Stage Criterion reflects possession of the

INRC group as a “minimum ” logical structure exhibited upon reorganizing the cognitive

assimilative structures. This suggests that EEG alpha coherence in the FLR-O index may

reflect the emergent properties required to generate the discontinuity associated with a

“new” stage of reasoning.

These overall findings are quite dissimilar to those of Dennen (1985) who studied

subjects from the same university setting using the same EEG coherence measures

obtained while subjects practiced Transcendental Meditation. Dennen found no

correlation between the FLR-O index and test scores of formal and concrete reasoning.

In fact, the correlation was negative at -.06, with p = .19. Of the 349 subjects,

33% were female, the same ratio as the current study. The EEG data was provided from

the school year 1979-1980 with up to four months elapsing before subjects took a pen

and paper test (CAP) designed to measure concrete and formal reasoning. The current

study used EEG data from the spring of 1981, with clinical interview tasks administered

immediately after the EEG session. Given the superficial similarities of the two studies,

the difference in lapse of time between EEG measure and cognitive testing between the

two studies could be a significant mitigating factor. Another factor could be the nature

of the Piagetian scores. In fact, Dennen questions the pen and paper test as a source for

the lack of relationship between the two variables, but cites a reported correlation of .7

with interview investigations of Piagetian stages in defense. Removal of the influence of

age, sex, and length of time practicing TM did not substantially change his findings.

Dennen concludes that his research fails to support a relation between the FLR-O index

and cognitive ability and leaves open the practical meaning of EEG coherence.

The current study, on the other hand, marginally supports previously reported

findings of FLR-O as an index of CNS maturation—statistically significant with regard

to the Vessels task (p = .048) and a strong trend for the Formal Stage Criterion (p

= .0558), and at least in the predicted direction for the Shadows, Combinations, and

Correlations task. The failure of Dennen’s CAP test to detect differences among his

subjects make the “biological” validity of pen-and-paper tests suspect. For example,

Stefanich, Unruh, Perry, and Phillips, (1983) administered three well-known written

group tests of concrete and formal reasoning to university students and failed to find

strong agreement with individual clinical Piagetian task interviews. The CAP test was

not among the written tests. However, generalization to the CAP appears appropriate as

the authors cite findings from other comparisons of about 50% agreement and

correlations of about .5 between written and clinical assessments. Additionally, Pratt and

Hacker (1984) found failure of a written test, Lawson’s classroom Test of Formal

Reasoning, to demonstrate a unitary dimension (formal reasoning) among the test items.

They hypothesize that the written test format fails to account for the element of

experimentation and subsequent feedback allowed by the clinical task setting. Without

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such feedback, they suggest, the written test merely examines the student’s current

knowledge.

In Dennen’s study, a lack of confirmation of the theory could arise because

qualified “pass” subjects do poorly on the paper test, or the otherwise “fail” subjects do

better on the paper test. In any event, interaction with task materials in an interview

setting seems, at face value, to demand different cognitive skills than interaction with a

pen-and-paper test. For example, the subject must select a strategy based on interaction

with physical objects rather than interaction with the printed word. Also, arousal levels

may be generated differentially between the two test settings, influencing the strategies

applied to the problem and the subsequent level of success. Frontal brain structures are

particularly affected by demands to organize and plan strategies of problem solving

(Stuss, 1992). It is these skills tapped in the interview setting that may be evidenced with

the FLR-O index in the current study. Further evidence of the possible inappropriateness

of the CAP test lies in the fact that Dennen found that physics and math majors,

presumably using more formal reasoning skills than students in other majors, measured

statistically significantly higher in alpha coherence than other majors together in F (p =

.006), L (p = .001), and R >.95 threshold (p = .046), all one-tailed tests. The other

majors included art, biology, business administration, education, interdisciplinary studies,

literature, philosophy, and psychology.

The current research indicates that the FLR-O appears to serve as an index of

central nervous system maturation in the context of formal operational reasoning for at

least one of the four studied tasks as well as marginally for the Formal Stage Criterion.

While only a modest confirmation, these results conform to the suggestion of Orme-

Johnson et al. (1982) who found that their version of the index was significantly related

to first-year university GPA and emotional health. Note that the methodology used by

Orme-Johnson et al. may be more sensitive than the methodology used in the current

research. Their index represented the percentage of coherence over .95 that occurred in

the 5 minutes of greatest coherence out of 30 minutes recorded. The choice of the “best

5 minutes” sought to capture the period of greatest wakefulness (drowsiness or sleep

reduces alpha coherence). In the current research, however, the dependent measure

consisted of average coherence for the total measurement period (which happens to be

5.3 minutes). Therefore the current research did not compensate for possible drowsiness

during the TM session, and low coherence levels could result as a confound. (Note that

one subject who passed on all four tasks had among the lowest FLR-O scores! Perhaps

he or she slept during the measurement period.) The above limitations may have reduced

the ability of the FLR-O measure in the current research to discriminate pass and fail

subjects in more tasks than the Vessels task.

Follow-up Analysis of Relationships Between Tasks and Other EEG Measures

An investigation was made to determine the underlying relationships between

task performance and each of the four derivations from which the FLR-O index is

composed. T-tests of the individual derivations F, L, R. and O were accomplished along

with tests of four associated ratios (F-L)/(F+L), (L-R)/(L+R), (R-O)/(R+O), and

(F-O)/(F+O).

Previous tests of differences in rates of passing tasks between male and female

groups suggested that females may suffer a “visuo-spatial” deficit. My results indicate

that significantly fewer females passed the Shadows task than males. Tests for

genderXtask interaction with each derivation and the four ratios as the dependent

variables indicated no significant interactions except for the Shadows task and the ratio

(F-L)/(F+L), p = .035. However, this result is suspect, with only one female in the pass

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group. Sheffé post hoc tests of all possible pairs indicated that the one pass female

measured less on the (F-L)/(F+L) ratio than the failing male group, p = .0665.

Pooling males and females, only one test among the tasks demonstrated a

statistically significant difference between pass and fail subjects—the (F-O)/(F+O) ratio,

p = .052—for the Shadows task. However, beyond this, all tests upheld any predicted

direction of pass-fail differences, with 13 tests demonstrating p < .1 and 7 additional tests

demonstrating p < .15 (See Table 24). Since this was exploratory, and some degree of

multicollinearity among task performance is expected, no Bonferroni correction was

made in the alpha levels for Type I error. Tests using the Formal Stage Criterion

revealed three instances of significant differences between pass and fail groups, each in

the expected direction, all involving the bilateral occipital deviation.

The patterns that emerge from Table 24 provide an insight into contributions

made by various brain regions to the differences between pass and fail subjects in the

FLR-O index. Foremost is the finding that the individual anterior derivations, F, L, and

R, are positively related to successful task performance and that the posterior, O, region

is negatively related. These findings reinforce the notion of “whole-brain” relationship

that I suggested may exist between the FLR-O index and performance on Piagetian tasks.

However, the lack of significance at the p< .05 level for four out of five tests suggest that

any claims be duly qualified.

In the current study, the absolute values of R discriminates pass from fail in three

tasks at p < .085, compared to discriminating pass from fail subjects with measure of

FLR-O coherence in only one task with value p < .085. Therefore anterior R appears to

play some role, in addition to the traditionally accepted role of the left hemisphere, in

logical reasoning. This refutes Samples’ (1975) claim that formal reasoning is solely a

left hemisphere function. Although the p values are not significant at less than .05, they

Table 24. Results Summary: EEG Component Measures By Task for p Values Less than .18 for All Subjects Together

_____________________________________________________________________________________

_ p Value for T-test Differences Between Pass and Fail Groups

EEG Parameter Formal Stage Criterion Vessels Shadows Correlations Combinations______________________________________________________________________________________FLR-O Index* (+) p = .0558 p = .049 p = .176 p = .156FLR-O (Adjusted)** p = .0500 p = .040

F* (+)L* (+) .086 .069 .159R* (+) .130 .084 .068 .082O* (-) .046 .118 .065 .179

(F-L)/(R+O)(L-R)/(L+R) .110 .057 .117

(greater = pass) (lesser = pass)(lesser = pass)(R-O)/(R+O)* (+) .044 .0625 .151 .125(F-O)/(F+O)* (+) .051 .0745 .052______________________________________________________________________________________*One-tailed tests where F, L, R, R-O, and F-O are predicted (and found) to be positively related (+) to pass scores; O is predicted (and found) to be negatively related (-) to pass scores.

**Adjusted for age and gender.

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support the finding of O’Boyle and Benbow (1990) that right hemisphere involvement is

associated with intellectual precocity. Since both R and L anterior and occipital

coherences appear related to formal reasoning, the remainder of the discussion will focus

on anterior/posterior functions rather than right-left differences. Essentially, the data

have suggested that the major EEG alpha indicators of formal reasoning among subjects

practicing TM are positive homolateral frontal and negative bilateral occipital alpha

coherences. I have previously discussed the significance of each in light of the existing

literature, as given in Chapter II, Literature Review.

Summary of Follow-up Analyses in Various Coherence Measures: The Effect of the TM Instructional Set

In summary, the occipital alpha coherence in the current research is found to be

negatively related to formal reasoning skills, significantly so for the Formal Stage

Criterion (p = .046) and with strong trend for the Shadows task (p = .065). This finding

supports similar negative relationships between cognitive skills and occipital coherence

whether the subject practices TM during the EEG session or merely rests with eyes

closed as given in the Literature Review, Chapter II.

On the other hand, the anterior R alpha coherence in the current research is

positively related to formal reasoning skills with most trends for Vessels (p = .085),

Correlations (p = .068), and Combinations (p = .082). Anterior L alpha coherence in the

current research is positively related to formal reasoning skills with trends for Formal

Stage Criterion (p = .086) and for the Vessels task (p = .069).

The Formal Stage Criterion demonstrates two significant results in tests of a ratio

between anterior and posterior coherences. (R-O)/ (R+O) distinguishes pass and fail

subjects at p = .044 and (F-O)/(F+O) distinguishes pass from fail subjects at p = .051.

This supports other studies of IQ and EEG alpha coherence measures taken while

subjects practice TM, but contradicts studies in which the subjects merely rest with eyes

closed. The conflict appears to reach some resolution by taking into account the

neurophysiological changes that occur as a result of the TM practice, namely that alpha

coherence increases globally and in the anterior regions especially. Cognitive skill and

IQ appear positively correlated to such changes. This implies that the set of instructions

that constitute the TM technique initiates a sequence of neurophysiological changes in

the brain that supports greater adaptability to cognitive demands. In Piagetian terms, this

implies movement toward higher levels of equilibration.

Limitations of the Study

I used the FLR-O index to test for a possible neurological “necessary but not

sufficient” condition for formal reasoning, as postulated by Piaget. However, some

subjects who failed the test of formal reasoning also had greater coherence than pass

subjects. This means that strictly speaking, alpha coherence as measured cannot be “a

necessary but not sufficient” condition. For example, one subject passed all four tests of

formal reasoning, yet demonstrated one of the lowest FLR-O indices of all the subjects.

On the other hand, the group means for the FLR-O index and other coherence

measures indeed showed differences between pass and fail subjects. The means were

normally distributed, therefore outlying values did not obscure any implications derived

from the difference in means. I can still conclude that, in general, subjects with lesser

coherence values tend to fail the task of formal reasoning as administered in this study.

However, only one of the four tasks demonstrated results that were statistically

significant at p ≤ .05. Interestingly, the Formal Stage Criterion demonstrated significant

results at p = .050 when adjusted for age and gender, and p = .0558 unadjusted. Note that

of the 39 subjects who passed the Formal Stage Criterion, 37 passed both or one of the

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Vessels and the Combinations tasks, reflecting the relative primacy of the INRC group

and the lattice structures represented by these two tasks.

Upon review of the measures and their outcomes, several limitations of the

current research emerge, with the following corrective actions.

1. Episodes of sleep during the EEG were not evaluated. Future research should

eliminate portions of the EEG alpha coherence recordings that reflect any sleep stage. It

is known that during TM, occasionally subjects will sleep, with consequent lowering of

the coherence measure. This implies that subjects must be visually monitored for signs

of sleep such as head nodding, heavy breathing, etc. Also, the EEG record can be

evaluated for low voltage, irregular frequencies that indicate Stage One sleep. Sleep

during the EEG measurement could account for the one subject who passed all four

tasks, yet had the lowest coherence measures.

2. No controls for experimenterXsubject interaction. Future research should insure

that experimenter gender does not interact with subject gender. For example, it is

possible that a male experimenter may cause anxiety more for female subjects than for

male subjects, or vice versa. If the subject pool is mixed gender, then the ratio of male to

female will reflect not only task performance differences but also “distraction” or anxiety

differences which will show up in the task performance. Several alternatives exist: use

subjects and experimenter of one gender only, or use several experimenters of the same

gender as the subjects. (Several experimenters would be required in order to randomly

balance out any difference in style of their clinical interviews.)

3. No selection of EEG epochs was used, beyond artifact rejection. Future research

should use portions of the EEG record that reflect “best” performance. EEG variability

presumably reflects cognitive variability. Since the task performance reflects a “best

effort,” likewise, the EEG record can be examined for epochs that reflect a best sustained

experience. This could be characterized as increasing the EEG signal-to-noise ratio. For

example, Orme-Johnson et al. (1982) used the “best” 5 minutes out of 30 minutes for

their FLR-O index.

4. Full characterization of a variety of brain regions was lacking. Future

research should use more derivations to characterize global brain functioning. For

example, the current index fails to measure posterior EEG within each hemisphere (e.g.,

P3O1 and P4O2) which would be analogous to anterior L and R measures. Therefore, no

statements can be made regarding the coherence within left or right posterior regions.

The current measure (O) only evaluates the degree of coherence between left and right

posterior occipital regions.

5. Insufficient number of females were tested. Future research should test

enough females to obtain a group passing the Shadows task large enough to provide

reasonable statistical power in tests of the FLR-O coherence index. The current research

found only one out of 19 females to pass the Shadows task.

Long-term Effects of the Practice of Transcendental Meditation on Cognitive Functioning: Toward an

Organicist Reduction Theory of Piaget’s Constructivist Principles

Although the results of the current research were significantly related only to the

Vessels task and can be generalized only to subjects measured while practicing the TM

technique, it is still instructive to pursue an explanation with the hope that later research

will draw linkages with neuropsychological processes among the larger, non-TM

population. Note also that the test of the Formal Stage Criterion resulted in near-

significant (p ≤ .0558) differences between pass and fail groups, and when adjusted for

age and gender, the test is significant at p = .050, lending encouragement to locating a

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theoretical link between equilibration and neuropsychological processes even though at

this time the theory must be in the context of subjects who practice TM.

This said, the theory in principle has potential for generalization. For example,

the TM technique is claimed to be “natural” and “effortless.” The technique purportedly

uses the “natural tendency of the mind” to attain a quality of restful alertness that over

time brings the mind to its full potential (Maharishi, 1963). This implies that the TM

technique enhances the individual style of cognitive or neurophysiological functioning

that would otherwise be limited by psychological and physiological stresses. TM is said

to accelerate the normal course of development presumably through alteration of

neurophysiological functioning. Thus, it appears reasonable to hope for theory to later

“bridge” the gap between TM and non-TM populations. The following discussion

attempts to build on current neurophysiological knowledge as well as TM research to

show in a heuristic fashion one possible explanation for a putative positive relationship

between the FLR-O index and cognitive skills. This effort attempts to meet Piaget’s

criteria of an organicist reduction model of genetic epistemology.

Regulation of Selective Attention and the Mechanics of TM

The most immediate point of departure for discussing the effects of the TM

instructions on the brain is a physiological model of selective attention and the

accompanying “orienting response” (OR or “what is it?”) response of Sokolov (1963).

