Excerpts from

MODELING INSTRUCTION INHIGH SCHOOL PHYSICS

by

Malcolm Wells

A Dissertation Presented in Partial FulfillmentOf the Requirements for the Degree

Doctor of Education

Arizona State UniversityDecember 1987

Scanned and converted to MS-Word in 2007 by Reba Wilson. Figures and other excerpts can be obtained by e-mailing David Hestenes <hestenes@asu.edu> or Jane Jackson

<Jane.Jackson@asu.edu>

Acknowledgments

I wish to express my sincere appreciation to the following members of my supervisory committee: Co-chairman from the College of Education, Professor John Bell; and committee members, Professors Gary Bitter, Anton Lawson, and Howard Voss. I wish to particularly thank my co-chairman from the Physics Department, Professor David Hestenes, who so patiently and skillfully assisted me in the development of a problem, planning and execution of the study, and preparation of my dissertation.

Abstract

Numerous studies have indicated that didactic methods of instruction have been ineffective in transmitting a predetermined body of knowledge in mechanics to introductory physics students. This study develops an instructional strategy based on the Atkin - Karplus learning cycle and the Hestenes theory of modeling instruction in physics. It utilizes a laboratory activity-centered program as the mechanism for model development and the Halloun-Hestenes taxonomy of misconceptions in mechanics to guide the development of the factual knowledge. A detailed application of this method of instruction is illustrated with a series of activities to develop and deploy kinematical models of constant acceleration.

The effectiveness of this instructional method was evaluated by diagnostic pretests and posttests in mechanics, comparing three high school classes of honors physics students taught by different methods. The didactic method of instruction was found to be the least effective, with a pretest-posttest gain of 4.7 (13%); the inquiry method was next, with a gain of 7.9 (22%); while the structured inquiry method was shown to be the most effective, achieving a gain of 12.4 (34%) on a 36-point test.

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Original Table of Contents

Page

List of Tables ……………………………………………………………. ix List of Figures …………………………………………………………… xChapter 1. Purpose of the Study ……………………………………………. 1

Introduction ………………………….…………………… 1 Experimental Question …………………………………… 5 Experimental Hypotheses and Predictions ……………….. 7Experimental Predictions …………………………………. 9Summary ………………………………………………….. 10

2. Review of Literature ………………………………………………. 12Summary …………………………………………………… 22

3. A Learning Paradigm ………………………………………………. 24Functions of Memory in Learning ………………………….. 26Summary ……………………………………………………. 34

4. Instructional Design ………………………………………………… 36Learning Cycle ……………………………………………… 40Modeling Theory of Instruction …………………………….. 42Exploration -- Description Stage …………………………….. 46Concept Introduction – Formulation Stage …………………... 46Discovery – Ramification – Validation Stage ……………….. 47Summary ………………………………………………………49

5. Instructional Method …………………………………………………. 51Instructional Variables ……………………………………….. 55Application of Instructional Method …………………………. 57Laboratory Activity – Uniform Acceleration ………………… 60Exploration – Description Activities …………………………. 61Concept Introduction – Formulation Activities ………………. 63Discovery – Ramification – Evaluation Activities …………… 66Taxonomy of Commonsense Beliefs About Motion …………. 71Sample Set of Study Group Problems …………………………75Summary ………………………………………………………78

6. Experimental Procedures ……………………………………………... 80Participant Selection ………………………………………….. 80Subject Selection ……………………………………………… 81Teacher Selection ……………………………………………... 84Selection of Pretest and Posttest Instruments ………………… 85Post-Posttest Preparation ……………………………………… 87

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Administration of Tests ……………………………………….. 88Instructional Procedure……………………………………….. 89Summary ……………………………………………………… 91

7. Experimental Results………………………………………......……… 93Initial Knowledge State of High School Students ……………. 93Posttest Evaluation ……………………………………………116Post-Posttest …………………………………………………..124Summary ……………………………………………………...130

8. Conclusions ………………………………………………………….. 132Implications for Instruction ………………………………….. 133Suggestions for Future Research …………………………….. 134

Bibliography …………………………………………………………………. 136Appendices ……………………………………………………………………141

A. Conceptual Test in Mechanics ………………………………………. 142B. Posttest in Mechanics …………………………………………………154C. Test of Reasoning Development ………………………………………166

List of Tables

Table Page1. Percentage distribution for Students’ Answers on Mechanics Pretest ….. 962. Percentage Distribution for Students’ Answers on Mechanics Posttest .. . 1073. Summary of a One-Way Analysis of Variance of Pre-Posttest Gain Data for Students Instructed with the Didactic, Learning Cycle, and

Modified Modeling Learning Cycle Methods of Instruction ……… 1254. Summary of the Scheffe Pre-Post Gain Comparisons on Data from Didactic, Learning Cycle, and Modified Modeling Learning Cycle Methods of Instruction ……………………………………………… 1265. Summary of t Values for CG-1 and TG Post-Posttest Data …………….. 129

List of Figures

Figure Page1. Flow chart illustration the learning paradigm utilized ……………… 312. Flow chart illustrating Hestenes’s theory of instructional modeling .. 443. Graphical representation of displacement vs. time data for uniform

acceleration ………………………………………………….. 644. Graphical confirmation of data manipulation for a straight line

curve fitting of displacement vs. time data for uniform acceleration… 655. Graphical illustration of instantaneous velocity while undergoing

constant acceleration………………………………………….. 676. Graphical representation of constant acceleration as the slope of a

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velocity vs. time curve ………………………………………. 687. Graphical representation of displacement as a function of the

area under a velocity vs. time curve………………………….. 698. Response profile for pretest-conceptual test in mechanics …………. 949. Response profile for posttest-conceptual test in mechanics …………11810. Response profile for CG-1 pre-post-change-conceptual test

in mechanics …………………………………………………12011. Response profile for CG-2 pre-post-change-conceptual test

in mechanics …………………………………………………12112. Response profile for TG pre-post-change-conceptual test

in mechanics …………………………………………………12213. Response profile for PHY 115 pre-post-change-conceptual

test in mechanics …………………………………………….123 14. Response profile for post-posttest …………………………………...128

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Chapter 1Purpose of the Study

IntroductionThe event of October 4, 1957, when the Soviet Union succeeded in launching the first

artificial earth satellite, focused the nation’s attention on the consequences of the neglect that education had experienced for nearly three decades. The shock and humiliation that the nation felt as a result of this event galvanized the national resolve to recapture our past technological preeminence.

The introspection that followed led to the conclusion that our technological preeminence had been successfully challenged because we were lacking, in both quantity and quality, an adequate pool of scientists and engineers. The reasons for these deficiencies were identified with outdated science and mathematics curricula and inadequately trained pre-college teachers.

A reordering of national priorities resulted in an unprecedented effort to address the problems identified. Morris Shamos, physicist, science educator, and past president of National Science Teachers Association has estimated that $5 billion were expended from 1957 until 1972 to improve the quality of science education in Grades K-12. The resulting federally funded curriculum development projects spawned a multitude of new science and mathematics curricula: Physical Science Study Committee (PSSC), Chemical Education Materials Study, Harvard Project Physics, Introductory Physical Science, Science Curriculum Improvement Study, etc. These new curricula, sponsored by the National Science Foundation (NSF), in turn had a profound effect on the philosophy that influenced textbook content by commercial publishers. The primary goal of this massive effort was to address the shortage of scientists and engineers in order to restore the nation to its technological preeminence. Our success toward fulfilling this goal was demonstrated by our being the first, and only, nation to successfully land men on the moon and then safely return then to earth.

