31? at 8 id no, 2
TRANSCRIPT
31? At 8 Id
No, 2<T?(
A COMPARISON OF THE PROBLEM SOLVING ABILITY OF
PHYSICS AND ENGINEERING STUDENTS
IN A TWO YEAR COLLEGE
DISSERTATION
Presented to the Graduate Council of the
North Texas State University in Partial
Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
By
John R. Martin, M.S.
Denton, Texas
December, 1986
Martin, John R., A Comparison of The Problem Solving
Ability of Physics And Engineering Students in a Two Year
College. Doctor of Philosophy (Higher Education), December,
1986, 106 pp., 8 tables.
The problem with which this study was concerned is a
comparison of the problem solving ability of physics and
engineering students in a two year college. The purpose of
this study was to compare the problem solving ability of
physics and engineering students in a two year college and
determine whether a difference exists.
Data was collected from an instrument administered to
twenty-six engineering students and twenty-three physics
students as a major examination in their regular courses.
The instrument was validated by being taken from
representative texts, by approval of the instructors using
the examination, and by approval of a physics professor at a
university. The instructors and professor were considered a
panel of experts. Comparison of test scores of students who
were registered in both physics and engineering and who took
the exam twice, established concurrent validity of the
instrument. A questionnaire was also administered to both
groups of students to determine their personal problem
solving strategies, if any, and to collect other demographic
data. Additional demographic data, as available, was
2
obtained from the registrar. Instructor profiles were
determined from interviews with each of the four instructors
involved.
Analysis of the data indicated there is a significant
difference in the ability of engineering students and
physics students to solve statics problems. The engineering
students scored significantly better in solving both
engineering problems and in overall problem solving, as
hypothesized. The engineering students also scored
significantly higher in problem solving ability on physics
problems, resulting in the rejection of the hypothesis that
there would be no difference in the problem solving ability
of the two groups on physics problems.
Copyright by-
John R. Martin
1986
TABLE OF CONTENTS
Page
LIST OF TABLES vi
Chapter
I. INTRODUCTION 1
Statement of the Problem Purpose of the Study Hypotheses Significance of the Study Definition of Terms Limitations Basic Assumptions Summary
II. REVIEW OF RELATED LITERATURE 17
III. METHODS AND PROCEDURES FOR THE COLLECTION AND ANALYSIS OF DATA 35
Research Design Instrument Population Procedures for the Collection of Data Treatment of Data Summary
IV. DATA ANALYSIS, PRESENTATION OF DATA, AND HYPOTHESIS TESTING 55 Introduction Data Analysis Presentation of Data Hypothesis Testing Instructor Profiles Student Profiles Summary
IV
V. SUMMARY, DISCUSSION OF FINDINGS, CONCLUSIONS, IMPLICATIONS OF FINDINGS AND RECOMMENDATIONS FOR ADDITIONAL RESEARCH 78
Introduction Summary Discussion of Findings Conclusions Implications of Findings Recommendations for Additional Research
APPENDICES 90
BIBLIOGRAPHY 1 01
v
LIST OF TABLES
Table
I. Results of Experiment and Descriptive Statistics
Page
59
II. Inferential Statistics for Testing of
Hypotheses 60
III. Summary of Hypotheses Testing. 62
IV. Probability-Values of Hypotheses Compared to the 0.05 level 65
V. Age, Sex, and Problem Solving Strategies . 68
VI. Statistics for Comparison of Cummulative Overall Grade Point Average
VII. Statistics for Comparison of Mathematics Background 7 3
VIII. Comparison of Probability—Value for Grade Point Average and Mathematics Background 7 4
vi
CHAPTER I
INTRODUCTION
Problem solving holds a time—honored position in
undergraduate and graduate physics and engineering
education. An examination of standard textbooks in either
discipline will show that each contains several problems at
the end of each section or chapter (3,4,5,8,9,11,13,14,16,
17,18,21,22,23,25,26). Typically, students are assigned a
certain number of these problems as homework and then given
similar problems on the examinations.
Reading through the introductions and prefaces of these
representative texts in both physics and engineering shows
that all the authors regard problem solving not only as a
skill to be developed, many say this is their objective, but
also as the sine qua non of mastering the content.
Physicists generally agree that the ability to solve
problems is the most important demonstration of an
understanding of physics (20, p. 1035). One engineering
text even goes so far as to say that if you cannot solve
textbook problems, then real world problems involving
economics, judgment, and cosmetics are out of the question
(14, p. x).
Categorically, physics deals with formulation of the
principles of natural science, and engineering deals with
the practice of those principles. Typically, engineering
students are required to take physics (usually two
semesters) but not vice-versa. Engineering students do not
always find the experience in physics pleasant or helpful
(15) .
For whatever reasons, the engineering curricula
includes a kind of halfway house between engineering
practice and physics theory, usually called engineering
mechanics, which is taught in a department by the same name.
Sometimes it is called interdisciplinary studies or
engineering science, and the courses are taught by the
various engineering departments, usually civil or
mechanical. These courses, usually five or six in number,
could be viewed as applied physics or theoretical
engineering designed to serve as a prelude to engineering
practice and design.
Generally, engineering majors in all specializations
are required to take at least one course from each area.