Several authors have suggested that the mechanics of TM can best be explained by

reference to the known properties and functions of the OR (Arenander, 1986; Wallace,

1986; Kesterson, 1986). The OR often is considered a response to some environmental

stimulus. However, the OR can also be elicited by internally oriented attentional

processes as well. For example, Maltzman, Gould, Pendery, & Wolff (1982) and

Maltzman (1979b) show that task instruction creates a mental set that gives rise to

manifestation of an OR beyond the OR normally elicited by novelty or stimulus change.

The central process of TM involves the “transending reflex” which purportedly functions

using brain mechanisms associated with the OR, as presented by Arenander (1986) and

discussed by Wallace (1986) and Kesterson (1986).

In brief, the model suggests a system that leads to regulation of selective attention

mechanisms through orienting and habituation processes linked to the instructions given

for the practice of TM. The practice utilizes a meaningless sound called a “mantra” that

is repeated according to instructions given to the individual. The precise instructions for

using the mantra are proprietary to the TM organization, but instructors of the technique

regularly state that the practice uses neither concentration nor contemplation. Therefore,

it can be inferred that the technique does not require effortful focus on the mantra, and

neither does it require wandering digression from the mantra. Between these two poles,

the TM technique apparently provides for an effortless engagement of the mind with the

mantra, allowing comfortable assimilation of intrusive thoughts. The use of the mantra

in meditation leads to a process of “transcending” the thought of the mantra, culminating

in a state of awareness without any object of a thought.

While transcending may be brief and hardly noticed at first by some individuals,

the nervous system responds with relaxation of the skeleto-muscular system and with

autonomic and EEG changes associated with relaxation. Meanwhile, the transcendental

state enhances the subjective alertness of the individual. Together, these effects have led

Wallace (1970) to dub the subjective experience of TM as “restful alertness.” The 20

minutes of TM is constituted by repeated encounters with the mantra and other thoughts,

interspersed with the experience of transcending on the mantra. The physiology attains

successively deeper stages of relaxation while the mind finds it easier to settle down the

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conscious attention. The cognitive effects of the long-term practice of TM have been

documented in several studies as follows.

Cognitive Effects of the Practice of TM

The following is a brief review of studies of longitudinal changes in EEG alpha

coherence during TM that relate to cognitive improvements or the number of months

practicing TM. Several other longitudinal studies give evidence for cognitive

improvement with the practice of TM outside of the context of alpha coherence.

Together, these studies suggest the efficacy of the TM set of instructions in optimizing

brain function and constitute the rationale for hypothesizing that alpha coherence

measured during TM should demonstrate a relationship with formal operational

reasoning.

As mentioned above, Orme-Johnson et al. (1982) report several significant

longitudinal changes in a one-year study of correlations between frontal, left, and right

anterior alpha coherence and various subtests of the Torrance Verbal and Figural Tests of

Creative Thinking. They also found significant inverse relationships between change in

bilateral occipital alpha coherence and the three verbal creativity subtests indicating that

posterior changes also result in conjunction with anterior changes.

Longitudinal enhancement of frontal alpha coherence over a mere two weeks is

reported by Dillbeck and Bronson (1981), however, no cognitive measure was included.

Nidich, Nidich, Orme-Johnson, and Wallace (1983) found the frontal, left, and summed

FLR EEG alpha coherence were positively correlated with the length of time practicing

TM among 37 Maharishi International University (MIU) students (range of 2 to 13 years

TM, mean of 6.77 years). The relationships remained significant even after partialling

out age. No relationship was found between time practicing TM and IQ.

In a study of math achievement prediction among college freshmen, Nidich,

Abrams, Jones, Orme-Johnson, and Wallace (1989) found that frontal and left alpha

coherence each significantly correlated with the math GPA of the subsequent

(sophomore) school year among 26 male MIU students (r = .476, and r = .336,

respectively). For comparison, the freshman year’s math and introductory physics GPA

correlated r = .613 with the sophomore year. The authors note that other researchers

find typical cognitive entry characteristics such as aptitude and science performance

correlate with academic achievement between .5 and .7 and affective characteristics

correlate with academic achievement an average of .4 when corrected for unreliability.

Therefore, the EEG coherence correlations compare well with these other predictors.

Longitudinal studies of cognitive measures, without EEG, also indicate cognitive

growth. (Given the results demonstrated in the above studies, it seems reasonable to

assume similar EEG changes occurred in these meditating subjects as well.) Shecter

(1978) found a 9 point increase on Raven’s Advanced Progressive Matrices after 3.5

months among high school students practicing TM. Aron, Orme-Johnson, and Brubaker

(1981) reported significant freshman-senior increases of eight points over four years on

Cattel’s Culture Fair Intelligence Test and on sets of California Personality Inventory

among students practicing TM at MIU. Dillbeck (1982) found subjects instructed in TM

showed an increase in flexibility of perceptual processes over a two week period

compared with control subjects practicing daily relaxation. Dillbeck, Assimakis,

Raimondi, Orme-Johnson, and Rowe (1986) reported a significant increase of nine points

in scores over a three-to-five year period on the Culture Fair Intelligence Test and the

Group Embedded Figures Test among 50 college students practicing the TM and a

related advanced meditation technique termed the TM-Sidhi program. Cranson (1989)

(see also Cranson, Orme-Johnson, Gackenbach, Dillbeck, Jones, & Alexander, 1991)

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conducted a controlled two-year longitudinal study in which MIU students practiced the

TM and TM-Sidhi programs. He found a significant five-point increase on the Cattell

Culture Fair Intelligence Test and significantly decreased reaction time (typically

inversely correlated with IQ) compared with a control group at a matched university.

Travis (1979) found significant gains over five months among TM subjects compared to

controls on scores from the Torrance Test of Creative Thinking: figural flexibility,

figural originality, and verbal fluency.

Development of ORs to Significant Events and Habituation to Distraction

Maltzman (1979a, b) vigorously defends the notion that the “OR is not dependent

on novelty alone but is predetermined by the set or dominant focus present at the

moment.” This suggests that, during TM, the individual attends to the “set” or

“dominant focus” and generates an OR upon thinking the mantra. Note that “set” implies

a cognitive direction while “dominant focus” implies a neuro-electrical state. Evidence

for the concept of “dominant focus” comes from the neurophysiological research of

Rusinov (1973) and others that suggests that the CNS can support a “focus of excitation”

that modifies or directs the neural activity to give responses that otherwise would not

arise. In other words, these researchers have provided neurophysiological evidence for

“the Wurzburg school’s formulation of set, determining tendency, or Aufgabe”

(Maltzman, 1979a, p. 280). Maltzman suggests that the dominant foci are the

physiological bases for attitudes and interests, and, through the mediation of instructions,

can determine the acquisition of stimulus significance in experimental studies.

“According to our view, task instructions induce a dominant focus which selectively

determines which stimuli will evoke an OR and which will not. It selectively influences

the transmission of information within the central nervous system” (p. 280). (For

additional discussion of the dominant focus, see Pribram, 1971, pp. 77-81, and Simonov,

1985.) This view of the human OR contrasts with Pavlov’s more simple model for dogs,

where novelty or stimulus change alone may have been the sole originator of the OR.

Similar limitations are found in Sokolov’s early formulation (1963) of the neuronal

model which requires the notion of a stimulus “mismatch” to create the OR. Maltzman

points out that even Sokolov and colleagues later accepted the occasion of an OR to a

significant stimulus in the absence of stimulus change, an outcome that does not require

the mismatch to a stimulus.

This subsequent interpretation of the OR (the voluntary OR resulting from

perceiving a stimulus imbued with significance) expands Arenander’s model of the

transcending reflex to include the mantra as a generator of the OR even if it did not

change in any way. It appears that the instructions given in TM serve to create a

“dominant focus” that “exercises” the brain in generating sustained ORs amidst a state of

physiological rest. Also, the instructions (and dominant focus) serve to define a class of

mental activity to which the subject habituates: namely thoughts, since the instructions

guide the subject towards an effortless response to thought, upon becoming aware that

awareness is on a thought other than the mantra. Presumably the long-term cognitive

benefits of TM result from extending this conditioning to daily life in which the subject

follows more attentively the train of thought associated with a task while simultaneously

habituating, or ignoring thoughts classified as distracting.

Note that Maltzman (1979b, p. 330) indicates that while anterior brain regions are

associated with voluntary ORs, involuntary ORs are associated with the more

perceptually-oriented posterior regions. This implies that anterior coherence may or may

not exert “control” over the posterior, less bilaterally coherent, regions depending on the

relative “balance” between anterior and posterior regions. The findings of the current

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research indicates that higher anterior homolateral alpha coherence correlates negatively

with posterior bilateral coherence (L and O r = -.38, p =.0031; R and O r = -.21, p

= .1163) . It is reasonable to infer that the L and R anterior derivations are activated,

based on other research that suggests increased anterior cross-correlation (Livanov, 1977)

or coherence (Busk & Galbraith, 1975, Sheppard & Boyer, 1990; Dillbeck & Vesely,

1986) result from higher demand “task” conditions. The negative relation of posterior

coherence suggests reduction in involuntary ORs, perhaps due to the selective attention

and preattentive mechanisms enhanced by the anterior activity. (This issue will be

discussed below in the section “Recommendations for Future Research” under “The

Question of Bilateral Occipital Coherence.”)

The notion of frontal executive functioning may underlie the acquisition of

schema. For example, Shute and Huertas (1990) administered a clinical version of the

Shadows task to 58 undergraduate students (mean age 22.7 years) together with a battery

of neuropsychological measures commonly used to detect deficits associated with frontal

lobe dysfunction, plus four additional cognitive measures, as well as another two

measures of verbal ability. Factor analysis accounted for 70% of the variance,

distributed among four factors. The Shadows task score loaded most strongly on the

tests used for frontal assessment and not on the other measures, including those of verbal

ability. The authors conclude that “the ability to identify patterns among environmental

stimuli and make accurate inferences from those patterns, described by Piaget as formal

operational reasoning, may be related to adequate frontal lobe development...It may be

that the ability to anticipate the consequences of one’s own actions is a function of

adequate frontal lobe development” (p. 9).

Frontal versus posterior functions relate to physiological research on selective

attention and distraction. Skinner and Yingling (1977) also suggest separate systems for

voluntary versus involuntary ORs looking primarily at the electro-anatomical evidence.

This occurs in the context of “central gating mechanisms” that underlie both behavior,

the occurrence of a frontal negative slow potential shift (CNV), and enhancement of

certain evoked response potential (ERP) components in response to “attention-evoking

situations.” They identify the mediothalamic-frontocortical system (MTFCS) as the

mediator of phasic changes in awareness (selective attention) through inhibition of

“ascent to the cortex of information evoked by irrelevant stimuli” (p. 55). The

mesencephalic reticular formation (MRF) underlies tonic shifts in vigilance through

excitation of brain activity as in more primitive behaviors such as orienting reactions.

They both converge on the thalamic reticular nucleus, “a structure which is a switching

mechanism that gates the ascent of thalamic activity to the cortex” (p. 31), with a balance

between excitation (MRF) and inhibition (MTFCS) determining the subject’s current

conscious state. The former controls the more general and reflex oriented attentional

states and the latter controls the selective and voluntary types of attention. Both control

bioelectric EEG activity. Therefore, evoked potentials (EPs) can reflect differing

contributions from each system, thus complicating interpretations of EP features. “For

example, the dual control of the thalamic gates by cortical and brain stem mechanisms

quite obviously parallels two of the most salient subjective characteristics of attention,

the selective filtering of sensory experience and the overriding of volitional attention by

reflexive orienting mechanisms” (p. 63). This description of attentional gating

mechanisms also supports Arenander’s model of the “transcending reflex.”

Implications of Frontal Functions for the OR and Adaptive “Stability”

Stuss (1992) summarizes the functions of the frontal lobes as executive functions

on the one level and as metacognition and self-reflectiveness at increasingly higher

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levels. The primary goal of the first level is the “conscious direction of the lower-level

systems toward a selected goal. This control may well be divided into specific functions

such as anticipation, goal selection, plan formulation, evaluation and monitoring of

behavior, and other anterior attentional functions such as selectivity and possibly

persistence” (p. 12). In the context of the current research, this analysis appears relevant

to the properties of formal operational reasoning which requires a systematic control of

variables as found in mental structures that reflect the propositional lattice and the INRC

group of transformations. But more to the point is the suggestion that the frontal lobes

are responsible for maintaining assimilative structures that govern accommodation to

observed discrepancies between expectation and actuality, i.e., passing judgment and

creating a plan for adaptation to the newly-perceived situation. Failure to equilibrate

may well be a failure of frontal functions. Berg and Sternburg (1985) suggest that

response to novelty is a major component of intelligence and that the ability to deal with

novel situations is prominent in Piaget’s theory of development. Also see Welsh and

Pennington (1988) for application of frontal functions to Piagetian development theory.

Stuss and Benson (1984) list several dysfunctions associated with prefrontal damage.

Note their similarity to dysfunctions of systematic reasoning in which a schema has not

been strongly developed:

1. Deficit in the ordering or handling of sequential behaviors2. Impairment in establishing or changing a set3. Impairment in maintaining a set, particularly in the presence of interference4. Decreased ability to monitor personal behavior5. Dissociation of knowledge from the direction of response6. Altered attitude (p. 222)

Piaget suggests that once a structure attains sufficient breadth to anticipate all the

combinations given it by actuality, then the structure is relegated to “automatic” status.

Likewise, Stuss and Benson (1984) suggest that “learned” cognitive skills reside in the

posterior regions. For example, “reported findings of IQ deterioration after frontal

damage are rare, whereas the number of studies reporting negative results is

overwhelming. Even studies that do report IQ deterioration admit that other factors may

be important” (p. 197). Luria (1973) indicates that patients with frontal lobe lesions fail

to orient to “informative attributes” that would lead to hypotheses concerning a given

problem. This means that posterior, automatic cognitive processes are able to solve

simple problems, but frontal, controlled cognitive processes fail under more challenging

situation.

As is known, formal logical operations may remain intact enough in patients with lesions of the frontal lobes...[S]uch patients easily cope with simple problems that have single solutions, i.e., that do not require any choice from several equiprobable alternatives; but they are unable to solve a problem that requires preliminary orientation within its conditions and formation of a hypothesis, which in normal subjects leads to a proper choice from several equiprobable alternatives and to the performance of some intermediate operations insuring attainment of the final goal...[Frontal] patients do not subject the conditions of the problem to preliminary analysis and do not confront their separate parts. Instead, as a rule, they single out random fragments of the conditions and begin to perform partial logical operations, without attempting to formulate a general strategy and without confronting this operation with other elements of the condition of the problem; neither do they match the result obtained to the initial conditions” (p. 20-21).

In Piagetian terms, posterior functions appear to take on the role of “necessity,” in

which “virtual” operations replace the slow, conscious effort required by the transitional

formal reasoner (Piaget, 1986). Anterior functions appear to take on the role of

“possibilities,” the mechanisms for accommodation leading to higher forms of

equilibration. Luria’s (1973) comments above illustrate the failure of frontal patients to

consider “all possibilities.” As Piaget suggests:

Access to new possibles takes place in a framework of previous necessities. This is because all accommodation is accommodation to an assimilation scheme. These turn-takings, which are in fact those of a ceaseless succession of access and closure, are due to the general law of equilibration between differentiations and integrations. They express one of the aspects of the essentially temporal character of cognitive constructions, even though in outcome they lead to systems whose necessity becomes atemporal. The possibles, by contrast, constitute phases in temporal formation. One of the turning-points marking the beginnings of modern

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physics is known to have consisted, following Galileo, in the belief in time as an independent variable. By the introduction of the genetic dimension in epistemology, it can be hoped that an analogous service will, with due proportion, be rendered, even if temporal formation terminates in atemporal structures. In this case, the atemporal is the outcome of the integration of the transcended in its transcendence. Such is the distinctive feature of cognitive equilibration (p. 303).