The social problems faced by the nation in the late 1960s and early 1970s, the Vietnamese War, the nuclear-power debate, pollution, genetic engineering, and numerous other social-technical issues demonstrated that while we had successfully met the nation’s needs for trained specialists, we had failed to meet the nations’s need for a scientifically and technically literate citizenry. Jerrold Zacharias, Massachusetts Institute of Technology physicist and NSF project director for the PSSC, reported in testimony on February 19, 1980, before the Subcommittee on Science, Research, and Technology of the Committee on Science and Technology, U.S. House of Representatives, that “we had aimed only at the college-bound and college students because we could not do everything at once.”

Thus, in spite of the massive efforts to improve the quality of scientific education in America, studies by the National Assessment for Educational Progress (1978) and a follow-up study by the Science Assessment for Educational Progress (1983) revealed a trend of constant decline, since 1970, in achievement test scores in science. The National Commission on Excellence in Education (1983) focused the nation’s attention on the ineffectiveness of instruction in science, referring to the educational deficiencies as a national crisis.

More recent reports have questioned the wisdom of secondary school science curricula that place so much emphasis on preparation of students who intend to major in science-related fields in college. This attitude ignores the legitimate needs of the majority of students who take science courses in high school but do not continue with training beyond high school.

Harms (1981) indicated that 90% of the science teachers emphasize goals for school

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science that are directed toward preparing students for further formal study in science; Halloun and Hestenes (1985b), however, indicated that having taken a high school course in physics had no measurable effect on the grades earned in an introductory calculus-based course in physics at the university level. This study indicated, additionally, that preinstructional students at the university level possess a broad range of misconceptions in mechanics that appear to be amazingly resistant to change by means of conventional instruction.

As a nation we are faced with a serious problem. Our national interests demand an ever-increasing supply of trained scientists, engineers, and scientifically literate citizens. Yet even with major curriculum reform and extensive teacher retraining programs, our educational system seems incapable of meeting these demands. This suggests that the nation’s educational system is mature; that is to say, it remains relatively resistant to change in spite of massive infusions of talent and resources intended to induce positive change. Past experience indicates that, barring the introduction of a new and basically different theoretical approach to science education, there appears to be little hope for significant change.

Fortunately, Karplus, Bruner, and other educational psychologists and science educators who participated in the national curriculum reform movement drew attention to the potential contributions from the learning theories of Piaget and other constructivists. These theories have suggested new questions, the answers to which seem to provide theoretical foundations for new instructional strategies that may usher in a revolution in science instruction.

Enough research has been conducted, by this time, to guide the development of some instructional designs to test the validity of the research findings. The time is ripe to move forward with efforts to validate an instructional theory that will capitalize on this new knowledge. These studies will carry with them the anticipation that an instructional theory will emerge that is firmly grounded in research and will contribute to a science of physics instruction with an explicable theory that will consistently yield reproducible results.

Experimental QuestionThe need for theoretical framework and explanatory models in science education research

has been a recurrent thesis in commentaries on research in science education. Kuhn (1962) characterized science as a paradigm-guided enterprise, noting that science resides primarily in the formulation and articulation of paradigms and only secondarily in methodology. Bowen (1975) noted that little progress has been made in conceptualizing the knowledge of the field. More information is available to science educators now than there was 50 years ago, but the structure of knowledge has not advanced appreciably.

Hestenes (1979) suggested that individual teachers who wish to improve their instructional effectiveness can do so by further refining their insights into teaching skills, processes, and techniques. However, he pointed out that the teaching effectiveness of the individual ultimately is limited by the state of one’s profession. If the teaching profession is ever to transcend the state of an art, it must be guided and supported by a program of profound educational research. Champagne, Klopfer, and Gunstone (1982) stated that an organized and systematically verified psychological foundation is an essential requisite for effecting substantial improvements in science instruction. Only when a science of instructional design exists will the design process cease to hide behind the cloak of “judgment” or “experience.”

Hestenes’ (1979) suggestions for direction in research in science education include, among others, three objectives that this thesis will address:1. An analysis of the mental processes that induce conceptual change.

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2. The articulation of a coherent instructional paradigm based upon the analysis of mental processes that induce conceptual change.3. The development of curricula consistent with the instructional paradigm. The design must include teaching strategies as well as the selection and organization of subject matter and the details of student and teacher activities.

Thus, the question asked by this study is: Can a learning paradigm be constructed from the existing information-processing theories and related research findings that can predict learning outcomes resulting from the instructional strategies dictated by the paradigm?

Experimental Hypotheses and PredictionsOne theory of information processing suggests that the human mind is basically rational,

internalizing any rational argument that is initiated at the appropriate level of complexity, and progresses by way of an appropriately ordered sequence of deductive arguments.

Hypothesis I. The most effective instructional technique for internalizing theories, so that they would be scientifically consistent, is the didactic instructional method, which utilizes a combination of lecture and textbook presentations. This method of instruction would present a summarization of a logically ordered sequence of arguments leading to the desired conclusion. This conclusion would be essentially complete and in its final form, requiring only some practice in its application to prescribed problems in order to understand the implications of the theory and full range of interrelationships among the essential elements that are defined by some system of concepts. Laboratory activities and/or teacher demonstrations are utilized by this method of instruction to emphasize important points from lecture-textbook presentations or to assist in deployment of the theory by illustrating “real-life” applications of the relevant scientific theories.

An alternate theory of human information processing suggests that preinstructional students possess mental structures by which all sensory input is interpreted and given meaning within a given context. These preinstructional mental structures have been constructed from the subjects’ interactions with their environments and have undergone numerous modifications as appeared necessary for their expectations to be consistent with their observations. These misconceptions are very persistent and frequently actually interfere with the development of concepts that are scientifically valid. The alternative theory of information processing is consistent with the following hypotheses:

Hypothesis II. Development and deployment of scientifically valid mental models is most effective when students are actively involved in the development of the targeted concepts by means of guided laboratory experiences, followed by further activities that encourage self-regulation by reinforcing, refining, and enlarging the content of the laboratory experiences.

Hypothesis III. Development and deployment of scientifically valid mental models is most effective when students are actively involved in the development of the targeted concepts by means of guided laboratory experiences, supported by a structured process for model development. Deployment is maximized when cognitive conflict with preexisting misconceptions is systematically induced. [Italics by editor]

Experimental Predictions1, Subjects instructed with the learning cycle method Atkin-Karplus (1962) will exhibit greater gains, as measured by the Halloun-Hestenes Mechanics Diagnostic Test (Appendix A), than will the subjects who are instructed with the didactic method of instruction.

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2. Subjects instructed with the learning cycle method in conjunction with the Hestenes (1987) modeling theory of physics instruction, which systematically addresses the identified preinstructional misconceptions, will exhibit greater posttest gains, as measured by the Halloun-Hestenes Mechanics Diagnostic Test, than will those instructed by either the learning cycle method alone or by the didactic method of instruction.

SummaryLong-range solutions to the problems in science education have been viewed, by several

prominent scientists and science educators, to reside in the development of principled theories of instruction that are grounded in vigorous programs of research in science education.

Three broad areas that have been identified as being worthy of research efforts in science education are (a) descriptions of mental processes that induce conceptual change, (b) articulation of an instructional paradigm based on the mental processes that induce conceptual change, and (c) development of a curriculum based on an instructional paradigm.

This study predicts learning outcomes resulting from the implementation of the didactic instructional method, the learning cycle method, and the modified modeling learning cycle.