“Integration of the Transcended in its Transcendence” (Piaget, 1986)

Frontal functions remain important even after attainment of formal schema. The

individual must, for example, select the appropriate schema when faced with a cognitive

challenge. This source of difficulty suggests that individuals who are formal in one

subject may fail to transfer their skills to another subject because of inadequate or

unprepared frontal functioning. In the preceding passage regarding “integration of the

transcended into transcendence,” Piaget uses the framework of his genetic epistemology

to describe the process of automatization of accommodative behaviors and operations.

Automatization, I suggest, converts the slow, temporal thought process of the individual

into higher-level assimilative schema that operate atemporally, using virtual

transformations to reach a logical outcome. This is not a new idea. In the context of

early cognitive psychology, for example, Schneider and Shiffrin (1970) outline

differences between “controlled and automatic human information processing.”

Controlled processing, I suggest, is a frontal activity. It requires the active attention of

the subject, and thus is limited to only one sequence of “memory nodes” at a time (Cf.

“temporal formation,” above). Automatic processing, I suggest, is a posterior activity. It

can handle several sequences at once because attentional resources are not consumed.

The authors point out that automatic processing can direct controlled attention

automatically, “regardless of concurrent inputs or memory load,” and “once learned, an

automatic process is difficult to suppress, to modify, or to ignore” (p. 2).

Other authors from “early” cognitive psychology such as Kimble and Perlmuter

(1970) suggest methods of deautomatizing, or in their terminology, restoring “volitional”

behavior. A research example is the conditioned pairing of a light with an air puff to the

eye (causing a blink), plus an instructed response to the subject to press a button with the

finger or to blink the eye upon getting the air puff. The finger press or eye blink become

automated (non-volitional) responses to the light. This is called “anticipatory

performance.” The classical theory of volition suggests that kinesthetic feedback of

consequences of self-initiated acts (Piaget would probably call this “actions on objects”)

is the primary source of deautomatization. In a conscious departure from their

behaviorally-colored ethos, Kimble and Perlmuter indicate that research shows

deautomatization is never totally prevented by the loss of kinesthetic feedback, implying

for them that mental images, or “centrally located feedback loops” also play a role in

restoring volition to involuntary behavior. Based on their research, the authors suggest a

developmental sequence for the development, initiation, and control of voluntary acts

which is of interest in the context of mental practices such as TM. In other words, they

suggest that volition plays an important role. Development of volition, I suggest, may

develop frontal structures that support equilibration of more adaptive mental structures,

such as support formal operational reasoning. Kimble and Perlmuter write “[T]he

individual first acquires voluntary control over initially involuntary responses and then

with extended practice allows these responses to retreat from consciousness and attention

and, in that sense, to become involuntary” (p.382).

I suggest that the TM technique trains the individual’s preattentive faculties

(“volition”) to minimize the involuntary lapses of attention when distracted by task-

irrelevant thoughts. This means the individual learns to habituate to distracting thoughts,

or in Piagetian terms, to decentrate. The TM technique, over time, allows this

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“voluntary” control over previously involuntary distractions to become automatic—such

as may be evidenced in the various improvements on IQ tests described in the TM

research findings above. In this sense, the brain must, by implication, be attaching

“significance” to task-oriented cognition, thereby enhancing voluntary OR responses,

otherwise known as “alertness”. Habituation to distraction reduces involuntary OR

responses, otherwise known as “decentration” and restfulness.

Note that the subjective experience during TM is one of mental alertness co-

incident with physiological restfulness. A recent review by Jevning, Wallace, and

Beidebach (1992) suggests that many of the measured physiological effects of TM reflect

a state of increased alertness or CNS activation especially at periods of subjectively

deepest transcending. “Such states are accompanied by high amplitude theta and/or fast

frequency beta bursts consistent with activation...[Outside of TM, findings indicate]

decreased reaction time and other improvements in sensory and motor performance [that]

can be associated with a more alert state of the central nervous system” (p. 421).

Increased CNS activation during TM is also indicated by increased coherence, as well as

increased cerebral blood flow and other changes in peripheral circulation and metabolism

to support the increased activation. In contrast to mental alertness, the authors also point

out that the subjective experience of deep restfulness is supported by measures such as

decreased whole body, muscle, and red cell metabolism, plus decreased plasma thyroid

and adrenocortical hormone production. Other indicators of rest include the decrease or

disappearance of EMG (muscle tension), and decreased galvanic skin resistance and/or

decreased phasic skin resistance response. Together, these features characterize TM as a

subjective experience of “restful alertness.

Let us examine further some ideas that illuminate Piaget’s concept of

“decentering” as an element of cognitive growth. In brief, decentering can be considered

as the ability to ignore distractions. In a sense, the history of science is movement away

from distracting concepts and towards more inclusive formulations of the laws of nature.

“Impulse” as the emotional correlate to cognitive distraction could even be included as

“centering.” The non-conserving child, for example, can be seen to act “impulsively,”

failing to take into account the requisite variables for conservation of weight or volume.

In another example, Piaget (1962) writes in response to comments from a fellow

developmental psychologist, Vygotsky:

On the affective level, it would require quite a dose of optimism to believe that our elementary interpersonal feelings are always well adapted: reactions such as jealousy, envy, vanity, which are doubtless universal, can certainly be considered various types of systematic error in the individual’s emotional perspective. In the field of thinking, the whole history of science from geocentrism to the Copernican revolution, from the false absolutes of Aristotle’s physics to the relativity of Galileo’s principle of inertia and to Einstein’s theory of relativity, shows that it has taken centuries to liberate us from the systematic errors, from the illusions caused by the immediate point of view as opposed to “decentered” systematic thinking. And this liberation is far from complete.

I coined the term “cognitive egocentrism” (no doubt a bad choice) to express the idea that the progress of knowledge never proceeds by a mere addition of items or of new levels, as if richer knowledge were only a complement of the earlier meager one: it requires also a perceptual reformulation of previous points of view by a process which moves backwards as well as forward, continually correcting both the initial systematic errors and those arising along the way. This corrective process seems to obey a well-defined developmental law, the law of decentering (décentration). For science to shift from a geocentric to a heliocentric perspective required a gigantic feat of decentering. But the same kind of process can be seen in the small child: my description, noted favorably by Vygotsky, of the development of the notion of “brother” shows what an effort is required of a child who has a brother to understand that his brother also has a brother, that this concept refers to a reciprocal relationship and not to an absolute “property.” Similarly, recent experiments (not available to Vygotsky) have shown that to conceive of a road longer than another which ends at the same point, thus separating the (metrical) concept of “long” from the (ordinal) “far,” the child has to decenter his thinking, which at first focuses on the end point alone, and to work out the objective relationships between the points of departure and arrival (p. 3).

The concept of decentering is central to Piaget’s theory because decentration is

prerequisite to disequilibration, which in turn is prerequisite to higher stages of

equilibration. In our current “translation” of Piaget’s formulation into neurophysiology,

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I speculate that decentration develops when the subject’s frontal (assimilative) structures

assert volitional control over automatized posterior (assimilative) structures. This

assertion of voluntary, “temporal” cognition by the frontal structures is itself the process

of accommodation. See Pribram (1969) for a discussion of the neurology of

accommodation and assimilation. The frontal function of “integration” and

“association,” he suggests, are carried out by frontal control over posterior input channels

(i.e., this is exercise of assimilative structures). In the current study, clear evidence was

found that for the Vessels task at least, greater anterior alpha coherence and lesser

posterior coherence during TM were related to formal reasoning. The evidence

supported similar implications for the Formal Stage Criterion (p = .0558, and p = .050

when adjusted for age and gender ). Amidst the possibility that gender effects would

complicate this simple assertion, the statistical tests revealed no differences in the

findings for males compared to females. Thus, I suggest that the concept of formal

reasoning implies neurological conditions that are necessary, but not sufficient: namely

frontal homolateral coherence sets the stage for decentration and consequent

accommodation to more complex challenges in the environment.

Various researchers have studied biological development in relation to cognitive

styles such as impulsivity vs. reflection (Nelson and Smith, 1989). Trait differences may

exert similar influences. For example, studies of sex differences in cognition have

suggested, among other things, that males “excel on more complex tasks requiring an

inhibition of immediate responses to obvious stimulus attributes in favor of responses to

less obvious stimulus attributes” (Broverman, Klaiber, Kobayashi, and Vogel, 1968).

These authors attribute these findings to “differences in relationships between adrenergic

activating and cholinergic inhibitory neural processes, which, in turn are sensitive to the

‘sex’ hormones, androgens and estrogens” (p. 23). They extend these ideas to Piagetian

developmental issues, irrespective of sex, by suggesting that

the relationship of simple perceptual-motor and inhibitory restructuring processes could be applied to all stages of development, that is, the more vigorous a given lower-level function, the more difficult is it to inhibit and and subordinate the lower function to a specific higher level function.... The varying outcomes of these contests in different individuals may underlie the consistent bipolar factors of ability found in the with-individual variance of abilities (p. 44).

Maltzman (1959) found that males performed better in a test of problem solving

(the water jar problem). He concluded that males were less influenced by “mental set” or

“Einstellung”, suggesting that

more rapid extinction of the dominant long solution responses in men may be due to a variety of different variables, for example more rapid accumulation of reactive inhibition in men than women. Another possible variable is a higher anxiety level in women, especially as induced by initial failure on the extinction problem (p. 242).

Bieri, Bradburn and Galinsky (1958) concluded from their study of college age

sex differences in spatial relations (Embedded Figures Test) that superior performance

by males was correlated with superior mathematical aptitude in combination with a

“conceptual approach approach to social and objective stimuli” (p. 11). This finding

parallels the findings in the current research in which males performed significantly

better than females on the Shadows task (a test of spatial proportions requiring a

conceptual, non-impulsive, approach) together with greater preference for math (and

science). Furthermore, irrespective of gender differences, the current study also indicates

that subjects who pass the tasks preferred math and science significantly more than those

who failed the tasks (implying a similar relationship between math aptitude and

conceptual, non-impulsive approaches to solving the task problems).

In summary, studies of “impulsive” individuals may characterize the failure to

decentrate. That is, subjects who fail to decentrate could be said to be “jumping to a

conclusion.” For example, Van den Broek, Bradshaw and Szabadi (1987) found that

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females independently classified as “impulsive” demonstrated poorer performance than

non-impulsive females when required to delay pressing a button for a given period after a

loud sound. Similarly, Wallman, Eylon, and Lawson (1980) suggest that the onset of

formal operations can be equated with development of the ability to avoid premature

closure in a problem-solving situation. Although Piagetian tasks were not used in the

cross-sectional study of student in grades 1-6, the authors found that training failed to

alter the native strategies for solving complex inferences. However, improvements were

noticed with increasing ages. The authors suggest that developmentally, high level

reasoning results when students “continue their thinking about the questions that had

been unanswered and reason hypothetico-deductively to generate and test their own

hypotheses” (p. 114). This appears to meet Piaget’s criteria for “decentration”. It

suggests jumping to conclusions—or impulsive thinking—has control mechanisms that

are indeed developmental in origin. To overcome impulsive thinking, the authors suggest

that teachers “emphasize the tentativeness and probablistic nature of knowledge” (p.

114). This suggests that growth requires an assimilative structure that controls or

overrides tendancies towards impulsive judgements.

I suggest that frontal coherence represents just such an assimilative structure and

that this is the assimilative structure that supports accomodation leading, ultimately to

higher forms of equilibration, or the growth of “novel” structures not otherwise predicted

from the lower level structures. (For more details on the significance of frontal

coherence, or “time locking”, see discussion associated with Damasio (1989) below in

Directions for Future Research, under “The Question of Information Transfer”). The TM

technique has been characterized to reduce impulsivity, or “limbic outflow”, as follows.

The mechanics of Transcendental Meditation have been discussed in the context

of research into the medical applications of TM, including notions of self-regulation and

EEG coherence. Stroebel and Glueck (1978) (also, Glueck and Stroebel, 1978, 1975),

investigating various meditation-relaxation techniques for treatment of mental illness and

stress, found that Transcendental Meditation was preferred to biofeedback for “general

relaxation and creating a state incompatible with emergency response” in psychiatric in-

and outpatients (p. 422). They speculate that during TM, “the usual affective outflow

from limbic structures is diminished, with enhanced transmission of signals between the

hemispheres via the corpus collosum or other commissures” (p. 421). They report on the

results of their EEG alpha coherence research on patients practicing the various methods,

and suggest that differences in coherence patterns result from the specifics of the

techniques. They speculate on the causal mechanisms for the differing patterns of

increased EEG coherence observed in several of the mantra-derived techniques. First, the

manta may be a “boring habituation stimulus leading to habituation of [left hemisphere]

beta activation and augmentation of alpha-theta synchrony” through normalization of

visceroautonomic homeostasis, regulated by the normally unconscious right temporal

cortex-limbic system. Second, the mantras may introduce a resonant frequency (6-7 Hz)

“which is in the high theta EEG range and also approximates the optimal processing of

the basic language unit, the phoneme, by the auditory system.” They theorize that

“when one thinks a mantra, a significant stimulus in introduced in the [dominant] temporal lobe and probably directly into the series of cell clusters and fiber tracts that have come to be known as the limbic system....[This] may act, with considerable rapidity, to dampen the limbic system activity and produce a relative quiescence in this critical subcortical area.

Since there are extensive connections running from the thalamic structures to the cortex, quieting the limbic system activity might allow for the inhibition of cortical activation, with the disappearance of the usual range of frequencies and amplitudes ordinarily seen coming from the cortex, and with the imposition of the appearance of very dense, high-amplitude, alpha wave production.

Similary, since the autonomic nervous system is controlled to a considerable extent by stimuli arising in the midbrain, the rapid changes observed in the peripheral autonomic nervous system—such as the GSR changes and the change in respiratory rate, heart rate, etc.—could be explained by the quieting of the limbic system activity” (p. 421).

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They also suggest that the reduction in activation results in increased access to the

non-dominant hemisphere (typically the right hemisphere), as in dreams or creative free

association, but without the accompaniment of any intense emotional affect that may

otherwise accompany such access.

Self-regulation of arousal and activtion can apparently enhance cognitive

development in children. Warner (1986) reports that children who practiced

Transcendental Meditation achieved significantly higher scores when tests of four mental

abilities (information-processing, attention, cognitive flexibility, reflectivity) and three

tasks of Piagetian conservation were taken together and compared with scores from a

non-TM, matched control group of children.

Educational Implications of theTheory

Much has been said in the past regarding “right brain” skills versus “left brain”

skills. The current research contradicts Samples (1975) claim that Piagetian formal

reasoning is solely left brain oriented and ignores right brain skills. Subjects who passed

the four tasks of formal reasoning demonstrated a higher coherence index than subjects

who failed the tasks. This was statistically significant for the Vessels task (p = .045) and

nearly significant for the Formal Stage Criterion (p = .0558). Note that when age and

gender were partialed out of the test for the Formal Stage Criterion, the differences

between pass and fail groups in the coherence index measurement were statistically

significant (p ≤ .050). However, three tasks did not show any statistically signficant

relationship. Therefore, the following educational implications are predicated on the

notion that the current research only partially supports an hypothesized relationship

between the coherence index measure and the development of formal operational

reasoning.

The coherence index consists of bilateral frontal homolateral left and right

anterior coherence as well as an inverse measure of bilateral occipital coherence: FLR-O.

This measure represents both anterior and posterior measures as well as left and right

hemisphere measures. Therefore, it may be termed a “whole brain” measure of CNS

development. Many educators have called for “whole brain” education, taking into

account the predilections and capacities of each hemisphere for gaining command of the

environment. In a monograph published by the Association for Supervision and

Curriculum Development, Caine and Caine (1991) suggest that the real challenge to

education is to create a more complex form of learning that takes into account integration

of “human behavior and perception, emotions and physiology. ” While not made explicit

in their book, I suggest that the Caines actually call for “frontal education” in their

apologia for “whole brain” education. They indicate that routine memorization, a

posterior brain function, remains insufficient for today’s educational challenges. For

example, they say

What we now appear to need is not individuals trained for the hierarchical and mechanical workplace but individuals who can govern themselves. Tomorrow’s successful employees will have to be problem solvers, decisions makers, adept negotiators, and thinkers who are at home with open-endedness, flexibility, and resourcefulness....The ironic point is that memorization, particularly as practiced in our schools, does not work to provide a foundation in basic skills and knowledge (pp. 14-15).

How to achieve this goal? At least we can exercise the frontal functions, so aptly

described in the above quote. This cannot be done in most “teacher-centered”

educational curricula. The Caines suggest that we support a richer academic

environment in which students solve problems along thematic lines, immersing

themselves in a “real world” of interacting parts, leading to holistic development. They

also suggest development of “relaxed awareness” in which the student learns to override

the jarring impulses, internal and external, that distract the learner from his or her task (p.

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136). (See Tobias, 1973; van den Broek, Bradshaw, & Szabadi, 1987; and Singer,

Cavanaugh, Murphey, Chen, and Lidor, 1991, in this regard.) I suggest that failure to

engage students in “whole brain” learning is functionally equivalent to administration of

a “frontal lobotomy” (Cf., Heath and Galbraith, 1966). This characterization suggests a

neuropsychological basis for the design of instruction (see Hartlage & Telzrow, 1983 and

Farley, 1981)). An alternative exists.

A series of studies has elucidated what I would term “frontal learning” in the

context of “student-structured learning in science” (SSLS) in contrast to “teacher-

structured learning in science” (TSLS). For example, Penick, Shymansky, Matthews, and

Good (1976) found that in the SSLS classroom

where the teacher removed virtually all restrictions on intellectual behavior and provided no directions or praise, the students exhibited (1) fewer patterns containing non lesson-related behavior, and (2) greater clustering of patterns, resulting in a more predictable set of behaviors than students in the TSLS science classroom where directions and evaluation were provided (p. 295).

These results appear somewhat puzzling in light of traditional educational

approaches. Less teacher direction and evaluation resulted in more predictable and

lesson-related behaviors. However, in light of the preceding discussion, I suggest that

students actually are a) learning to control their own levels of voluntary ORs, b) through

habituation to involuntary ORs arising from distractions, both internal and externally

generated. This line of thought has been expressed by Sanders (1983) in terms of “states

of stress” resulting from failure to control levels of arousal and activation, and elaborated

by Rothbart and Posner (1985). Penick et al. suggest, similarly, that

giving direction and other restrictive behaviors force the less-than-conforming student into a variety of patterns to reduce tension or anxiety. The lack of clustering of patterns and the consequent large numbers of infrequent patterns may be a function of ambiguous directions or a lack of task orientation to someone else’s task, a perception which could arise with a directive teacher....In addition, it should be noted that SSLS students did not as often exhibit patterns involving watching the teacher. Thus, it may be concluded that SSLS science students were more involved in on-task behavior with the materials than were

TSLS students. This involvement, since it was not produced by teacher directions or shaping, consisted of students identifying problems and solving them in their own way (p. 295). (Italics are mine.)

Some evidence exists that student self-control of arousal (i.e. distraction control)

is associated with higher levels of reasoning. For example, in a study of conservation

among students in grades 1-5, Good, Matthews, Shymansky, and Penick (1976) found

that conservation on tasks of number, area, weight, displacement, perimeter, perimeter-

area, and internal volume influenced how the pupil interacted with the teacher and with

sets of manipulated materials. They found that

teacher’s directions, evaluations, etc., seem to divert the nonconservers’ attention away from more productive activities with science materials to a greater degree than for conservers. Because of this, a TSLS strategy could work to the disadvantage of the “slower” students in a classroom even though they may have the most to gain from a science class rich with manipulative materials (p. 537-538).

The advantage of the conservers is their greater ability to monitor and plan their

own behaviors. Essentially, a TSLS strategy works against “frontal” education, perhaps

unwittingly administering a functional “frontal lobotomy” to its students. The solution

lies in the directions offered by SSLS strategies that place responsibility on the students

for governing their investigative behavior. Thereby they learn to govern their own

arousal patterns. Similarly, Maltzman (1960) was able to train college subjects in

“originality” of word associations by encouraging the frequency of uncommon behavior

in response to lists of words used in training. Maltzman speculates that the transfer of this

training to other situations was actually a result of “the effects of inhibition” that

“produce a decrement in the excitatory potential of other common responses” (p. 240).

Attempts have been made to explicate these approaches, using concepts at hand,

for various authors. For example, Greeson and Zigarmi (1985) relate pedagogical

technique to achievement of Piagetian development in the context of “visual imagery”

and “visual literacy.” They suggest that teachers should “encourage students to generate

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images themselves instead of constantly imposing images on their students.” They

specifically recommend the “discovery method” which reinforces problem solving and

demands creative recombinations of images and verbaliztions to solve problems” (p. 47).

It is reasonable to encourage skills self-regulation of arousal and activation in order to

avoid premature closure, impulsivity, or jumping to conclusions (my terms). Greeson and

Zigami suggest techniques that exercise the student’s capacity for self-regulation of

arousal and activation levels such as Jacobson’s progressive relaxation, meditation

strategies, and creative visual ideation techniques. They point out that...

Problem-solving skills that involve transformations and combinations of anticipatory images can be developed through curriculum activities ranging from charades to building mock-ups of complex molecular models (p. 48).

Note that O’Boyle and Bembow (1990) suggest that intellectual precocity may be

related to right hemisphere functions, presumably related to visuospatial skills as related

above. However, more to the point may be the speculation that enhanced frontal

involvement may lead to the metacognitive controls that permit judicious application of

right hemisphere strategies, when appropriate. See Milner (1971), Fischer, Hunt, and

Randhawa (1982), and Tucker (1987) for discussions of hemispheric arousal levels and

anterior controls over lateralized and posterior functions.

One author in particular has explored the role of various brain-mediated functions

in the context of neo-Piagetian developmental theory. Pascual-Leone (1989) particularly

investigates a neuropsychological model of field-dependence/independence. Among

other things, he describes excitatory and inhibitory processes that govern attention and

are localized in the prefrontal lobe. He relates the mechanism of mental attention to the

notion of “centration” (p. 62), as well, suggesting that automatization of schemes is

associated with the reallocation of schemes from the frontal to the posterior areas. The

congruence of the current theory developed in this dissertation with Pascual-Leone’s

theory is striking, in light of the total independence of these two research efforts. (I had

not been introduced to his theory until completing this dissertation with the associated

theory.) Further explication of Pascual-Leone’s theory can be found in de Ribaupierre

(1989) and in Johnson, Favian, and Pascual-Leone (1989). Elsewhere, Pascual-Leone

(1990) cites the coherence research mentioned in this dissertation (e.g., Dillbeck and

Bronson, 1981; Nidich, Ryncarz, Abrams, Orme-Johnson, and Wallace, 1983) to build

the case that coherence may be a neurophysiological component of “wisdom”. He

suggests that

Coherence should appear in the EEG under proper meditation conditions whenever the person has developed numerous manifold structures spanning over the brain: whenever the cortex is sufficiently integrated as a totality. This is, I believe, a distinct structural mark of wisdom. Thus, wise persons placed under proper meditation conditions and after some meditation training should exhibit high-coherence spread over the cortex, particularly in prefrontal and vertex areas (areas corresponding to regions where high-level executive, metaexecutive, and knowledge processing takes place) (p. 272).

Summary of the Theory

Extrapolating from Piaget’s theory, it appears that frontal functions support

volitional thought processes through mechanisms such as accommodation, decentration,

and growth towards awareness of “all possibilities.” Posterior functions appear to

support assimilative structures, i.e., automatic thought processes such as anticipation and

the regulations of “necessity.” Development of formal reasoning requires “whole brain”

interaction of frontal and posterior regions, possibly constituting the steps of successive

equilibrations through integration and differentiation of successively broader and more

stable schema, culminating in the “structural whole.” Piaget (1986) himself describes the

steps of development as a process in which linear, temporal thought becomes

simultaneous, atemporal competence. He suggests that “the atemporal is the outcome of

the integration of the transcended in its transcendence.” This implies “going beyond” or

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transcending the lesser stage with temporal, linear, perhaps left-hemisphere, but

definitely frontal-oriented, cognitive activity. Once the lesser structure is transcended,

the new structure, however, must be integrated back into the atemporal, automatic,

perhaps right hemisphere, cognitive processes supported by the posterior regions. It is

not unreasonable to suggest that the “transcending reflex” hypothesized to give rise to the

benefits of TM is similar in functional characteristics to Piaget’s description of the

“integration of the transcended in its transcendence” that gives rise to the atemporal

structure.

This theory must be taken somewhat tentatively with regard to the current

research. Although a statistically significant relationship exists between the Formal Stage

Criterion and the alpha coherence index (p = .050, with age and gender partialed out, p

= .0558 without partialling out age and gender), only one out of four tasks displayed a

significant relationship with the coherence index (Vessels, p = .045, without partialling

out age and gender).

However, other studies demonstrate that TM increases frontal alpha coherence

over time and they also demonstrate a statistically significant relationship with cognitive

skills. Therefore, the collective body of findings can reasonably demand explanation

from a neuropsychological perspective. I suggest that both the practice of TM and the

development of cognitive skills engage functions of transcending, or “going beyond”

current mentation (i.e., voluntary orienting) and integrating the new observation so that it

makes sense (i.e., habitutation of the orienting response).

Assuming that neurological conditions pose a necessary but not sufficient

condition, low levels of frontal activation may be one of several reasons for reports of a

low incidence of formal reasoning among high school and college students today.

Alternatively, we could suggest that individuals failing to attain formal reasoning

structures could be aided by enhancement of a “dominant focus” that supported a habit of

attention to task and habituation to distraction.

Note that the current research did not uncover any alpha coherence differences

between males and females that interacted with task performance. This was an

unanticipated outcome, especially surprising in light of known advantages in spatial

Piagetian tasks for males as given in the Chapter II literature review and known

interactions between gender and psychometric spatial skill in measures of coherence

(Petsche & Rappelsberger, 1992). In the current study, the two spatially oriented tasks

demonstrated no taskXgender interaction, only main effects: males performed

significantly better on the Shadows task and pass subjects demonstrated higher FLR-O

coherence index measures than fail subjects on the Vessels task. On the other hand, the

lack of statistical interaction between gender and task performance simplifies the

implications of the study, suggesting that the conclusions apply equally to males and

females.

The lack of a genderXtask interaction suggests that reasons other than lack of

coherence hold back development of formal reasoning for females in the Shadows task.

Such impediments could include any that have been given previously in the literature

such as lack of exposure to manipulative learning opportunities, imposed role

expectations, and genetic or gender-related predispositions.

In closing, I suggest that the current research and the accompanying theory sheds

light on Piaget’s advocacy of “active learning.” Physical action on objects necessarily

involves the student in different arousal and activation patterns than they experience

sitting in a chair, listening to a teacher. These learning situations culture (and require)

different dominant foci. Educators should provide “ecological validity” by giving

students opportunity to learn control of their arousal and activation patterns under

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varying problem-solving challenges. Brezin (1980) suggests that instructional design

techniques can benefit from knowledge of “cognitive monitoring,” i.e. metacognitive

awareness made explicit in the design of instructional materials.

All this suggests that a main challenge in education is development of self-

regulation of the orienting reaction (e.g., Pribram, 1979; and Jeffery, 1968). I suggest

that educational methods that remain “teacher-centered” unwittingly administer a

functional “frontal lobotomy” to the unsuspecting students. It appears that teacher-

centered instruction shortsightedly focuses on posterior functions, treating the student as

a passive receptacle of information. Knowledge gained without active and intentional

inquiry—a frontal activity—fails to become integrated within successively more

encompassing mental structures.

Without active and intentional inquiry, the student is more likely to fail to

decentrate from automatic responses and thus fail to transcend old schemata. Without a

dominant focus of intentionality, the student fails to orient to discrepant occurrences or

fails to habituate to non-task related distractions such as a felt need to “check with the

teacher” or gain “teacher approval” (e.g., Shymansky & Matthews, 1974, p. 166).

Piaget’s recommendation of “active learning” in which students interact with objects to

discover regularities and laws appears to exercise important frontal executive functions.

The student gains experience and confidence in letting go of preconceptions and thereby

experiencing a larger sample of “all possibilities.” This is an adaptive dominant focus.

Piaget’s elucidation of the “structured whole” suggests a new outlook on the

neurophysiological prerequisites to education. The current findings suggest that students

can learn to govern their own level of frontal and posterior arousal and activation by

learning a mental technique such as TM to enhance “restful alertness”. Alternatively, in

terms of the goals of science education, self-governance of frontal and posterior arousal

is probably best supported in a “student-centered” science curriculum.

The emphasis on development of purposeful (frontal) control of arousal and

activation by the subject also fits the “manifesto” regarding the proper use of visually

oriented instructional technology as stated by members of the Visual Scholars Program at

the University of Iowa. Cochran, Younghouse, Sorflaten, and Molek (1980) suggested

that

Research in cognitive approaches attempts to provide adequate treatments of internal order and adaptation to external order. Similarly, we believe that visual literacy research should proceed on two fronts: the characterization of the development of internal structures in cognitively valid ways and the characterization of the external structures the developing individual finds salient” (p. 261)....One axiom of the research approach we advocate is that research must recognize that humans are purposive and intelligent begins who, individually or collectively, make plans for action....Another axiom is that visual processes are mediating systems of noteworthy complexity...and not simply a neutral mechanism for the transmission of information (or instruction)....The study of visual literacy as the human ability or set of abilities to use visual processes as mediating systems must ...adopt a theoretical position than can encompass the purposive or intentional aspects of the use of visual processes and visualization (p. 263).

Recommendations for Future Research

The Question of Bilateral Occipital Coherence

A major topic has to now been postponed. This involves the developmental

significance of the bilateral occipital coherence measure (O). I suggest this is an area for

future research, but the recommendation follows from a perspective that both follows and

enriches the current findings. The topic has two boundaries that together, suggest a

model of brain functioning to support recent inquiries into “induced rhythms” in the

brain (Basar & Bullock, 1992). First, we note an inverse relationship between O alpha

coherence and performance on tasks of formal reasoning (as well as other indicators

reported above, such as GPA and creativity). Second, we note that longitudinal studies

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of subjects practicing Transcendental Meditation demonstrate an increase in bilateral

occipital coherence. Additionally, during periods characterized subjectively as

“transcendental consciousness” (sustained periods of awareness without thoughts), the

EEG record displays sharp and global increases in coherence, including bilateral

occipital coherence (Badawi, Wallace, Orme-Johnson, & Rouzere, 1984; Farrow &

Hebert, 1982). Behavioral correlates included spontaneous respiratory suspension

without being followed by significant compensatory breathing.