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Chapter 4Instructional Design

The validity of an instructional design must be judged by the predictability and explicability of the instructional outcome as suggested by the theory of learning from which it evolved.

The first stage of the learning paradigm addressed the intent to learn. The subjects for this study were students taking an elective honors physics course who, as such, were highly motivated to excel academically. Because of these motivational factors, the instructional design for this study did not address the intent to learn.

The second stage of the learning paradigm, as previously described, concerns the processing of sensory input for recall or concept development and problem solving. In the educational process, academic achievers have been programmed, from the beginning, to learn facts, even in science and mathematics; carefully study the sample problems; learn the parts of an insect; learn the formulas and valences for some given ions; etc. The reaction of students to a course in physics that is structured around concept development—nothing to memorize—initially induces high frustration levels, accompanied by frequent requests to be told what they should “know” for the tests. The apparent lack of appropriate information-processing schemata to deal with problem solving expectations seemed to pose a significant impediment for introductory physics students. This problem was not dealt with in this study, but it is a problem area identified by the learning paradigm that warrants further investigation.

The third stage in the learning paradigm raises some very fundamental questions with respect to instructional design. The questions involve the meaning of the information as inferred from sensory input and the organization of that meaning in WM’s (Working Memory) conceptual matrix.

If the learning paradigm reasonably represents the essential processes that take place during the learning process in introductory physics, then utilization of this paradigm should indicate the points in the paradigm and the process modifications that would be most likely to induce the desired changes in the preexisting mental structures. An analysis of the learning paradigm indicates that the opportunity exists to utilize instructional procedures to significantly modify the learning process at the point where the WM must infer meaning from the sensory input. The conceptual matrices generated for this function are dependent on the systems of concepts that are stored in the preexisting memory cells to generate interpretative structures that process the sensory input so that it may be effectively utilized for meaningful learning.

Halloun and Hestenes (1985b), Maloney (1984), McCloskey (1983), Clement (1982), Peters (1982), Trowbridge and McDermott (1980b), and McCloskey et al. (1980) identified many misconceptions in mechanics that are held by preinstructional physics students. Nussbaum and Novick (1982) noted that students are likely to use their preconceptions in the classroom to interpret information such as to give it meaning that differs from or even conflicts with the meaning intended by the teacher. Norman (1980) noted that as students gave meaning to information gained from lectures and textbooks, information that seemed discrepant to the model was ignored; sentences, even paragraphs of text, seemed to be skipped. Ganiel and Idor (1985) observed that considerable discrepancies arise between the teachers’ assumptions about what students obtain from classroom experiences and the reality as described by objective tests and

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observations. It is extremely difficult to diagnose how each student interprets what has been taught.

A brief summary of the cited studies indicates that:1. Learning theory (Piaget)—All incoming sensory input is interpreted in terms of preexisting mental structures.2. Pretests of high school students show that they possessed inconsistent misconceptions.3. Verbal or written attempts to develop accurate mental structures are misinterpreted to the extent that their preexisting mental structures are incorrect.4. The desired outcome of instruction is to develop a situation wherein the subject’s interpretation of the proposed model is perceived to be reconcilably in conflict with the preexisting structures and, additionally, is perceived to be more effective in dealing with the subject’s environment than was the preexisting structure. This situation will induce self-regulation, and thus learning, in the broader sense.5. In some instances preexisting mental structures are so unstructured and noncoherent that any attempted linguistic model development is interpreted to be consistent with their misconceptions. No conflict is thus seen to exist, and their misconceptions remain unaltered by instruction. In fact, in such cases this misperception that their preexisting structure is in agreement with the authority’s model reinforces the misconception.6. In some instances, the proposed model is interpreted to be irreconcilably in conflict with the preexisting structures. In these instances, the proposed model is rejected and no learning takes place.7. The proposed learning paradigm suggests that the linguistic inadequacies may be avoided by developing the modeling process by way of exploration activities in the laboratory, which provides concrete experiences from which the modeling process can proceed. There is no effort at this time to generate cognitive conflict.

A design decision is necessary at this point to minimize the impact of the preinstructional misconceptions. The choice is essentially between a linguistic presentation—lecture/textbook—or concrete laboratory experiences from which the targeted concepts could be developed. Since the abstract symbolism of language presented the greater likelihood of misinterpretation, a decision was made to utilize a laboratory/activity method of instruction.

Learning CycleIn order to utilize a thoroughly tested laboratory design, an instructional method was

selected that utilizes the learning cycle as developed by Atkin and Karplus (1962) and refined by Karplus and others of the Science Curriculum Improvement Study at the University of California, Berkeley (SCIS, 1974). Since this learning cycle is a generic model that is equally appropriate across the entire range of grades, a theory of modeling instruction in physics as proposed by Hestenes (1987) was integrated with the learning cycle to provide the basic framework for the experimental instructional design, referred to as the modified modeling learning cycle.

The SCIS model is basically a three-phase process: exploration, invention, and discovery. A clarification of the SCIS method was provided by Lawson (1967), as follows:

The exploration phase involves the students in concrete experiences with materials. As a result of these initial explorations, which sometimes may be fairly structured by the teacher or on other occasions relatively free, learners encounter new information for which they do not have

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available mental structure to allow its immediate assimilation. These experiences may produce disequilibrium.

At an appropriate time, the teacher introduces the invention phase of this process. The term invention is analogous to Piaget’s structure-building and may promote a new state of understanding or equilibrium. In most cases, however, the invention phase will not immediately allow students to mentally coordinate the new terminology and assure a way of ordering the explorations. It could thus be expected that disequilibrium would, in some cases, persist.

The discovery phase, which provides activities that involve the same conceptualizations, then enables students to self-regulate and, additionally, to reinforce, refine, and enlarge the content of the invention.

The learning cycle as described above is a generic process that does not address techniques peculiar to any specific set of targeted concepts. A mode of learning that is of functional value for instruction in introductory physics must be specified in terms of the unique nature of the concepts targeted. In order to ensure that a learning cycle is designed so that it will have direction and achieve the outcome goals of instruction in introductory mechanics, it is necessary to utilize some system to provide an explicable and principled procedure.

Modeling Theory of InstructionFor instruction at the introductory level, the modeling technique as proposed by Hestenes

(1987) for modeling in mechanics is easily integrated with the above learning cycle and provides a clearly defined and explicable procedure with which to develop curriculum materials.

The modeling process proposed by Hestenes suggests four stages in the development process: the description stage, the formulation stage, the ramification stage, and the validation stage. This process is schematically illustrated in Figure 2. [Editor’s note: This is the same as Fig. 1 in Hestenes (1987.]

The description stage provides an object description, a motion description, and an interaction description. The object description requires a description of the type of model to be developed. This phase requires a specification of the stated variables required for the model. It also characterizes the motion as a whole, at least qualitatively, and specifies any known values of the state variables. In the interaction description, each agent acting on the object is identified, along with the type of interaction. Then interaction variables are introduced to represent the interaction, and features of the interaction are described qualitatively using diagrammatic techniques. The main output of the descriptive stage is a complete set of names and descriptive variables for the model, along with physical interpretations for all of the variables.

In the formulation stage of model development, the physical laws of motion and interaction are applied to determine definite equations of motion for the model object and any subsidiary equations of constraint. It is in this stage of the process that the mathematical relationships between the descriptive variables are developed from the experimental data. It was during this stage that interpretations were developed that provided physical significance for all of the descriptive variables assigned during the description stage. For example, the physical significance of the geometric properties of the graphical representations of experimental data, such as slopes and areas under curves, are developed and discussed. Physical interpretation is considered to be a critical component of the modeling process. Without interpretation the mathematical relationships among the descriptive variables represent nothing to most students except some abstract and incomprehensible mathematical symbolism.