How is it that O alpha coherence on the one hand correlates negatively with a

psychological trait (e.g., formal reasoning) and yet on the other hand correlates positively

with a major indicator of the putative mechanism of developmental growth (e.g.

transcending)? The direction of research is indicated by the fact that the occipital lobes

do not, as far we know, share direct communication via the collosal connections, and

therefore, interhemispheric “transfer time much more likely depends on the association

areas where the stimulus is processed, and on the part of the corpus collosum that unites

these [association] areas” (Zaidel, 1986, p. 442). This implies that the frontal and

association areas support interhemispheric communication, whereas the occipital area

does not. Therefore, upon use of the frontal lobes, and in the absence of primarily visual

input (as in eyes-closed TM), it is reasonable to assume that brain activity is “pulled” into

coordination first on a homolateral basis, then bilaterally for more anterior regions, and

lastly, across the occipital lobes.

I call this a “tuning fork” model in which the tips of the tuning fork represent the

unconnected occipital lobes, whereas the fork of the tuning fork represents the more

anterior areas that have bilateral commissural connections. The fork portion of the

instrument will be the major junction between the otherwise independent frequencies of

each prong (this tuning fork has prongs of variable length!). Owing to the lack of direct

interconnection, the tips of each prong will vibrate more out of synchrony than the fork

portion. Meanwhile each prong will have its own independent frequency except as

checked by the influence of the fork. Analogously, coordination of activity within a

hemisphere is important and will lead to electrical activity that is homolaterally

organized. Activities include monitoring and controlling primary sensory areas that

initially process stimuli, processing in the association areas, and coordination within the

motor areas. All activity presumably falls under the control of prefrontal executive

activity to one degree or another, perhaps developmentally influenced. For example,

several studies support the notion that cognitive development is associated with

homolateral alpha coherence. Thatcher (1991a) suggests that “each cognitive stage is

marked by extended periods of equilibrium between competing and cooperative neural

networks punctuated by brief periods of dis-equilibrium....Among the most dominant

cortico-cortico connections are those that develop between different regions of the frontal

cortex and posterior intracortical regions.” Thatcher, Walker, and Giudice (1987) trace

the developmental sequence of homolateral coherence (.5 to 22 Hz) in 577 subjects

between the ages of 2 months to early adulthood (26+ years old). They concluded that

coherence between frontal and various homolateral posterior regions increased in a

developmental sequence. They suggest that “spurts” in the rate of increased coherence

“overlap quite well with the timing for the Piaget theory of human cognitive

development.” In a further exposition of these developmental processes, Thatcher

(1991b) suggests that

the frontal lobe developmental spectrum is consistent with models of the frontal lobes that postulate an executive type function that is called into operation for novel and task demanding situations, especially when task demands exceed the capacity of current categories of experience and action....[D]evelopmental growth spurts result in a relatively sudden increase in the neuronal capacity of a subset of frontal lobe connections. (p. 415)

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Further discussions along similar lines are available in Thatcher (1992), Case

(1992), and Hudspeth and Pribram (1990). Although not Piagetian oriented, Gasser,

Jennen-Steinmetz, Sroka, Verleger, and Möcks (1988) identify developmental coherence

increases among subjects from 6 to 17 years of age. They classify 3 components of

change: overall level of coherence, coherence of occipital with all other regions, and

anterior-posterior versus left-right coherences.

Given these findings, it is no longer an issue that homolateral coherence

accompanies human growth. However, links to developmental stages made by Thatcher

et al., Case, Hudspeth, and Pribram are currently inferential, based on ages assumed to

represent pre-operational, concrete, and formal reasoning. The current research is the

first study to actually link tests of Piagetian cognitive development with increases in

homolateral L and R anterior coherence. The current study has also shown that clinical

Piagetian tests give results not otherwise available from pen and paper tests of Piagetian-

defined reasoning skills. Obviously, in light of this momentum in tracing neurological

development in a Piagetian context, it seems reasonable to suggest follow-up studies

using clinical tests of Piagetian-defined reasoning, and link them with studies of EEG

coherence development.

To guide future research, I hypothesize that three stages of coherence reflecting

“whole brain” functioning could be identified, at least in subjects practicing TM,

following the “tuning fork” model. That is, upon cognitive task demands (e.g., TM), the

first stage will reflect homolateral coherence increases. These increases causes the “free”

ends of the tuning fork model (posterior lobes) to assume the frequency characteristics of

the more anterior portion of each hemisphere (this is essentially the definition of

increased homolateral coherence). First stage activity will therefore be evidenced by

decreased bilateral occipital coherence representing the fact that the free “ends” of the

tuning fork are pulled into synchrony with their respective anterior hemispheric

executive functions (Cf., Tucker, 1987). Recall the findings of Berkhout and Walter

(1980) in which decreased posterior interhemispheric coherence resulted from behaviors

that tended to increase levels of arousal (i.e., cognitive orienting).

The second stage involves anterior bilateral coherence in which each hemisphere

takes on the frequency characteristics of the other, indicating integration of left and right

representational modes (Cf., Goldberg and Costa, 1981) (this is essentially the definition

of frontal bilateral coherence). This activity will be evidenced by increased bilateral

frontal coherence as well as possible slight increases or no change in bilateral occipital

coherence.

The third stage occurs when frontal bilateral and homolateral coherence is

sufficiently strong as to completely control the primary sensory areas, thereby causing

the anterior frequency characteristics to be reflected in the “ends” of the tuning fork.

This activity is represented in the sudden and dramatic global increase in coherence

across all frequency bands and brain regions during subjective reports of “transcendental

consciousness.” The fact that subjects experience spontaneous respiratory suspension

suggests the widespread nature of influences, which in the case for breathing appears to

be inhibitory. The global coherence could represent the framework for supporting

coordination required to “bind” functional components of thought (Cf., Damasio, 1989).

Component theorists have made significant progress in demonstrating the “distributed”

nature of mental functions, especially visuospatial (e.g., Kossyln, 1987; Posner, Inhoff,

and Friedrich, 1987; Mesulan, 1981; and Farah, 1984, 1988).

The Question of Information Transfer

Any discussion of optimizing brain function must cope with issues surrounding

the question of “how does the brain communicate within itself?” Some researchers such

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as Sheppard and Boyer (1990) suggest that EEG coherence reflects “information

transfer.” Apparently the nature of “transfer” is indicated by the definition of coherence,

which states that two spatially separated points on the scalp share electrical activity at an

identical frequency for a specified period of time. However, it is reasonable to ask, if the

frequency remains the same, how is information, i.e., variation in a signal, transferred?

Topics covered under the rubric of “induced rhythms” in the brain attempt to address this

issue, e.g., Basar, Basar-Eroglu, Parnefjord, Rahn, and Schurmann (1992). In general,

researchers point to phenomenon such as 40 Hz “oscillations” that are highly organized

in space and time across the entire scalp. Llinaas and Ribary (1992) suggest that

“ultimately this coherent 40-Hz activity may serve as the basis for the conjunctive

property that characterizes the unity of cognitive experience....We hypothesize that this

coherent sweep of 40-Hz response could reflect a scanning of the brain with a focus on

the activated sensory area in order to generate a single percept from multiple sensory

components.” (p. 153).

Similarly, Eckhorn, Schanze, Brosch, Salen, and Bauer (1992) indicate that their

research on the cat shows that synchronization “forms the basis of a flexible mechanism

for feature linking in sensory systems...by synchronizing the activities of those neurons

that are activated by a coherent visual stimulus” (p. 47). These authors suggest that the

brain supports a specific network for generating synchronizing signals, and that authors

who speak of a similar need for “binding” brain functions, such as the University of Iowa

medical researcher Antonio Damasio (1989), get support for their theories in findings

that indicate synchronization of stimulus-related brain activities (see also Buzsáki, 1991).

For example, Damasio suggests that consciousness is a function of the entire brain...

Posterior cortices require binding mechanisms in anterior structure in order to guide the pattern of multiregional activations necessary to reconstitute an event...Processing does not proceed in single direction but rather through temporally coherent phase-locking amongst multiple regions. Although the

convergence zones that realize the more encompassing integration are placed more anteriorly, it is activity in the more posterior cortical regions tthat is more directly related to conscious experience....

It is not enough for the brain to analyze the world into its components (sic) parts: the brain must bind together those parts that make whole entities and events, both for recognition and recall. Consciousness must necessarily be based on the mechanisms that perform the binding. The hypothesis suggested here is that the binding occurs in multiple regions that are linked through activation zones; that these regions communicate through feedback pathways to earlier stages of cortical processing where the parts are represented; and that the neural correlates of consciousness should be sought in the phase-locked signals that are used to communicate between these activation zones (pp. 129-130).

While 40 Hz and similar high frequencies have been observe in this role, a

companion study of computer models of feature linking mechanisms suggests that alpha

frequencies also play a role. Eckhorn, Dick, Arndt, and Reitbroeck (1992) built

computer models of neural network stabilizing mechanisms that enabled simulations of

EEG phenomenon such as “isolated bursts” as well as rhythmic behavior. Their models

demonstrated that rhythmic activity results even under conditions of irregular

stimulation. This suggests for these authors that rhythmic linkages among regions can

actually served to enhance stimulus registration. Phase shifts in the linkages serve to

magnify or reduce the strength of response to a stimulus.

Basar, Basar-Eroglu, Parnefjord, Rahn, and Schurmann (1992) found that human

rhythmic 10 Hz (alpha) activity increases under certain conditions, and is associated with

improved performance. “[D]uring cognitive tasks, it is possible to measure almost

reproducible EEG patterns in subjects expecting defined repetitive sensory stimuli.

While paying attention to an omitted stimulus, the subjects probably anticipated with 10-

Hz waves time-locked to the stimulus, showing almost reproducible patterns” (p. 172).

All of this work suggests that rhythmic activity plays a role in coordinating other, non-

rhythmic activity. At least two hypotheses have been suggested, such as “linking

networks,” as explored in the computer models by Eckhorn, Dick, Arndt, and Reitbroeck

(1992) and the notion that EPs are a superposition of evoked rhythmicities, as explored

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by Basar, Basar-Eroglu, Parnefjord, Rahn, and Schurmann (1992). However, there still

remains a missing link in the question of what is the mechanism that underlies the

adaptive value of global EEG coherence, especially alpha, as found by these researchers

and in the phenomenon of the transcending reflex?

Investigators of the alpha wave have, at times, suggested that the role of the alpha

rhythm may be to serve as an “neuronic shutter,” or a gate that admits or ignores

incoming synaptic impulses, thus organizing the process of information transfer into

orderly packets of regular transmission exchanges. This hypothesis is also studied in the

context of a “scanning model” or “cortical excitability cycles” (Harter, 1967). For

example, visual stimuli can be presented at different portions of a single alpha wave

cycle, and it will be seen with greater or lesser probability, depending on the phase of

presentation. Nunn and Osselton (1974) used GSR measures (a typical OR measure) to

detect responses to a word (“Danger”) that was presented briefly (30 msec) and then

masked with a bright flash, thus in most of the 12 trials, obscuring conscious perception

of the word. Evaluation of the GSR response at each of four phases of the alpha cycle

indicated that perception of the word (increased GSR) occurred statistically significantly

more often “at a descending phase or trough in the parietal-occipital channels, and when

it occurred at a descending phase, trough, or ascending phase in the frontal-occipital

channels” (p. 300). Of interest in terms of preattentive models of selective attention that

I have proposed, the authors point out that

conscious perception was not necessarily involved because Shevrn and Fritzler (1968) have shown that unconscious percepts can be encoded in the visual evoked response, while experiments quoted in the introduction indicate that this response varies according to the alpha phase at which the stimulus is presented (p. 301).

Other studies have suggested further refinements. For example, it appears that

excitability cycles apply much less to reflex action generated by the subject compared

with reports of positive findings with perception of incoming stimuli (Boxtel, 1979).

Shevelev, Kostelianetz, Kamenkovich, and Sharaev (1991) found that the phase of alpha

sensitivity depends on visual parameters such as the number of degrees the figure appears

in the visual field away from the direct line of vision as well as the visual angle, or size,

subtended by the figure. Varela, Toro, John and Schwartz (1981) found that two lights

flashed with small intervals between them varied in being perceived as simultaneous or

sequential. The lights were more likely to be perceived as simultaneous during the

positive phase of the occipital alpha cycle. The authors conclude with an outline of the

postulated neurophysiological functions involved and suggest that

the connections of cortical afferent (and efferent) signals might be synchronized via the temporal course reflected in the local alpha rhythms, providing an integrative mechanism over extended regions of the brain. For two visual stimuli to be perceived as separate in time, it seems that they must occur across the temporal boundary provided by this cortical activity (p. 684).

Rice and Hagstrom (1989) found an auditory equivalent to the above research in

visual stimuli, thus laying to rest the criticism that any findings in the visual modality

could be attributed to eye tremor, which is correlated in phase and frequency with the

alpha rhythm. They found that auditory detection was significantly better at the negative

peak of the alpha cycle at the temporal derivation T5.

In summary, I propose that future research investigate cognitive correlates to

EEG coherence taking into account the “excitability cycle” hypothesis and its more

general forms discussed under the rubric of “induced rhythms” that coordinate global

brain functions. This implies that research can begin to define a consistent system of

functions that support cognition from not only from the level of global coherence, but

also from the level of electrical activity at the cell. This research would probably find

that self-regulation in many cases consists of changing frequency and phase relationships

between brain areas, thus altering their excitability levels. As is known from bio-

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feedback and TM research, subjects indeed can change EEG frequency and phase

relationships at will under conducive situations.

Future research can delineate the processes of cognitive growth in terms of the

development of EEG self-regulation. Several lines of thought already converge in this

direction. Human factors studies of performance under conditions of stress look towards

a taxonomy of stress states (Hockey & Hamilton, 1983). Sanders (1983) links arousal

and activation stress patterns to neurophysiological substrata initially proposed by

Pribram and McGuinness (1975) (also McGuinness and Pribram, 1985). Grones and

Thompson (1970), as well, cite early expressions by Pribram of the same theory in their

exposition of the dual process theory. Dual process theory holds that orientation

(“sensitization”) and habituation are independent processes for which neurophysiological

evidence can be adduced.

The oft-cited model presented by Pribram and McGuinness has found

considerable following. Lateralization has been linked to their mechanisms of “self-

regulation” by Tucker and Williamson (1984) as well as by Sanders (1983). Similarly,

Simonov (1984, 1985) suggests mechanisms of self-regulation in terms of a calculus of

motivation in contrast to “drives,” again linking his theory to the same

neurophysiological substrata given by Pribram and McGuinness. In each case, the

substrata links frontal structures to whole brain function. For a clear picture of this

approach specifically in the study of Piagetian formal operational reasoning, see

McGuinness, Pribram, and Pirnazar (1990).

CHAPTER VI

TOWARD A NEUROPSYCHOLOGY OF EQUILIBRATION (ADDENDUM TO THE ORIGINAL DISSERATION)

Orienting and the “Transcending Reflex”

As discussed in Chapter V, Arenander (1986) suggests that the process of

transcending can be understood in the framework of the orienting response (OR). The

current chapter explores the implications of this claim in greater physiological detail,

meanwhile organizing evidence across a range of literature that suggests a strong link

between OR phenomenon and intelligence, or cognitive success in general. The

mediating mechanics of the linkage will be shown to be EEG evoked potentials and their

relationship to coherence, particularly alpha coherence. This implies that the practice of

TM may strengthen the voluntary OR phenomenon that underlies intelligence. This

enhancement of the voluntary OR is hypothesized to occurvia the mechanism by which

EEG coherence reduces variability among averaged evoked potentials associated with a

particular stimulus.

The primary effect of the OR, as indicated in the general research (Lynn, 1966),

is to increase the sensitivity and speed of the sensory system, and to increase the signal-

to-noise ratio of the mental processing. While the OR is normally associated with

external, novel stimulation, it can also be elicited by attention to stimuli with subjective

significance or by attention toward a goal (Cf. Gruzelier & Eves, 1987). The theory of

the OR, and particularly the internally generated OR, contributes to our understanding of

the “transcending reflex” as outlined in the following summary of Arenander’s

presentation to the Society for Neuroscience Annual Meeting (1986).