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In the ramification stage, the special properties and ramifications are worked out. The equations of motion are solved to determine trajectories with various initial conditions, the time dependence of derived descriptors such as energy is determined, and results are represented analytically and graphically and then analyzed. In this stage of model development, the implications are explored for the development of a system of concepts that share commonalities in conceptualization. A model object together with one or more of its main ramifications could be referred to as a ramified model.

The validation stage is concerned with empirical evaluation of the ramified model. In textbook problems this may amount to no more than assessing the reasonableness of numerical results. However, in scientific research it may involve an elaborate experimental test. For a more detailed description of this modeling theory of instruction, refer to Hestenes (1987).

A summary of the instructional model utilized in this study follows.

Exploration--Description StageThe targeted phenomenon is analyzed, as a class activity, in an effort to identify the

characteristics of the targeted system, which in some way depend on each other (identification and classification of variables). Direct observations and measurements that describe the identified relationships between targeted variables are recorded.

Concept Introduction--Formulation Stage1. Evaluation of data—This activity includes techniques of graphic representations of data, where possible.2. Physical interpretation of the graphical representations is emphasized. Hestenes (1987) pointed out that students need to recognize the physical interpretation as a critical component of a model. Without interpretation, the equations of a model represent nothing; they are merely abstract relationships among mathematical variables.3. Terms (concepts) are invented for physically significant characteristics of the phenomenon.4. Equations are developed to mathematically model the observed phenomenon (abstract model of object). The physical significance of equations and terms within the equation are emphasized at this time. These activities accomplish the formulation stage of the modeling theory of instruction as proposed by Hestenes. It should be noted that as yet no attempt has been made to induce cognitive conflict during concept development—students have simply been observing and developing mathematical descriptions, coupled with verbal descriptions, to describe common physical phenomena.

Discovery—Ramification—Validation StageTwo types of knowledge are addressed in this discussion: factual and procedural.

Factual knowledge is characterized by terms, formulas, rules, laws, and models. Procedural knowledge is characterized by strategies, tactics, and techniques for developing, validating, and utilizing factual knowledge. DiSessa (1979) noted that physicists generate solutions to problems; they do not know them. It is not that facts are irrelevant, but that the higher activity level of deciding when to evoke a fact or use an algorithm is more characteristic of scientific knowledge than the relevant facts. He further stated that procedural knowledge generally is not verbalized and may, furthermore, be inaccessible in the sense that the student himself does not realize that it is knowledge and how this knowledge can be put to use. Thus:1. Students at this point are divided into small study groups of three or four, with even

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distribution of formal reasoners, as determined by scores on the reasoning test (Lawson, Karplus, & Adi, 1978) as modified to reflect a physical science orientation (see Appendix C). [Editor’s note: an updated version is on the password-protected “participant resources” web page of http//modeling.asu.edu.]2. Groups are given problems that require the application of the concepts developed from common experiences and techniques of mathematical analysis as developed in previous activities.3. Newton’s laws of motion, the conservation laws, and numerous other generic laws of classical mechanics identify the system variables universally relevant to the modeling process, which provides explicability to our physical environment. These laws are examples of factual knowledge. In order for these laws to have functional value, it is necessary, however, to develop supporting procedural knowledge that defines and describes the tactics and techniques with which the factual knowledge can be utilized for original problem solving and for transfer to problem-solving strategies in related areas. It is at this point that some mechanism is useful that will systematically induce a recognized conflict between their newly developed scientifically consistent model and as many of their unstructured pre-instructional concepts as possible.4. The deployment process that directly addresses the development of procedural knowledge is supported by means of careful problem selection, which utilizes motion maps and force diagrams. These maps and diagrams necessitate the repeated analysis of the problems by way of the variables identified by Newton’s laws as the common threads that run through kinematical and dynamical relationships. A broad selection of problems is utilized to encourage transfer by way of exposing the students to a large number of seemingly unrelated phenomena that share common defining parameters. These activities achieve the goals of the ramified model as described in Hestenes’ model development theory.

SummaryAn analysis of the learning paradigm suggests the existence of at least three distinct and

identifiable processes necessary to effectively induce meaningful learning. The first of these is the valid interpretation of sensory input. The second is a recognition of a reconcilable conceptual conflict between the conceptual matrices constructed from sensory input and the preexisting mental structures. The third process involves the development of cueing mechanisms, which involve procedural knowledge characterized by the techniques and tactics necessary for the utilization of the factual knowledge.

A three-stage instructional design was developed that combined the learning cycle method with the theory of modeling instruction proposed by Hestenes (1987). The three stages are described as follows:1. Exploration-description stage, which involves directed but unstructured laboratory activities

intended to identify and describe the variables that are relevant to the phenomenon under consideration.

2. Concept introduction-formulation stage, which involves the evaluation of data representations, development of mathematical relationships between the relevant variables, and the physical interpretation of the relationships.

3. Discovery-ramification-evaluation stage, in which the tactics and techniques necessary for the utilization of the laws and relationships developed in section two are deployed.

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Chapter 5Instructional Method

All of the subjects in the three experimental groups selected for this study were high school honors physics student. The group that received instruction by the didactic method was designated as Control Group 1 (CG-1), the group that received instruction bys the learning cycle method was designated as Control Group 2 (CG-2), and the group that received instruction by the learning cycle method with directed deployment tactics was designated as the treatment group (TG). A more detailed description of the experimental groups is provided under subject selection in Chapter 6.

The learning paradigm as developed in Chapter 3 provided the principles of learning that guided the development of the instructional design presented in Chapter 4. The validity of a principled instructional design can, however, be demonstrated only to the extent that it can be transformed into an instruction method that yields predictable and explicable learning outcomes.

Different instructional methods were employed with each of the three experimental groups compared in this study.

The method of instruction utilized for CG-1 had the following goals and objectives. The students would:

1. Learn all terms, laws, theories, formulas, and other relevant information associated with some defined knowledge domain.

2. Learn the techniques and methods of mathematical analysis.3. Learn the methods and techniques of laboratory data manipulation and evaluation.4. Learn proper laboratory methods and techniques of manipulation of physics apparatus.

The goals and objectives utilized for the instruction of CG-1 assumed that physics is a closed, content-centered system, that is, a body of knowledge that is essentially complete as presented. The goals of instruction are narrowly defined: to teach some predetermined domain of knowledge as preparation for technical professional training at the university level. This theory suggests that the axiomatic content of physics should be presented hierarchically in a clear and concise manner. This instructional method utilizes lecture/demonstration and/or reading assignments for information acquisition. Lecture and/or reading materials are reinforced with homework and/or laboratory activities. Laboratory activities are also used to reinforce important concepts from lecture or reading, or to confirm some important scientific principle. The homework assignments are followed with detailed explanations that demonstrate proper techniques for solving homework problems. Laboratory activities are followed by detailed discussions of laboratory data evaluations and conclusions. Teacher demonstrations are followed by clear, concise, and complete explanations of the phenomenon. Tests measure the attainment of knowledge in the given domain. These tests measure the student’s ability to recall information from text and/or lecture and to solve problems similar to those assigned as homework.

By contrast, the goals and objectives of the learning cycle and modified modeling learning cycle methods, as described in Chapter 4, are to provide a learning environment in which each student can:

1. Develop qualitative physical intuition.2. Develop mental models, usually mathematical, that define and describe the relationships

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among the system variables related to the phenomenon of interest.3. Develop the procedural knowledge necessary for effective model utilization (model

deployment).4. Learn the factual information incidental to the model development.

This instructional method is process centered, utilizing activities in the laboratory as the principal vehicle for concept and model development and deployment laboratory activity for model development is to begin with enactive representations, move on to iconic representations, and then convert to an appropriate symbolic representation. This process increases the complexity of the representation only as the student is able to relate the more complex representational to one of the simpler representations that preceded it.

The instructional modeling process as proposed by Hestenes (1987), and summarized in Chapter 4 for instructional implementation, is emphasized throughout the instructional activities utilized by the treatment group. While the different aspects of model construction are not emphasized by name, the steps in the process are repeatedly emphasized operationally with the students. The role of the model in problem solving is explicitly discussed throughout the deployment process. It is emphasized that physicists do not “know” the answers to problems—they generate them.

Instruction by this method has as its goal to make the student a self-sufficient problem solver. The instructor using this strategy corrects the student in a manner that permits the student to eventually assume corrective function.

The instructor utilizing the modified modeling learning cycle selects the concepts to be targeted, basic experimental activities, data processing techniques, and other apparatus and activities necessary to support the instructional agenda leading to the desired instructional outcomes. These management functions are intended to be relatively transparent to the students, encouraging them to accept responsibility for the learning process. The instructor’s primary responsibility is providing and supervising activities that lead to the attainment of the targeted learning outcomes. These include keeping the group on task, offering advice that helps them avoid pursuing unproductive discussions and activities, assisting them in interpreting the graphical analysis, and assisting in concept development in general. All discussions are student centered, with instructor intervention in the Socratic tradition.

Instructional VariablesWhen trying to compare the effectiveness of the individual techniques that constitute the

different instructional methods examined in this study, comparing CG-1 with either CG-2 or TG, it is noted that CG-1 utilized no significant instructional techniques in common with either of the other two instructional methods. As such, conclusions could reasonable by drawn with respect to the relative effectiveness of the overall strategies, but attempts to identify specific instructional techniques that contributed to the differences would be precluded.

The instructional variables, however, between CG-2 and TG varied only for the process of deployment. CG-2 and TG had the same instructor and utilized the same laboratory activities and the same instructional modeling techniques (Hestenes, 1987) for both the exploration-description and the invention-formulation stages. Thus, the instructional strategies that differed critically between CG-3 and TG were utilized for the discovery-formulation-evaluation stage. For the CG-2 instruction, questions and problems were selected from the textbook without any clear strategy guiding their selection. Traditional numerical solution of textbook problems was

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encouraged as a means of model deployment.The instruction provided to implement the discovery-formulation-evaluation stage for the

TG, however, utilized the Halloun-Hestenes taxonomy as a guide in the generation of questions and problems to ensure repeated cognitive conflict between the subjects’ preinstructional mental process of “knowing” the answer and the instructionally developed mental process of utilizing a modeling process to formulate an answer. For each problem assigned, if appropriate, a motion map or force diagram was specified and required. Numerical solutions were not emphasized; in fact, most questions and problems were constructed so that only semiquantitative responses would be appropriate.

Application of Instructional Method

Laboratory activities in mechanics. Eight laboratory activities were utilized for this study. All of the activities are descriptively listed below, along with the concept(s) and/or the model(s) to be instructionally targeted.

Activity Concept/Model1. Toy tractors 1. Constant velocity

2. Experimentally develop a mathematical model of relationship between displacement and time for constant velocity

3. Physical interpretation of the velocity vs. time graph.2. Inclined rail 1. Constant acceleration

2. Experimentally develop a mathematical model of relationshipbetween:

a: Velocity and time b. Displacement and time

3. Instantaneous velocity (tangents slope)a. Slope of v vs. t graph

b. Area under curve of v vs. t graph3. Friction 1. Experimentally develop a mathematical model of relationship

between normal force and frictional force 2. Effect of surface area

3. Effect of velocity4. Effect of the nature of surface

4. Newton’s 2nd law 1. Experimentally develop a mathematical model of relationship between net force, mass, and acceleration

5. Uniform circular motion 1. Experimentally develop a mathematical model of relationship among the force along a radius, mass, radius of orbit, and period of revolution6. Collisions 1. Momentum

a. Conservation of momentum (elastic)b. Conservation of momentum (inelastic)Note: This laboratory activity is used primarily because of the opportunities to utilize it in deployment activities.

7. Hooke’s law 1. Experimentally develop a mathematical model of relationship between applies force and elongation

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Note: See note in #68. SHM (oscillating mass on spring) 1. Experimentally develop a mathematical model of

relationship between mass and period of oscillation. Note: See note in #6.

It should be emphasized that the purpose of the laboratory activities, as discussed earlier, was to provide a nonlinguistic vehicle for development the modeling process. The critical aspect of the series of laboratory activities was not the specific laboratory activities selected, but, rather, the technique of model development discussed in Instruction Design, Chapter 4.

Laboratory activities were not treated in any way as special activities; rather, the laboratory activities constituted the core of the instructional activities. Laboratory activities were not scheduled for any special time or discussed before the activity was undertaken, the class moved quite spontaneously between laboratory activity and computer and discussion activities.

The following activities illustrate the general technique utilized in this study for model development. Model deployment, utilizing the Halloun-Hestenes taxonomy, follows in the next section.

[Editor’s note: pages 60 to 79 are omitted here, because sample activities used for model development and problems used for model deployment are on the modeling website (curriculum section). The Halloun-Hestenes taxonomy that guided the generation of problems for the ramification stage is at http://modeling.asu.edu/R&E/research.html. ]

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Chapter 6Experimental Procedures

Participant Selection The subjects selected for this study were from the Tempe Union High School District in

Tempe, Arizona, Tempe is predominantly an upper-middle-class bedroom community of people, contiguous to Phoenix. The largest employer in Tempe is Arizona State University. The presence of this large research institution tends to attract “high-tech” industries to the area; thus, most employment opportunities in the area are for the more highly educated and technically trained people who tend to fully appreciate the value of education

The pride, heightened intellectual awareness, and intellectual leadership experienced by the community as the result of the presence of this large university have resulted in a tradition of strong community commitment to, and enthusiastic support of, public education at all levels.

The Tempe Union High School District consists of four high schools with a total population of 8,100 students.

The student subpopulations for the four high schools in the Tempe district were as follows:

HS-1 had a student body of 2,091, consisting of 1,555 whites, 63 blacks, 324 Hispanics, 62 American Indians, and 87 Asians or other.

HS-2 had a student body of 2,191, with an ethnic distribution of 1,874 whites, 75 blacks, 173 Hispanics, 32 American Indians, and 37 Asians or other.

HS-3 had a student body of 1,996, of whom 1,700 were white, 57 were black, 169 were Hispanic, 18 were American Indian, and 87 were Asian or other.

HS-4 had a student body of 1,806, consisting of 1,263 whites, 232 blacks, 240 Hispanics, 23 American Indians, and 48 Asians or other.

Subject SelectionThe selection of subjects for this study was guided by the necessity of minimizing

random variables that might have compromised the validity of the study. The experimental design thus emphasized the selection of subjects with the least possible variation in their social, economic, ethnic, and educational backgrounds.