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First, Arenander suggests that during TM, the individual alternates experiences of

orienting and habituation. Various brain systems control the process such that a state of

alertness is maintained, while the physiology experiences more and more de-excitation.

Second, the mantra (or other thought) is the focus of attention and is analyzed in

the appropriate thalamocortical channels related to the various senses. The hippocampal-

based comparator seeks a possible match to the mantra (or other thought) and generates a

match or mismatch outcome, based partially on the significance of the stimuli.

Third, when a match is determined (usually the mantra leads to a match) then the

comparator signals other brain areas. The basal forebrain system (BFS) activates to

accomplish internal inhibition (II) and the mesencephalic reticular formation (MRF) and

associated brain structures are shifted into the oscillatory mode that reduces their internal

excitation (IE) role. The oscillatory mode gives rise to the observed increases in slow

EEG waves including alpha coherence. This functions to reduce thalamic responsiveness

to incoming sensory information, much as in the case of habituation to a stimulus. The

de-excitation associated with the match gives rise to transcending. Note that activation

of the BSF has been shown to induce sleep behavior and EEG synchronization, similar to

results of classical conditioning (habituation) paradigms. BFS stimulation has also been

shown to induce respiratory arrest in primates and human. Respiration suspension has

also been found and experimentally measured during TM related to subjective reports of

transcending (Kesterson, 1986; Farrow, & Hebert, 1982; Badawi et al., 1984).

Fourth, when a mismatch is detected the opposite occurs. The II system

deactivates and the IE system activates. Typically this brings the awareness to the level

of excitation required to repeat the process of transcending. Arenander suggests that the

flow of attention can be quite complex and could result in daydreaming unless the

prefrontal cortex asserts an influence by a) controlling thought-provoking interferences

that give rise to distractions and b) providing a cognitive plan to guide the attention (i.e.,

the instructions for TM). He points to the research that indicates increased frontal

coherence with the practice of TM. Frontal coherence and increases at other derivation

pairs occur because of changes in thalamocortical “temporal integration” (i.e., EEG

coherence) which in turn depends upon prefontal cognitive functions. The

thalamocortical activity may be reorganized, Arenander suggests, through the repetition

of orienting and habituating during TM so that it supports a more distributed and

integrated mode of processing. The enhanced distribution and integration are reflected in

the reported increased spread of coherence across the brain in subjects participating in

longitudinal studies. Although low activation of the thalamus (inhibition) normally

would lead to loss of awareness (sleep), the increased connectedness of the brain permits

maintenance of awareness with the added benefit of increased allocation of brain

resources for stimulus evaluation. The thalamus contributes to high levels of cortical

coherence through the mechanism of the nucleus reticularis thalami (NRT). The NRT

exerts inhibitory influences on the thalamocortical sensory circuits by increasing its

oscillatory behavior. Such NRT-thalamus feedback loops are reinforced by the cortico-

thalamic discharges back upon the NRT and thalamus creating a stable basis for shifts of

attention during the TM process.

Note that Arenander suggests that the OR and habituation alternate. However,

other investigators (Thompson, Berry, Rinaldi, & Berger, 1979) suggest a “dual-process”

trend in which sensitization of the OR can occur independent of habituation to repeated

stimulus. This causes two independent processes in the nervous system: habituation in the

reflex pathway and a more generalized sensitization of the “state” of the system. These

results suggest that sensitization may even serve as a necessary substrate for more

complex forms of associative learning (p. 37). This model could possibly provide a

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mechanism for Sokolov’s “stimulus-model formation process,” according to the authors.

This dual process model supports the notion of the co-existence of two opposing states,

“restful alertness,” during TM more intuitively than the alternation of orientation and

habituation.

Fifth, overall, the individual experiences the alternation of ORs (according to

Arenander) and transcending (habituation) leading to progressively less excited states of

the central nervous system. Arenander notes that to maintain conscious awareness (and

not fall asleep), the MRF activity cannot be reduced completely. The maintenance of

MRF activity may result from the ORs that continue to be re-evoked as the attention

repeatedly shifts.

Sixth, Arenander outlines the mechanisms of selective attention in greater detail.

In addition to any pre-defined task sequence, a direction of thought can also be defined

by the affective or motivational valence attributed to a particular stimulus or thought.

Cognition and affect are linked by the amygdaloid complex (AC), acting as part of the

limbic system. The AC can associate “reward” stimulus thereby giving it an affective

“match” and transferring it to the hypothalamus and BFS, leading to inhibition of the

physiology. The AC can also control cortical orientation by affective loading of selective

attention on the increased significance of lesser excited states of thought, leading to alert

awareness even while relaxed.

Seventh, focus of attention may also be aided by the activity of the locus

coeruleus (LC), known to control the ongoing state of the brain and behavior such as

wake and sleep. The LC acts to inhibit most neuronal cells in preparation for sleep state.

Arenander suggests that the LC may facilitate states of less physiological excitation that

appear in transcending. For example, reduction in the spontaneous activity of a cell

receiving an impulse dramatically increases the signal-to-noise ratio. Thus, the ORs that

do arise would be detected at earlier stages of processing, thereby biasing the thalamo-

cortical structures towards supporting the focus of attention on transcending as well as

ignoring distracting stimuli. The LC, then, helps maintain high vigilance during the de-

excited state of the brain and contributes to enhanced reliability and efficiency of feature

extraction during shifts of attention. Perhaps of greater interest is the outcome of recent

studies on the LC that suggest its role in cortical learning and plasticity. Arenander

suggests that the activation of the LC during transcending may modify the

thalamocortical system to allow new modes of neural organization to function during

ordinary activity. “Long term enhancement of brain function corresponding to least

excited states may support the conscious appreciation of a wider range (vertical) of

cognitive activity outside of meditation” (Arenander, 1986). Evidence supporting this

conjecture follows.

In summary, Arenander’s “transcending reflex” is hypothesized to increase the

EEG coherence in a fashion that enhances the adaptive functions of the brain. What

additional support can be given for Arenander’s model? Let us examine other evidence

regarding orientation and habituation in relation to cognitive aptitudes.

The Adaptive Significance of the Orienting Response

In her presidential address to the Pavlovian Society, Kimmel (1985) discussed the

“functional stability of the nervous system: a neurobiological basis of intelligence,” and

suggested that such functional stability may be modified by experience. Among other

evidence for a neurobiological basis for intelligence, Kimmel reports that gifted

intelligence children maintain larger and more persistent orienting responses (ORs) in the

form of skin conductance responses to visual stimuli than do average intelligence

children (DeBoskey, Kimmel, & Kimmel, 1979). Kimmel draws the concept of

”functional stability” from the work of Nebylitsn, who in turn joins Pavlov’s idea of

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strength of the central nervous system (CNS) with Teplov’s concept of CNS “weakness”

or high reactivity to stimuli. Strength, in this case, refers to the “ability of the system to

continue responding under repeated stimulation.” Weakness refers to “the more sensitive

CNS (that) may be changed from a state of rest to one of catabolic, or destructive,

activity by extremely weak stimuli” (p. 59). Kimmel writes: “Strength and sensitivity

both are reflections of the same property of the CNS....Where strength is manifested in

the ability to tolerate excitation without reduction in response, sensitivity is manifested in

an instability and vulnerability to outside influences” (p. 60). According to Kimmel, a

well-known researcher of OR and habituation phenomenon, contemporary measures of

the functional stability of the CNS are the resistance to habituation over many repetitions,

and the continued positive magnitude of the OR, both shown to be significantly

correlated with intelligence measures.

ORs Support Cognitive Success

Kimmel (1985) gives examples where intelligence measures have been influenced

by training or motivation. In DeBoskey, Kimmel, and Kimmel (1979), money was

paired with an OR-eliciting stimulus (a geometric form that changed shape or color in

each trial) for the experimental group, while the control group received no reward for

observing the stimulus. Half of each group was average intelligence (mean of about 101

IQ) and half was gifted children (mean of about 145 IQ). Mean age was about 10 years.

Among both groups, the rewarded children maintained ORs with greater magnitude

implying that motivation enhances attentiveness towards successful performance. The

gifted children made lesser increases in OR, perhaps manifesting a ceiling effect not

experienced by the average children for whom monetary incentive did cause a gradual

increase in OR changes over the 18 trials. This evidence of “plasticity” (i.e., changes in

ORs) in CNS functional stability must be viewed with some caution, according to

Kimmel, given only a few and inconclusive studies.

However, not mentioned by Kimmel, Zeiner’s (1979) study reported a significant

correlation of r = .47 between OR magnitude (skin resistance response) and four-year

cumulative college GPA among 19 subjects preselected for high and low ORs. Zeiner

suggests the results indicate that the OR is an objective index of attention, which is

related, in turn, to academic performance. Zeiner also notes that his high OR subjects

were biased towards science majors (math, physics, electrical engineering, and

psychology). The low OR subjects selected majors in Spanish, physical education,

dance, and business.

ORs may reflect when individuals respond to attentional challenges not only

momentarily, but habitually as in the case of gender-related predisposition. For example,

Castelman, Brennan, and Kimmel (1979) studied a visual-spatial task of field

independence, the Embedded Figures Test, in relation to gender differences in auditory-

evoked ORs. They found the predicted higher performance in males on the EFT, and

also slower habituation across trials upon listening to three randomly alternating tones.

While there was no correlation between habituation rate and EFT performance, the

authors ventured to speculate that the females habituated faster to the varying tones

owing to acculturation–socialization history and environmental factors.

The emotionally sterile laboratory environment may have been intrinsically less interesting to the females, which would cause the stimuli to be perceived by them as irrelevant or inconsequential, while appearing to the males as a part of the problem to be analyzed (p. 663).

The authors also report prior research in which males displayed higher skin

conductance responses to visual stimuli than females presumably for similar reasons,

although they indicate that the male physiology may also be responsible.

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More specific to the attentional role of ORs, Maltzman (1979b) finds evidence

indicating that the “signal value” of a stimulus can be non-verbal, as well as verbal in a

problem-solving situation. He discusses at length findings of Russian researchers that

link stages of chess game problem solving with OR-related changes in the GSR. In

seven cases, the GSR occurred simultaneously with the verbal solution, but in 31 cases, it

occurred perhaps a minute or so prior to the verbal solution. This suggests that variation

of problem-solving schema may be related to OR phenomenon, which have also been

shown to vary across individuals relative to their cognitive skills. Maltzman (1979b)

relates Luria’s clinical research that the voluntary OR depends on the normal functioning

of the prefrontal cortex, loss of which leads to loss of normal ORs and purposive

behavior. EEG changes were shown to be different, as well, for frontal patients

compared with posterior-lesioned patients. Posterior patients show deficits in the

reception and processing of auditory, tactual, or visual information. But their goal-

directed or purposive behavior is relatively intact. In contrast, patients with lesions in the

prefrontal cortex show a deficit in voluntary or goal-directed behavior, although their

speech and the reception and processing of sensory information are relatively intact (p.

329).

Relating these ideas of CNS functional stability and training to Arenander’s

transcending reflex model, it can be hypothesized that during TM the individual develops

the neurophysiological prerequisites for enhancing resistance to habituation and for

generating continued ORs to stimuli to which significance has been attached. Among

TM subjects, these changes have been reflected physiologically in longitudinal increases

in anterior coherence and psychologically in longitudinal cognitive improvements as

described in Chapter II. I suggest that the experience of TM conditions the mind to adopt

a mental set whereby preattentive mechanisms separate “task” stimuli from distracting

thoughts, creating for the subject a voluntary OR when exposed to the thought of the

mantra (an intentional thought), and habituation when exposed to distracting

(unintended) thoughts.

This preattentive mechanism may carry over into daily activity, thereby giving

rise to the increases in cognitive skills listed above. For example, Öhman (1979)

describes the relation between OR and preattentive mechanisms, suggesting that

identification of a stimulus does not require central processing. Unattended stimuli can

be completely processed, such as detection of one’s own name or becoming influenced

by an unattended verbal source when interpreting the meaning of the attended phrase (p.

448). The results of preattentive processing can lead to activation of the central attentive

processors in two cases: when the “mismatch” of stimuli and short-term memory

representations appear to have adaptive consequences, or when the “match” identifies the

stimulus as significant.

In the current study, the fail groups’ relatively poorer performance on the spatial

tasks, Vessels and Shadows, may result from failure of preattentive processes to identify

the INRC group operations as salient to the subject. The lack of salience may result from

lower ORs that in turn result from an inability of the brain substrata to support attentive

ORs in the hemisphere devoted to visual-spatial representations, typically the right

hemisphere. Note that the lack of salience could also be partially an outcome of personal-

historical influences during development (e.g., parents do not encourage any INRC group

activities).

See de Pibaupierre (1989) for a discussion of individual differences in acquisition

of Piagetian operations, particularly differences that tend to be dichotomized by INRC

group vs. combinatorial lattice operations. Another dichotomy appears to be verbal vs.

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spatial. Taken together, there appears to be “at least four different says to enter the

formal operational stage” (p. 89).

Stable Evoked Potentials Support ORs

In the same address mentioned above, Kimmel also discusses evidence of

“functional stability” from studies that related intelligence and EEG, in this case, evoked

potentials (EPs). She points out that Hendrickson and Hendrickson (1979) demonstrated

correlations of .773 between intelligence and a measure of auditory-evoked potential

(AEP) complexity—the total length of positive and negative excursions of the AEP,

called the “string measure.” The clarity of the peaks and troughs of a set of averaged

AEPs are a function of the stability or nonvariance in their shape across the numerous

trials required to obtain the AEP. This suggests that low intelligence results from the

random transmission errors that hypothetically destabilize the timing of the peaks and

troughs of the AEP, presumably the result of a “functionally unstable” CNS. These

random errors then smooth out the peaks and troughs, thus “shortening” the positive and

negative excursions. The above correlation may be an overestimate due to the use of

groups of predetermined high and low IQ children. However, a follow-up study of adults

with the Raven’s Advanced Matrices test found a correlation of .47, perhaps attenuated

owing to a limited range of IQs.

As evidence of “plasticity” of CNS orienting capabilities, Kimmel reports several

instances where the habituability of evoked potentials was modified either using

instructions to perform a task, which postponed habituation indefinitely, (i.e.,

maintaining an OR)., or using biofeedback to directly influence a visible segment of the

AEP. The feedback paradigm, incidentally, improved subjects’ ability to detect and

locate visual stimuli, which Kimmel interpreted to indicate greater sensitivity to “weak

stimuli” in Teplov’s sense. However, we must recall that increased sensitivity is a

hallmark of the OR in general. Kimmel’s address offers much to the current discussion.

The several topics will be addressed in order, and then taken up from the perspective of

the “standard cognitive state” (TM) used in the current research.

IQ and Evoked Potentials (EPs) in Relation to Orienting of Attention

While much can be found to criticize in the Hendrickson and Hendrickson work

(Stowell, 1985) and although some studies have failed to replicate the findings (Shagass,

Roemer, Straumanis, & Josiassen, 1981; Vogel, Kruger, Schalt, Schnobel, & Hassling,

1987), there still remains compelling evidence regarding neural correlates to IQ that

motivates continued investigation (see Chen & Buckley, 1988, and Mackintosh, 1986 for

reviews). For example, Haier, Robinson, Braden and Williams, D. (1983) found that

stimulus intensity for visual-evoked potential research was systematically related to the

degree the evoked potential (EP) correlated to intelligence (Raven’s Advanced

Progressive Matrices test), perhaps explaining some of the inconsistencies in previously

reported studies. Under optimum intensity conditions, these writers found correlations

up to .5 for the string measure and up to .59 for P200 amplitude, and up to .69 for the

peak-to-peak excursion between N140 and P200. (Note: “P200” is the postitive peak that

occurs roughly 200 msec after stimulus onset. “N140” is the negative peak that occurs

roughly 140 msec after stimulus onset.) They also concluded that the string measure was

explained primarily by the N140/P200 excursion with a maximum correlation of .80

between the two.