The limited pool of honors physics students available at any one high school made impossible the random selection of both treatment and controls groups from those in the same school who were taking courses in honors physics during the same year. Additionally, the limited population of honors physics students at two of the high schools in the district (HS-3 had only 9 students who completed the course in honors physics, and HS-4 had only 12) made inclusion of the two schools with the limited honors physics populations unacceptable for participation in this study.

In order to test the two hypotheses to be examined in this study, three instructional designs were utilized, requiring the selection of two different control groups and one treatment group.

The experimental design utilized with TG (Treatment Group) shared common instructional parameters with CG-2 (Control Group–2) except that the treatment group was subjected to an instructional procedure utilizing a modeling process that specifically addressed the misconceptions found to be characteristic of preinstructional students, while the other control

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group utilized the traditional didactic method on instruction. HS-1, which was selected to test the modeling hypothesis, had only one section of 1986-87 honors physics students. A design decision was therefore made to utilize the 1983-84 honors physics class. This class had participated in a doctoral study at Arizona State University, using the same testing instruments that were to be utilized in this study, the test results of which were available. Utilizing this group as a control group had the added advantage that it had been taught by the same teacher, using the same textbook, laboratory activities, and instructional techniques except for the modeling and deployment procedures designed for this study. The 1983-84 control group (CG-2) from HS-1 consisted of 24 students - 10 females and 14 males - with an average age of 204 months. The 1986-87 treatment group (TG), which was chosen from HS-1 also, consisted of 22 students - 6 females and 16 males - with an average age of 207 months. The control group used to test the second hypothesis (CG-1), to measure the relative effectiveness of the more traditional approach, was selected from HS-2 and consisted of 26 students - 6 females and 20 males - with an average age of 211 months.

The honors programs vary somewhat within the Tempe Union High School District. In this case, the students taking honors physics at HS-1 had taken 1 year of biology and 1 year of chemistry in the honors program before taking physics. The students in the honors program at HS-2 had taken 1 year of a combination of chemistry and physics, 1 year of biology, and 1 year of chemistry in the honors program before taking physics.

All of the students participating in this study who were classified as honors program students were required to meet one or more of the following criteria: (a) attain a minimum score of 94 on the School and College Ability Test, (b) rank at or above the 90th percentile on the Scholastic Aptitude Test, (c) score at or above the 90th percentile on the Iowa Test of Basic Skills or the Stanford Achievement Test, (d) by teacher recommendation.

Participation in the honors program infrequently is based on teacher recommendation alone. Students participating in the honors program are, almost without exception, highly motivated to excel academically.

Teacher Selection Both participating teachers held master’s degrees in the content area, had been teaching

physics for at least 14 years, and had been recognized as exemplary teachers within the district and within the physics education community.

The teacher of CG-2 and the TG would be classified as a constructivist who utilized the learning cycle as the basis for the instructional models utilized for CG-2 and TG.The teacher of Control Group 1 (CG-l) would be identified with the didactic method of instruction.

Selection of Pretest and Posttest InstrumentsPretest and posttest instruments served two purposes in this study: to determine, for

curriculum design purposes, the pre- instructional knowledge state of high school students enrolled in honors physics courses; and to determine the relative effectiveness of the different instructional designs utilized in the study.

Development and validation of a test that was appropriate for the goals of this study was carried out by Halloun (1984). During the 1981-83 academic years, over 1,200 students at Arizona State University were administered various versions of the diagnostic test. Participating students were enrolled in three university courses: PHY 101 (Introduction to Physics), PHY 111

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(College Physics - without calculus), and PHY 115 (University Physics - with calculus). Students’ ages ranged from 16 to 46 years, with an average age of 21 years (S.D. = 3.83). Twenty-eight percent of the students were females and 72% were males. Of 289 students enrolled in PHY 115 in the 1983 fall semester, 71% had taken one or more semesters of high school physics, 37% had previously taken one or more semesters of university-level physics, 49% of the students had previously taken one or more semesters of high school calculus, and 71% had taken one or more semesters of calculus at the university level.

The questions for the diagnostic test were selected from the concepts and laws pertaining to primary models of particles subjected to a zero or a constant net force. The items selected were the ones judged by the physics community to be the most relevant to indicate a Newtonian view of mechanics. The instrument underwent testing and revisions for 2 years. The original tests required the students to provide written responses with statements that explained their answers. The final version was formatted as a multiple-choice test, which offered as response selections the five most popular responses, including a correct response, offered by students during the development period.

Questions included in the final version were those that had previously correlated, p < .05, with student performance in the various physics courses. Halloun indicated that for the final multiple- choice version, as utilized in this study, the Kuder-Richardson coefficient of reliability measured .86 on the pretest and .91 on the posttest. These high values on the Kuder- Richardson coefficients are indicative of a highly reliable test. The Kuder- Richardson coefficient values reveal the reliability of the final version in measuring the same skills as the experimental test, with the more efficient multiple-choice format.

Test-retest effects were measured in the fall semester of 1982, when the average score of students who took both the pretest and the post test was 22.64 (S.D. = 4.86) on the posttest. At the end of that same semester, 29 students took the posttest without having taken the pretest. The average test score for these students was 22.45 (S.D. = 4.86). This result shows that having taken the pretest had very little effect on the posttest scores.

Post-Posttest Preparation The instructional design used with the treatment group in this study emphasized

systematic model development and deployment by means of a laboratory-oriented Atkin-Karplus learning cycle that supported a modeling theory of instruction as proposed by Hestenes (1987). This instructional model would suggest that subjects should excel in retention and transfer of knowledge. This method deemphasized instruction and practice in the more traditional formula-centered, textbook-type manipulation and problem solving. Therefore, it was of interest to determine how effectively the subjects could deal with the more traditional test questions.

A post-posttest was developed to measure subject competency in traditional-type problem solving. This test consisted of the 24 mechanics questions and problems from the 1983 NSTA-AAPT standardized examination, along with 16 carefully selected questions from Harvard Project Physics unit tests and PSSC tests that emphasized Newtonian conceptual responses. This test is displayed in Appendix B.

Administration of TestsThe conceptual pretests in mechanics were administered to all subjects in a 55-minute

test period, just before instruction in mechanics was commenced (September 1, 1983, for CG-2 and September 12, 1986, for CG-l and TG). It should be noted that none of the subjects needed

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the entire test period; in fact, most of the subjects completed the test within 35 minutes or less. The conceptual posttest in mechanics was administered to all subjects immediately upon completion of instruction on linear and circular motion in mechanics (March 29, 1984, for CG-2 and March 6, 1987, for CG-1 and TG). Both participating teachers had copies of the test instrument; however, during the prestudy discussions it was agreed that teaching to the test would be judiciously avoided. An analysis of posttest responses indicated that the gains were generally no greater in any of the three groups on the items that were more easily taught to (lower-order knowledge questions) than on those less easily taught to (higher-order comparison, analysis, and synthesis questions) , suggesting that the test was not directly taught to in any of the three groups.

The post-posttest was administered during a 55-minute test period on the last day of the school year before final examinations began (June 1, 1987, for CG-1 and TG). Most students completed the test in 40 minutes or less. All test questions were scored as 1 point for a correct response, and 0 points for an incorrect response.

Instructional Procedure Control Group 1 received instruction utilizing Elements of Physics (9th edition). This

presentation consisted of lectures and demonstrations (80% of class time), with homework questions and problems selected to reinforce important concepts from lecture and to provide practice in problem solving.

Laboratory activities (20% of class time) were designed and/ or selected to emphasize important concepts from lecture and/ or to develop laboratory skills.

Control Group 2 was instructed using the learning cycle. This group received instruction utilizing the PSSC fourth-edition textbook (30% of class time), with homework and class study group questions and problems selected from textbook and teacher developed to reinforce and expand on concepts developed in the laboratory activities.

Laboratory activities (70% of class time) were all either teacher developed or modified from the Harvard Project physics handbook. The laboratory activities were designed to target concepts derived from Newton’s laws of motion.

The treatment group was instructed utilizing the learning cycle model in conjunction with the Hestenes modeling theory. The fifth- edition PSSC textbook was used. Most of the homework and in-class study group questions and problems were semiquantitative motion map, force diagrams, and discussion type, which were teacher generated, using the taxonomy of misconceptions in mechanics as a guide.

Laboratory activities (70% of class time) were either teacher developed or modified from the Harvard Project physics handbook. The laboratories were designed to target concepts derived from Newton’s laws of motion.

All laboratory activities for CG-2 and TG were the same. The instructional difference was in the model deployment techniques. The total instructional time devoted to the study of mechanics was the same for all three groups, extending from the first week in September until mid-March. All participating groups covered the same topics in mechanics, on nearly the same time line, as had been agreed to previously by the participating teachers. However, the instructional procedures for the didactic method were significantly different from those utilized by either of the other two methods; thus, the time devoted to the various instructional activities varied significantly from the didactic to the other two methods. The learning cycle method and

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the directed modeling learning cycle both utilized the same laboratory activities, taught with inquiry techniques, conforming to the same instructional time line. As such, the time devoted to the various instructional activities for these two methods were very nearly the same.

Summary Seventy-two high school honors physics students participated in this study. These

students were distributed over two control groups and one treatment group. Test data from 478 university physics (PHY 115) students at Arizona State University who took the same pretest and posttest as part of a doctoral study by Halloun in 1984 provided external corroborating data. The study was designed primarily around two classes of high school honors physics students, CG-2 and TG, who were taught by the same teacher, using the same three-stage modified learning cycle instructional design, differing only in the method of third-stage implementation, which addressed model deployment.

The study utilized a pretest-posttest instrument that was designed and validated by Halloun (1984) to determine the initial knowledge state of introductory university physics students and to determine the relative effectiveness of instruction. The pretest was administered to all groups before instruction was commenced in mechanics and the posttest was administered to the same groups at the conclusion of instruction in mechanics.

A post-posttest was used to determine the relative long-term conceptual retention and numerical problem-solving skills. This test was administered to CG-l and TG on the last day of the year.

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Chapter 7Experimental Results

Initial Knowledge State of High School Students The validity of the claim that the taxonomy developed by Halloun and Hestenes ( 1985a)

can be used in the design of the instruction to be utilized with the high school treatment group rests on the ability to demonstrate that the misconceptions in mechanics held by preinstructional high school physics students are essentially the same as those held by preinstructional students at the university level.

An examination of the response profiles for the mechanics pretests taken by the three high school groups and the one university group studied indicate a striking similarity in response patterns, as indicated by Figure 8. [Editor’s note: Figure 8, Tables 1 and 2, and discussion comprise pages 93 to 116. They are available by e-mailing hestenes@asu.edu].

Posttest Evaluation The purpose of this study was to compare the relative effectiveness of three methods of

instruction, which were identified as didactic (CG-1), learning cycle (CG-2), and the modified modeling learning cycle (TG). The relative effectiveness of the different instructional methods was measured in terms of a transition from what has been described as a “naive” to a Newtonian view of mechanics. This transition was measured by the average gain registered during the pre to post mechanics diagnostic test evaluation. The items selected for the pre-posttest instrument were judged by the physics community at Arizona State University to be valid indicators of a Newtonian view of mechanics.

The students in the PHY115 group did not participate in this study; however, they were participants in Halloun’s 1984 study in which the students from CG-2 were participants. The PHY 115 students were instructed with the didactic method of instruction, so the available scores were included for external data corroboration (see Figure 9) [e-mail hestenes@asu.edu.]. An analysis of the posttest scores yielded the following results:

CG-1 Pretest mean = 15.7 (S.D. = 4.58)Postest mean = 20.4 (S.D. = 4.73)

Gain = 4.7 (S.D. = 3.37)

Students scoring at or above the pretest mean = 75%

CG-2 Pretest mean = 11.0 (S.D. = 3.54)Posttest mean = 19.0 (S.D. = 5.15)

Gain = 8.0 (S.D. = 5.67)Students scoring at or above the pretest mean = 91%

TG Pretest mean = 13.6 (S.D. = 5.97)Posttest mean = 26.0 (S.D. = 5.65)

Gain = 12.4 (S.D. = 4.93)Students scoring at or above the pretest mean = 100%

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PHY 115 Pretest mean = 18.5 (S.D. = 5.66)Posttest mean = 23.1 (S.D. = 5.53) Mean Gain = 4.6

The student group that was subjected to the didactic treatment (CG-1) achieved a gain of 4.8, those subjected to the learning cycle (CG-2) treatment experienced gains of 8.0, and those subjected to the modified modeling learning cycle (TG) experienced gains of 12.4.

The posttest response profiles as illustrated in Figures 10 through 13 indicate broader gains for CG-2 and TG than for CG-1 or PHY115.

The response profiles indicate that TG scores declined from pretest to posttest on only three questions, CG-2 had declines on five questions, and PHY115 had declines on seven questions.

A one-way analysis of variance of mean pre-posttest gains for students instructed with the didactic (CG-l), learning cycle (CG-2), and modified learning cycle (TG) methods of instruction (see Table 3) [available by e-mail] indicated that there were significant differences among the mean gains of the three groups at the 1% confidence level (p < .01). Following the analysis of variance, the Scheffe test was utilized for a multicomparison of significant differences among the three experimental groups (see Table 4). This test indicated that there was no significant difference between the mean gains for didactic (CG-1) and learning cycle (CG-2) instructional groups at the 5% confidence level; however, there was a significant difference between mean gains for the didactic (CG-1) and the modified learning cycle (TG) as well as between the mean gains for the learning cycle (CG-2) and the modified learning cycle (TG) groups at the 1% confidence levels.

Post-Posttest The post-posttest could be administered only to the CG-1 and TG, because it was not part

of the Halloun (1984) study. There were questions as to both the retention of concepts and the ability of the students in TG to demonstrate the ability to work problems that required the selection and manipulation of formulas. The TG instruction deemphasized quantitative problem solving in favor of an emphasis on verbal articulation of qualitative and semiquantitative problems analysis (motion maps and force diagrams) as it supports concept development. The post-posttest consisted of the 24 questions from the 1983 version of the NSTA-AAPT test and 16 other conceptual questions from other sources (see Figure 14) [ e-mail]. The grade breakdown is as follows:

CG-1 TGMean score = 18.0 26.2

SD = 5.72 6.13High score = 34 37Low score = 8 15

A t-test analysis of mean scores on the post-posttests (see Table 5) indicates that there is a significant difference between the mean scores of the didactic (GC-1) and the modified learning cycles (TG) treatments at the 1% confidence level.

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Figure 14 [e-mail] shows the post-posttest response profiles. Except for several conspicuous exceptions, the treatment group (TG) exhibited a superior grasp of concepts as well as a superior ability to solve numerical problems.

SummaryThe initial knowledge state of high school honors physics students was examined with

the Halloun-Hestenes mechanics diagnostic test and found to be very much the same as that of introductory university students. Student response patterns were examined for coherence. The conclusion was reached that preinstructional high school students possess unstructured and noncoherent misconceptions.