Haier et al. (1983) identify several sources of the imputed IQ/EP relationship.

Both of them relate to Kimmel’s concept of “functional stability” as reflected in less

variability among EPs. First, other studies report that high-IQ subjects demonstrated

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more stable waveforms across the EP samples than low IQ subjects. The authors suggest

these findings are analogous to the EP differences between the IQ groups that is

produced by the more intense stimulation: for both cases, higher IQ and increased

intensity, the N140-P200 excursion is greater. The excursion is greater due to less

variation among the EP samples (i.e., greater “stability”). Second, other studies indicate

that the EPs can be affected by “state” changes or the deployment of “attention,” as well

as stimulus intensity. Each point is developed in the following. Both points suggest that

CNS functions determine how well the subject attends to significant stimuli.

Regarding the first point, Haier, et al. suggest that the influence of intensity in

discriminating IQ levels “supports the view that higher intelligence is a consequence of

greater activation in general of central processes (mediating N140-P200 amplitude in

particular) in response to normal levels of stimulation.” They cite support from

Robinson (1982a, 1982b, 1983) who found that WAIS performance scores and

Embedded Figures Test scores were positively related to a measure of “balance” in

strength, as defined in Pavlovian terms. Robinson defined “balance” by measures of

cortical responsivity to a large-field, diffuse illumination that is sinusoidally modulated at

various frequencies. Robinson suggests that his statistically significant results link the

optimum function of the diffuse thalamocortical system (DST) with optimum balance of

excitation and inhibition, as represented in Pavlov’s concept of CNS “strength.” In other

words, the EEG amplitude (at Pz) is driven neither too much nor too little by variations

in the light source. Said another way, with “balance,” the CNS neither orients too little

nor habituates too much to stimuli.

Based on these results, Robinson suggests that CNS “balance” influences

variation in psychological style among his subjects: field independence (Embedded

Figures Test) and intelligence (WAIS performance test), both indicators of

discrimination skills. Robinson suggests future research into the relationship of WAIS

subtests with “different patterns of DTS mediated background activation of the cerebral

cortex,” suggesting specifically future research with EEG coherence. Of course, this was

the general intent of the Thatcher (1983) and Hernandez (1985) studies or any study,

including the current study, that investigates links between EEG coherence and cognitive

individual differences.

Haier et al.’s second point suggests attentional factors play a role in the strength

of the OR. This implies that “strength” of the CNS (ability to sustain the OR) must take

into account the notion of the “significance” or “voluntary” OR. (Olst, Heemstra, &

Kortenaar, 1979; Maltzman, 1979 a,b). Also, “weakness” (susceptibility to stimuli) must

take into account whether the stimulus is indeed salient or whether it is distracting (for

which the ability to habituate the OR would be best). In both cases, the notion of a

direction of attention becomes important. Direction, or selectivity of attention, is

controlled by the subject’s level of development. The adult has far greater resistance to

distraction, and far greater access to goal-directed attention, than the child (Stuss, 1992;

Cooley and Morris, 1990). The adult is far more capable of “gating out” such

distractions. In Piagetian terms, selective attention in the service of a goal would be

called “anticipation” whereas the ability to resist distraction (defined as non-goal

directed) would be called “decentration.” These terms will be discussed in greater detail

below. First, let us examine the background for this higher-level understanding of

“gating out” of distractions--also known as decentering.

Gating Out Distractions

Waters, McDonald, and Koresko (1977) explore the behavioral implications of

gating mechanisms by addressing the question of whether selective attention consists

solely of the ability to maintain strong ORs in the face of repeated stimulation, or

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whether it also requires the ability to habituate to distractions “whereby irrelevant and

distracting stimuli are ‘gated out’ (removed from attention and further processing)” (p.

229). To test this hypothesis, the authors compared four groups on their ability to

respond with a correct answer after listening to a taped male voice reading simple

mathematical problems. Various measures of autonomic reactivity evaluated the strength

of the OR throughout the experiment. The groups differed in the type of distraction

(female voice, 500 Hz tone, none) during the math problems and in amount of prior

opportunity to habituate to the distraction. The results indicated that prior habituation to

stimuli that later became distractors resulted in better task performance and resulted in

less skin resistance fluctuations than subjects performing undistracted. The authors

conclude that the process of attention is

at the very least a dual process. One, an attention facilitation process, likely involves the sensitization of responses (phasic and tonic ORs) that enhance sensory reception, arouse the organism for energy expenditure and action on stimuli, and prepare the organism for central processing of further input. Attention facilitation responses are most probably elicited by stimuli labeled as salient, perhaps on the basis that they are part of an active reinforcement contingency (Mackintosh, 1975). It is this attention facilitation process that has been the primary focus of psychophysiological research on attention (c.f., Raskin, 1973). The other process, an attention inhibition process, likely involves the habituation of responses that enhance sensory reception, arouse the organism for energy expenditure and action on stimuli, and prepare the organism for central processing of further input....Interaction between attention facilitation and attention inhibition processes would enable selective attention (p. 235).

These “gating” functions represent activity conducted by the anterior portion of

the cortex, the frontal lobes. For example, Brunia (1993) extends Skinner and Yingling’s

(1977) model for control of sensory input to include control of motor outputs. The

frontal cortex selects input or outputs by activating inhibitory neurons associated with the

unwanted input or output, thus leaving the selected pathway uninhibited. This resultant

access to the cortex from the thalamus is manifested as a local cortical arousal.

“Selection implies excitation within an environment of inhibition...Thus, the

investigation of motor preparation and attention will reveal signs of both excitation and

inhibition” (Brunia, 1993, p. 328). Thus, while the previous discussion of cognitive

excitation and inhibition could refer to “alertness,” (a cognitive feature), Brunia’s model

of motor excitation and inhibition could refer to “restfulness” (a motor feature). The

transcending reflex, then, could shift various regulation mechanisms in the direction of

co-existing “restful alertness” with subsequent positive effects.

Mackintosh (1986), looking critically at various psychophysiological measures

that seem to correlate with IQ such as reaction time, the “string measure,” or inspection

time, suggests that they may reflect differences among subjects in concentration or

sustained attention, a more “basic” function that the other measures reflect to varying

degrees. An obvious candidate for this more basic function is selective attention, with

OR and habituation mechanisms supporting it. Regarding the string measure in

particular (Cf. Haier et al., 1983, discussed above), Mackintosh observes that the

variance among the EPs correlates with IQ as highly as the string measure of their

average (r =.72 for the string measure and r =-.72 for the variance) implying that the

variance indicates variation of attention. Makintosh confirmed this inverse relation

between variance and IQ by finding lower correlations between IQ and string length

calculated on each individual trial (r =.52, significantly different than r =.72). This

implies that relative to IQ, the cumulative measure of EPs reflects attentional variance

more than the single EP reflects brain function. Mackintosh also points out that the

standard deviation of reaction time holds up as the best correlate of g (general

intelligence) in relatively homogeneous groups at a variety of ability levels, with r’s

from -.3 to -.45. The simplest explanation for each of these findings, according to

Mackintosh, who indicates confirming studies, “is an association between IQ and

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willingness or ability to maintain concentration on a routine task” (p. 14). Again, this is

a function of maintaining OR to significant stimuli, which, in turn, is a function of the

anterior, frontal cortex.

Further evidence comes from Segalowitz, Unsal, and Dywan (1992) who

compared 18 “bright” 12 year-old children with 22 normal peers on skills related to

executive functions associated with the prefrontal area, simple attention and memory

tasks, and auditory oddball P300s, among other measures. Twenty-two adults (mean age

of 32.5) provided a second control group on the EP data. Congruent with the discussion

above regarding Kimmel’s concept of “functional stability” and EPs, the P300 amplitude

correlated significantly with scores on the vocabulary test from the WAIS-R measured

across both groups of children. Relative to the above discussion of EP variance, the

researchers found that among the normal group of children (and the combined groups of

bright and normal children) the P300 “amplitude jitter” was significantly less for those

who show better performance on the frontal measures (r’s ranging from -.42 to -.56).

The authors find that the stability of the P300 amplitude is a “strongly developmental

phenomenon,” able to predict a variety of intellectual measures including those

associated with the frontal system. They suggest that the amplitude stability is

determined, in this experiment, by

the cognitive effort or attention allocated to the stimulus...Thus, perhaps amplitude jitter is an indication of the subject’s consistency in focusing on the stimulus...What is still developing after 12 years of age is not the ability to generate a P300 response to a stimulus, but rather the control over attention that is necessary for the consistent production of P300 waveform components (p. 293, my italics).

Also, the authors conclude from their electrophysiological measures that the

functions of the posterior area mature earlier than the prefrontal portion. “Our data

represent the first documentation that the prefrontal area shows electrophysiological

activity suggesting very slow maturation in humans. This is consistent with the notion

that the prefrontal lobe is not functionally mature until young adulthood, whereas

posterior systems are functionally mature in middle childhood” (p. 295). These

observations suggest that a person may do well on a standard psychometric test of

intelligence or even traditional academic, teacher-centered curricula, yet do less well on a

test of formal reasoning, because the frontal area has yet to mature. This may also

suggest a causal mechanism by which some students can do well in a college non-science

curriculum, yet do poorly on tests of formal reasoning. Presumably, the non-science

curriculum taps less frontal skills than the science curriculum which is typically oriented

towards solving novel problems that demand self-originated solution patterns.

Decentration Consists of Resistance to Involuntary ORs

Kimmel (1985) suggested that “functional stability” is associated with decreased

variability between EPs and with increased amplitude of EPs. While Kimmel discussed

this topic in the context of paying attention to presumably significant stimuli, we can

adduce implications for EP behavior under conditions of non-significant stimuli.

Ignoring irrelevant stimuli is the process of “decentration” according to Piaget, as

explained in Chapter V. The literature suggests that subjects exposed to stimuli perceived

as irrelevant to their current task should have diminished EPs, if they have any EPs at all.

For example, Federico (1985) administered distracting clicks randomly with an

average interval of 1.5 seconds to subjects studying a training booklet on pulsed radar.

The auditory evoked potentials were measured in terms of the mean EP amplitude and

standard deviations over a period of 512 msec after the stimulus (Cf. variance among EPs

constituting the “string measure” of Hendrickson and Hendrickson (1979) discussed by

Kimmel (1985) and Mackintosh, (1986)). The measured sites were F3, T3, P3, and O1

as well as the homologous sites on the other hemisphere. Federico found that the below-

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average learners demonstrated higher mean EP amplitudes and greater standard

deviations than the above-average learners. Note that the auditory clicks were a

distraction, therefore, the larger amplitude of the EP (and greater SDs) represent failure

to habituate to the distraction while reading the instructional material. The larger

amplitude EPs were recorded in the right hemisphere frontal, temporal and parietal

regions, as well as the left parietal area indicating that the poor learners engaged these

areas less in the concept learning task than their counterparts who learned better.

Frederico concludes that the right hemisphere appears significantly associated with

concept learning, “not only LH regions as proposed in the popular asymmetric model of

the brain” (p. 249). This supports the findings of the current study, as well. Frederico

reviews similar studies of EPs and cognitive performance and links the findings to

proposed anatomical sites for fluid, Gf, and crystallized, Gc, abilities. Not consonant

with the theory I am developing, Frederico equates the crystallized abilities with frontal,

temporal and parietal regions, based on his prior EP research that link these areas with

general aptitude (i.e. comprehending language, solving arithmetic problems) and verbal and reading skill (understanding English words and prose passages), which are chiefly measures of Gc. ERPs evoked in the occipital areas were generally associated with spatial ability (i.e. manipulating spatial patterns), field dependence-independence (i.e. processing analytically vs. globally), reflection-impulsivity (i.e. deliberating vs. acting impulsively), tolerance of ambiguity (i.e. inclining to accept complex issues) and cognitive complexity (i.e., perceiving the environment in a multidimensional manner), which are chiefly measures of Gf (p. 244).

More investigation is required to reconcile this approach with my own

conclusions. As a start, however, it appears reasonable to suggest a reinterpretation of

the putative Gf posterior functions as more “automatized” than volitional functions, thus

restoring them to the class of crystallized functions. The putative Gc frontal functions

must be examined in the light of the actual tasks. Perhaps frontal, adaptive, volitional

processes (as mentioned in Chapter V, Kimble and Perlmuter, 1970) were required to

perform them well, even though at face value, the listed tasks appear to represent

automatized knowledge. For example, Shallice and Evans (1978) tested patients with

localized posterior and anterior cerebral lesions using questions that apparently required

general knowledge available to almost all subjects, but for which estimation was required

and no immediately obvious strategy was available. (E.g., “How long is an average

man’s spine?”, “What is the largest fish in the world?”, “How many slices in a sliced

loaf?”) The frontal patients responded with significantly more “bizarre” answers than the

posterior patients, even after covarying for intelligence as measured by Raven’s Matrices

test. The authors concur with Luria (1966)

that the selection and regulation of cognitive planning is one of the main functions of the human frontal lobes. Such planning functions would presumably be mediated through high-level programs which control the operation of lower-level cognitive programs themselves more posteriorly sited....On this view routine motor skills and routine cognitive skills such as the performing of mechanical arithmetic calculations would mainly require the use of only the lower-level programs. Even conventional intelligence tests, where a series of problems of the same type is presented with gradually increasing difficulty, seem to demand the use of relatively routine even though complicated cognitive operations (Shallice and Evans, 1978, p. 301).

This view contradicts the Frederico findings, thus suggesting the need to

investigate the source of the apparent discrepancy.

However, both Frederico’s work and the work of Shallice and Evans illuminate

Piaget’s concept of “decentering” as an element of cognitive growth. To decenter

requires the subject to ignore outmoded or inapplicable schema that have been

automatized. To overcome automitized responses to stimuli requires that the subject

exercise volitional control, at least until the higher level schema is automatized.

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A Role for Coherence in Accommodation and Reequilibration

How does the subject make the automatized behavior volitional? Given the

previous discussion, the frontal regions appear responsible for supporting the

“assimilation scheme” that governs all accommodation. The frontal regions are

responsible for “paying attention.” Kimble and Perlmuter (1970) point out that

automatized responses become volitional upon “paying attention” to the action, with

subsequent inhibition of the action. Piaget would suggest that the individual must

become aware of some contradiction between the behaviors of the objects themselves and

the concepts used to explain the behavior of objects. It appears reasonable to suggest that

this, too, is a form of “paying attention” and is prerequisite to higher forms of

equilibration.

“Paying attention” may have its neurological representation in increased

synchrony of EEG between various parts of the brain. Livanov (1977) reports that his

research on “cross-correlation” of EEG during mental arithmetic (multiplication of two

two-digit numbers) indicates “a sharp increase in the number of cortical areas with high

cross-correlation coefficients” (p. 120). (Note that cross-correlation is an analog of

coherence that measures the “coherence” across all frequencies at once.) Immediately

after the solution, the cross-correlations drop back close to their initial values. Increase

in synchrony apparently also depends on subject expertise because two experienced

mathematicians demonstrated no increase in cross-correlations during the mental

mathematics. This possibly indicates that automaticity in mathematical calculation is

inversely related to synchrony. Experienced mathematicians did not need to “pay

attention” with their frontal structures. For the non-mathematicians, the synchronous

sites were mostly located in the prefrontal lobes and the motor centers, with high

correlations between many of the sites.