An analysis of variance of the pre-post gains indicated that the gains by the students instructed with the learning cycle method were not significantly greater than those instructed with the didactic method. However, the students instructed with the modified modeling learning cycle demonstrated gains that were significantly greater than either the didactic or learning cycle methods at the 1 % confidence level (p = .01).

A t-test analysis indicated that the post-posttest scores of the students instructed with the modified learning cycle were significantly greater than the didactic method at the 1% confidence level (p = .01) in spite of the fact that problem solving was deemphasized with the modified modeling learning cycle. Comparisons with CG-2 were not possible, as they did not take the post-posttest.

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Chapter 8Conclusions

The instructional experiment reported in this dissertation supported the following conclusions:

1. Subjects instructed with an inquiry method exhibited greater learning gains, as measured with the Halloun-Hestenes mechanics diagnostic test, than did the subjects instructed with the didactic method.

2. Subjects instructed with an inquiry method in conjunction with a structured theory of model development that specifically addressed model deployment displayed greater learning gains, as measured with the Halloun-Hestenes mechanics diagnostic test, than did those instructed with the inquiry method without structured deployment techniques or those instructed with the didactic method of instruction.

3. Post-posttest results indicated that students instructed with the inquiry method of instruction in conjunction with structured model deployment techniques displayed better concept retention and superior numerical problem-solving abilities than did students instructed with the didactic method.

In fact, the students instructed with the inquiry method utilizing structured deployment techniques showed achievement superior to that of all other groups in every category considered.

An analysis of the diagnostic pretests indicated that the university students’ responses differed significantly from those of the high school students only on descriptive questions that had been discussed in previous courses. When responding to questions that required a clear understanding and application of scientific principles, university students did not have an advantage over high school students.

An analysis of certain selected questions from the Halloun-Hestenes diagnostic test in conjunction with the gains scored by the TG indicated that high school students did not hold firmly embedded preinstructional concepts that interfered with activity-centered concept development. The data did, however, support the theory that misconceptions interfere with linguistic concept development as utilized by the didactic method of instruction.

Implications for Instruction This study demonstrated that student achievement in introductory high school physics

courses could be improved significantly. The study indicated that instruction should focus on the development of modeling techniques rather than the acquisition of subject-specific content.

The results of this study suggested additionally that effective deployment of mental models depends upon the ability of the instructor to induce cognitive conflict between the students’ misconceptions and the mental models that were developed through guided activities. This procedure was possible in this study by utilizing the taxonomy of misconceptions in mechanics as developed by Hestenes and Halloun. Thus, one must be aware of student misconceptions in order to develop effective mental models.

Suggestions for Future ResearchThe utilization of the taxonomy of misconceptions in mechanics has been repeatedly

referred to as the critical difference between the instruction of CG-2 and TG. Without being fully

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aware of student misconceptions, model deployment must progress by trial and error. Therefore, before modeling instruction in introductory physics can be effectively implemented, taxonomies in the other areas commonly taught must be thoroughly and completely developed.

Another area suggested for further research is the commonly perceived differences between initial knowledge states in physics for males and females, the reasons for these differences, and necessary modeling techniques needed to accommodate the differences, if any.

Partial Bibliography (Including only the references cited in these excepts)

Atkin, J.M., & Karplus, R. (1962). Discovery of invention? Science Teacher, 29(5), 45.Bowen, B.L. (1975). The need for paradigms in science education research., Science Education,

59, 423-430.Champagne, A.B., Klopfer, L.E., & Gunstone, R.F. (1982). Cognitive research and the design of

science instruction. Educational Psychologist, 17(1), 31-53.Clement, J. (1982). Students’ preconceptions in introductory mechanics. American Journal of

Physics, 5, 66-71.diSessa, A.A. (1979). On learnable representations of knowledge: A meaning for the

computational metaphor. In J. Lochhead & J. Clements (Eds.) Cognitive process instruction (pp. 239-266). Philadelphia: Franklin Institute Press.

Ganiel, U., & Idar, J. (`985). Student misconceptions in science--How can computers help? Journal of Computers in Mathematics and Science Teaching, 4(3), 14-19.

Halloun, I.A. (1984). The use of models in teaching Newtonian physics. Unpublished Ph.D. dissertation, Arizona State University.

Halloun, I.A., & Hestenes, D. (1985a). Common sense concepts about motion. American Journal of Physics, 53, 1056-1065.

Halloun, I.A., & Hestenes, D. (1985b). The initial knowledge state of college physics students. American Journal of Physics, 53, 1043-1055.

Harms, N. (1981). Project synthesis: Summary and implications for teachers. In. N. Harms & R. Yeager (Eds.) What research says to the science teacher (Vol. 3). Washington, DC: National ScienceTeachers Association.

Hestenes, D. (1979, April). Wherefore a science of teaching? The Physics Teacher, pp. 235-242.

Hestenes, D. (1987). Toward a modeling theory of physics instruction. American Journal of Physics, 55, 440-454.

Kuhn, T. S. (1962). The structure of scientific resolutions. Chicago: University of Chicago Press.

Lawson, A. E., Karplus, R., & Adi, H. (1978). The acquisition of proportional logic and formal operational schemata during the secondary school years. Journal of Research in Science Teaching, 15, 465-478.

Lawson, C.A. (1967). Brain mechanisms and human learning. Boston: Houghton Mifflin.

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Maloney, D.P. (1984). Rule governed approaches to physics—Newton’s third law. Physics Education, 19, 37-42.

McCloskey, M. (1983, April). Intuitive physics. Scientific American, pp. 122-130.McCloskey, M., Caramazza, A., & Green, B. (1980, December). Curvilinear motion in the

absence of external forces: Naïve beliefs about the motion of objects. Science, pp. 1139-1141.

National Assessment of Educational Progress. (1978). Report #08-S-00. Education Commission of the States.

National Commission on Excellence in Education. (1983). A nation at risk: The imperative for educational reform. Author.

Norman, D.A. (1980). Discussion: Teaching, learning and the representation of knowledge. In R.E. Snow, P. Federico, & W.E. Montague (Eds.), Aptitude, learning and instruction: Vol. 2. Cognitive process analyses of learning and problem solving (pp. 237-244). Hillsdale, NJ: Earlbaum associates.

Nussbaum, J., & Novick, S. (1982). Alternative frameworks, conceptual conflict and accommodation: Toward a principled teaching strategy. Instructional Science, 11, 183-200.

Peters, P.C. (1982). Even honors students have conceptual difficulties with physics. American Journal of Physics, 50, 502-508.

Trowbridge, D.E., & McDermott, L.C. (1980b). Investigation of student understanding of the concept of velocity in one dimension. American Journal of Physics, 48, 1020-1028.

BIOGRAPHICAL SKETCH

Malcolm Wells, born in Phoenix, Arizona on February 6, 1931, received his elementary and secondary education in the Phoenix Elementary and Phoenix Union High School districts. He graduated from Arizona State University with a Bachelor of Arts degree in science education in 1957, a Master of Arts degree in physics education in 1961, and a Doctor of Education degree in physics education in 1987. He has been employed by the Tempe Union High School District, teaching chemistry and physics, since 1957. Throughout his professional career he has been very active in professional associations, including the American Association of Physics Teachers, the National Science Teachers Association, the Arizona Science Teachers Association, and the Arizona Nevada Academy of Science. Awards include the Science Teacher of the Year—High School Division, awarded by the Arizona Science Teachers Association in 1984; Award of Excellence from the Tempe Union High School District in 1985-86; and the Presidential Award for Excellence in Science and Teaching in 1986.

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