Livanov points out that the frontal lobe activity is “a crucial factor in human

activities which involve initiative. It determines the course of complex behavioral

patterns and seems to be largely responsible for human intellectual activity” (p. 123).

The motor centers coordinate with the frontal regions in the form of “ideomotor acts.”

Synchronization of cerebral sites is also reported for physical movements, with greater

anterior synchronization at the beginning of the activity. After “transition to a stable

regime of work,” anterior sites demonstrate greatly reduced amounts of cross-correlation

between hemispheres and between the prefontal and motor areas. Other evidence

indicates that the number of positive correlations increases with age, with adults showing

more correlations than children during performance of voluntary motions. These

outcomes suggest that volitional activity engages the frontal area, manifesting in

increased synchrony. Adults presumably act with greater intent and more developed

frontal areas than children, therefore, resulting in greater anterior cross-correlations.

Livanov’s work compares with similar findings for Busk and Galbraith (1975)

who found 4-20 Hz EEG coherence high during the learning phase of a 60 rpm pursuit-

rotor task. The degree of coupling depended on the difficulty of the task, with frontal

premotor (Fz) to motor (C3 and C4) coupling decreasing with practice. Coupling

between visual areas and premotor (OzFz) did not decrease, suggesting that the visual

input remained stable during the task. These authors concluded that the coherence

measure they used reflected not only some aspects of anatomical pathways, but more

importantly, reflected dynamic functional brain organization that supported the task.

Posterior regions support learned activity, but with slower responses, when

unaided by frontal functions. For example, Livanov (1977) cites one study in which 5

subjects received a dosage of chlorpromazine while performing mental arithmetic.

Chlorpromazine is known to inhibit the “tonic effect of the ascending reticular activating

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system (RAS), which is most closely associated with the anterior parts of the cerebral

cortex” (p. 126). The cross-correlations decreased markedly in the frontal areas, while

the infraparietal and other regions maintained their level of synchrony. Notably, the

calculations were made at a slower rate. Livanov concludes that the infraparietal zone

“represents a posterior association zone which seems to be able to ensure all the

necessary forms of integrative cerebral activity” (p. 126), granting that the frontal lobes

still participate with much reduced activity. The association of the RAS with anterior

functions suggests the importance of “alertness” in the process of problem solving and

other frontal activity that may not show up in traditional IQ measures.

Note that the subjective experience during TM is one of mental alertness co-

incident with physiological restfulness. A recent review by Jevning, Wallace, and

Beidebach (1992) suggests that many of the physiological effects of TM reflect a state of

increased alertness or CNS activation especially at periods of subjectively deepest

transcending. “Such states are accompanied by high amplitude theta and/or fast

frequency beta bursts consistent with activation...[Outside of TM, findings indicate]

decreased reaction time and other improvements in sensory and motor performance [that]

can be associated with a more alert state of the central nervous system” (p. 421).

Increased CNS activation during TM is also indicated by increased coherence, as well as

increased cerebral blood flow and other changes in peripheral circulation and metabolism

to support the increased activation. In contrast to mental alertness, the authors also point

out that the subjective experience of deep restfulness is supported by measures such as

decreased whole body, muscle, and red cell metabolism, plus decreased plasma thyroid

and adrenocortical hormone production. Other indicators of rest include the decrease or

disappearance of EMG (muscle tension), and decreased galvanic skin resistance and/or

decreased phasic skin resistance response. Together, these features characterize TM as a

subjective experience of “restful alertness.”

Relationships Between EEG Alpha Coherence and Increased EPs for Voluntary ORs

The coherence research cited above and in Chapter II suggests that enhanced

rhythmic coordination between spatially distant anterior locations (coherence) somehow

improves cognitive performance. I have suggested the improvements result from

enhanced voluntary ORs (anticipation),and the enhanced ability to resist distraction

(decentration) which in turn result from changes in the on-going EEG. Empirically, the

phenomenon of enhanced ORs in relation to ongoing EEG has been studied in several

contexts. For example, Galbraith (1967) studied a special “weighted coherence” average

to evaluate the effects of increased coherence on the visual-evoked response in the rhesus

monkey with implanted electrodes. He found that many of the derivation pairs

demonstrated greater EPs when immediately prior to the flash of light the pair had

weighted coherence above the mean, compared with instances when the coherence was

below the mean. In several derivations, the opposite held, suggesting that certain brain

centers hold responsibility for inhibiting visual signal processing. More important,

however, is Galbraith’s observation that “complex patterns of ongoing brain coupling

occurring just prior to, and at the moment of, stimulation, exerted a marked influence

upon the brain’s response to the stimulus. These results suggest that trial-to-trial

variability in evoked response amplitude is not a form of CNS ‘noise,’ but a predictable

consequence of dynamically organized functional brain states” (p. 226). This implicates

the role of coherence in the improvement of cognitive functions, both anteriorly

(increased coherence) and posteriorly (decreased coherence).

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Basar (1980) has spearheaded continued investigation into the brain dynamics

that link the nature of the EP with the on-going EEG. Recent research on humans (Basar

& Stampfer, 1985) has implicated on-going alpha with enhanced auditory and visual EPs

that demonstrate greater amplitude, and more importantly, decreased variability in timing

relative to the stimulus onset. They write:

We have presented evidence that expectancy and selective attention are associated with regular, frequent target stimuli [and] result in highly synchronized EEG activity. This regular “limit cycle” activity occurs in various frequency ranges between 1 and 40 Hz...Accordingly, we tentatively conclude that 1-4 Hz, 4-7 Hz and 8-13 Hz activities serve as “operators” in the selective filtering of expected target stimuli....Furthermore, experiments in this study have shown that a regular pattern of stimulation can induce a “preferred” phase angle, which appears to facilitate an optimal brain response to the sensory input [i.e., a particular phase of the alpha cycle is time locked to the stimulus presentation] (p. 175).

The authors indicate that subjects’ EEG was flexible, and that unconscious,

preattentive mechanisms adjusted the phase of the EEG alpha to meet stimulus demands

for optimum processing.

When subjects were not informed that target stimuli would be presented regularly and alternately, their EEG activity appears to have developed an “operator state” spontaneously....[the] EEG operators appear to modulate the response characteristics as a function of learning (p. 175).

In a companion paper, Basar, Basar-Eroglu, Rosen and Schutt (1984) suggest

that, “At present, it can be only stated in general that the preparation rhythms may reflect

several cognitive processes such as expectancy, conditioning, habituation, attention, and

even short-term memory” (p. 19). However, at this time, it is reasonable to link these

phenomenon with learning processes and, as mentioned above, enhanced amplitude and

decreased variability of the EPs, indicating greater attentiveness.

Some evidence has accumulated that the practice of TM is related to EP changes.

Goddard (1989) reports that a group of elderly TM practitioners demonstrated

significantly shorter P300 latencies in a visual oddball paradigm compared with matched

controls. No differences were found however, on an auditory oddball task. Goddard

suggests that long-term practice of TM may retain a more youthful style of functioning

(i.e., maintain shorter latencies). Kobal, Wandhofer, and Plattig (1976) found shorter

latencies in a TM group, both in an awake state and in meditation, compared to a control

group in both awake and semi-somnolent states. The authors suggest the shorter

latencies “may be connected with an improvement or acceleration of the sensory

perception.” But of greater interest, in relation to findings related by Basar and Stampfer

(1985), Kobal et al. suggest that, “These results seem to be due primarily to the very

characteristic change in the background activity of the EEG in meditators as compared to

controls. During the period of activity between meditation sections we find an increase

of the 8-9 Hz components of the alpha band” (p. 827). This indicates that outside of TM,

subjects evidenced greater 8-9 Hz activity, a frequency that Basar and Stampfer suggest

serve as an “operator” for selective attention.

Conclusion–A Neuropsychology of Equilibration Processes in the Context of TM

In a sense, Kimble and Perlmuter (1970) present their research as a volitional

“stimulus-response” (SR) behavioral model for “transcending” (Piaget’s term) prior

“involuntary” SR conditioning. This supports the potential for a mental technique such

as TM (Transcendental Meditation) to enhance frontal skills in enhancing significance

ORs and diminishing involuntary ORs using the “transcending reflex” described by

Arenander. I suggest that the “transcending reflex” is a volitional event that generalizes

to allow acquisition of control over involuntary responses. For example, in the context

of their own research, Kimble and Perlmuter write:

Such studies as there are of these processes suggest that the acquisition of control over involuntary responses is always accomplished with the aid of supporting responses already under voluntary control. The desired response is elicited

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initially as a part of a larger pattern of reactions. With practice the supporting responses gradually drop out, an accomplishment that required a careful paying of attention to the desired behavior and a simultaneous ignoring of the others. With still further practice the now voluntary reaction becomes capable of being performed without deliberate intent. What was once involuntary and later became voluntary is now involuntary again, in the sense of being out of awareness and free of previous motivational control” (p. 382).

Even given the obvious differences between this paradigm of rather simple SR

conditioning and Piaget’s more complex topic of mental structures, I am still willing to

suggest this is a picture of what Piaget calls the “turntaking” between “new possibles”

and “previous necessities” mentioned in Chapter V. Kimble and Perlmuter suggest that

volition over voluntary response can be attained by “paying attention.” For Piaget the

picture would be viewed as the cycle of accommodation to an assimilation scheme, and

the expression of growing equilibration between differentiation and integration. The

“new possibles,” “accommodation,” and “differentiation” represent the “temporal,” or

sequentially contemplated form of cognition (i.e., “paying attention”). Kimble and

Perlmuter appear to identify this as the “voluntary” act.

These authors, as well as Piaget, suggest that one of the outcomes of the

voluntary act, (“cognitive construction” for Piaget) can be a consolidation into a new

“automatized” action (which Piaget terms an “atemporal structure,” or “necessity”).

Piaget suggests that the individual “transcends” the temporal cognitive construction,

thereby “integrating” the temporal construction into the atemporal schema. The same

concept in neo-behavioral terms is that the volitional behavior becomes automatized.

I suggest that in each case, the constructive or volitional process is handled by the

anterior, frontal regions of the brain. The resulting consolidated structure then is handled

by the posterior regions of the brain. Lack of development of one or more of the frontal

regions could impede successful adaptation or accommodation to new circumstances.

The current study indicates, to varying degrees, that failure on the formal tasks is

associated with diminished anterior L and R coherences. Also, in Chapter V, Directions

for Future Research, I suggested that bilateral occipital coherence, positively correlated

with fail performance, may be a necessary correlate, within certain boundaries, of

diminished L and R coherence. These points round out my attempt to bring together two

major thrusts of contemporary psychological research: neuropsychology and

constructivist developmental psychology.

APPENDIX

Subject Release and Background Letter

Approval Letter for Use of Human Subjects

Chemicals Scoring Sheet

Communicating Vessels Scoring Sheet

Projection of Shadows Scoring Sheet

Correlations Scoring Sheet

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Dear Research Participant,The development of successful instructional methods at MIU can be aided by

systematic research into the variety of problem solving methods students use. Your participation contributes directly toward structuring instructional methods which are oriented toward student interests and aptitudes at MIU. Thank you for your cooperation. Please sign the agreement below:

Sincerely,John Sorflaten

“I agree to participate in the study.” _________________________________________name date

Background Data

1. Major___________________________ 2. Year__________________

3. Age_________________ ________ 4. Years of college prior to MIU _______ years months Years at MIU________

5. Your most fulfilling areas of activity (list types of work or academic subjects or hobbies):

6. Your most successful areas of activity in the eyes of others (list work, subjects, hobbies, etc.):

7. Your least fulfilling areas of activity (list):

8. Your least successful areas in the eyes of others (list):

9. Now, considering number 7 as your highest level of fulfillment and success combined and number 1 as your lowest level of fulfillment and success combined, circle the number which best reflects your general feeling toward these areas:

Lowest HighestArt (kind: ) 1 2 3 4 5 6 7

Science (kind: ) 1 2 3 4 5 6 7

Verbal disciplines such as literature, humanities, foreign language(kind) ) 1 2 3 4 5 6 7

235

Mathematics (kind: ) 1 2 3 4 5 6 7

10. Your current course at MIU: 11. Do you consider yourself left-handed or ambidextrous in any regular activity such as writing, eating, or sports? (list)

Chemicals Scoring SheetIdent________Date_________

Mark “g” where S starts with “g”Draw line to show where E asks if all possible ways have been tried.

1. Does S use systematic scheme to keep track of trials?no yes mental = m Indicate on each trial S’s

paper = p system (m,p,vo) and the cumulative number of cups

visual objects = vo1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 2 3 4 1 2 3 4 1 2 3 4 1 2 3 41 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

2. “Have you made all the possible ways of mixing the solutions?”S says: yes no don't know maybeActually: yes noS continues: yes no

3. “Can you tell me what each chemical does?” “How can you prove it?”S appears to have been working with eye toward proof:

yes no maybeS’s proof relies on deduction from table

physical demonstrationimpression

4. (Optional) “Which chemicals are necessary for creating the color?”“How do you know?”

237

Communicating Vessels Scoring SheetIdent______Date ______

1. Introduction

2. Single tube prediction:

Water level will go: up down remain the same

3. Identical tubes: Movable is at _____(E)

Tube B is at _____(S)

S measures? yes no

4. Conical tube: Movable tube is at _____(E).

Conical is at _____(S).

5. Bubble tube: Movable tube is at _____(E).

Conical tube is at _____(E).

See drawing: Bubble tube is at _____(S) (approximate per S or estimate on drawing)

Conical tube is at _____(S) (if different from E's)

Questions to subject:

Please describe what you would see when the contents of tube A are poured into tube B:

First, draw in the levels of tube A and the conical tube as they exist on the apparatus you

have been working with. (Use pen.)

Then draw in the outcome of pouring tube A contents into tube B. (Use pencil.)

Please describe what you would see when the contents of tube A are poured into

tube B...

• First draw in the levels of tube A and the conical tube C as they exist on the apparatus you have been working with. (Use pen.)

• Then draw in the outcome of pouring tube A contents into tube B. (Use pencil.)

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A B C

241

Projection of Shadows Scoring SheetIdent_______Date________

1. “Do you see the shadow?” no yes

2. Green ring compared with red ring shadow prediction:

larger smaller same

3. Green ring moved closer to screen prediction:

larger smaller same

4. One shadow with red and green: possible impossible will try

4a. 0. . . . . 1. . . . . 2. . . . . 3. . . . . 4. . . . . 5. . . . .

6. . . . . 7. . . . . 8. . . . . 9. . . . . 10

4b. 0. . . . . 1. . . . . 2. . . . . 3. . . . . 4. . . . . 5. . . . .

6. . . . . 7. . . . . 8. . . . . 9. . . . . 10

4c. 0. . . . . 1. . . . . 2. . . . . 3. . . . . 4. . . . . 5. . . . .

6. . . . . 7. . . . . 8. . . . . 9. . . . . 10

5. One shadow with white, red and green:

possible impossible will try

5a. 0. . . . . 1. . . . . 2. . . . . 3. . . . . 4. . . . . 5. . . . .

6. . . . . 7. . . . . 8. . . . . 9. . . . . 10

5b. 0. . . . . 1. . . . . 2. . . . . 3. . . . . 4. . . . . 5. . . . .

6. . . . . 7. . . . . 8. . . . . 9. . . . . 10

Correlations Scoring SheetIdent_________Date__________

Set I

1. Relationship observed by S? yes no

2. (4,2,0,0)_______

3. (0,0,2,4)_______

4. (4,0,0,4)_______

5. yes no a______b______c______d______

6. (4,2,2,4) ________

Set II

7. Relationship observed by S? yes no

8. Relationship of set I is more same less than set II.

9. Group a:

b.

c.

d.

10. Set I a______b_______c_______d_______

Set II a______b______c______d______