The content of these courses, statics, dynamics, mechanics
of solids, fluid mechanics, circuits, and thermodynamics, is
common to both physics and engineering, but the emphasis and
formalism applied by the two areas are different. One
physics professor has noted that you can tell the difference
in emphasis and formalism just by looking at the pictures in
the books (2) .
Thus, even though all engineering is based on physics,
not all practicing engineers recognize the connection in
spite of the fact that they have had physics (1). This lack
of connection is not surprising when one reads through the
early chapters of representative engineering texts
(9,13,14,16,17,22,23). The term "physics" does not appear
as the basis of engineering but rather "mechanics," "the
physical science of mechanics," or "Newton's mechanics" but
never the word "physics." Sometimes the text will even list
the physical laws on which the content is based, but never
do these engineering texts say that engineering is based on
physics per se.
It has been charged (15, pp. 3,4) that a bachelor's
degree in physics, while broad, is in no way adequate
preparation for a career in engineering design. The claim
is also made that some view a baccalaureate in physics as a
degree which does not prepare one for anything practical
except to go on to graduate school, and spending one's life
trying to understand theory and never able to do or
practice, that is, apply the theory (15, pp. 3,4).
Physicists would counter with the claim that while
engineers probably do routine engineering design problems
better than physicists, physicists are better equipped to
handle nonroutine engineering design problems because of
their in-depth understanding. Perhaps the best example of
this is the Manhattan project at Los Alamos during World War
II. Contrary to popular opinion the work at Los Alamos was
not science but engineering, nonroutine to be sure but
nevertheless engineering (7, p. 108). In fact, in the view
of one Nobel laureate at Los Alamos, all science and
scientific research stopped during the war (7, p. 108).
The conflict between the physics elite and the
non-physicists at Los Alamos was perceived by one chemist,
who made significant contributions to the implosion problem,
as being ganged up on because he was not a physicist (10, p.
134). His complaint was answered with the reply that
chemists were actually very good third-rate physicists
(10,p. 134).
The situation between physics and engineering can be
summarized by noting that a nonroutine project, such as the
one at Los Alamos, that has never been done before, is
better left to the physicists, but if you want to design a
nuclear power plant, a nuclear engineer would be preferred
over a physicist. The question of which student, physics or
engineering, is better able to solve problems, at least in
areas which are common to both students, is a question which
still arises.
Statement of the Problem
The problem of this study is a comparison of the
problem solving abilities of physics and engineering
students in introductory calculus-based courses with common
content but different emphasis and formalism.
Purpose of the Study
The purpose of this study is to compare and determine
whether there is a difference in the problem solving ability
of engineering students enrolled in a beginning
calculus-based statics course and physics students enrolled
in a first course in calculus-based physics at a two year
college. The content and concepts necessary to solve the
problems are common. The development of the formalism, how
the general equations are written for the application
necessary to solve the problems, is different. Physics
formalism aims at generality while engineering formalism
aims at applicability.
Generally, the engineering problems are more applied
than the physics problems, and engineering students spend
more time in practice and drill in solving similar types of
problems. Physics students, who probably solve just as many
problems, concentrate on problems which are considered to be
interesting and designed to give additional insight into the
principles involved. All of the problems in this study can
be solved by the application of only two basic equations, so
obviously the same concepts and principles are used for the
solution of both types of problems.
The main differences between the two methods of
instruction are the kinds of applications to which the
equations are applied, how the equations are written and
applied, and how much time and practice is spent on a
particular topic. The depth of the coverage between the two
courses is different. But even here the concept of depth of
coverage means one thing to a physicist and another to an
engineer.
In covering friction, for example, an engineer would
say that depth of coverage is related to applying the basic
equations to various kinds of friction such as journal
bearings, axle friction, thrust bearings, disk friction,
wheel friction, rolling friction, and belt friction (4, p.
330-339). None of these topics would be covered in the
typical treatment of friction in physics texts or
instruction.
A physicist would say that the depth of coverage
involves looking at the subtleties of the phenomenon of
friction and discovering that there is no theory of friction
based on first principles, that everything must be done
empirically, that tables of frictional coefficients are
crude estimates at best because we do not know what the
mechanism of friction is, and that tables which list values
for, say, copper on copper are completely erroneous (6, p.
12-5). It should be noted that being aware of these
subtleties does not imply a greater ability to solve
problems of the type considered in engineering. in fact,
being aware of these subtleties may reduce problem solving
ability (20, p. 1035). It should also be noted that typical
physics texts and instruction do not cover the subtleties
mentioned here.
Depth of coverage in this study was taken to mean the
application of the basic equations to various kinds of
different situations. Using this definition, the depth of
coverage for statics is greater in engineering instruction
than in physics instruction.
Hypotheses
To achieve the purpose of this study, the following
hypotheses were tested:
1. On problems typical of those in engineering
texts, engineering students will score significantly higher
than will physics students.
2. On problems typical of those in physics texts,
there will be no significant difference between the scores
of the two groups.
3. The composite scores of the engineering students on
these problems will be significantly higher than the
composite scores of the physics students.
Significance of the Study
While problem solving is assumed to be a fundamental
si n e n o n in physics and enginieering education, it is
possible that the results of this study may support the idea
that current theory and practice, in both the physics and
engineering approach, produces an equal ability in problem
solving. it is also possible that the study may indicate a
needed modification in current theory and practice of one,
or the other, or both.
The current chairman and the former chairman of the
physics department of a large university without an
engineering college in the Dallas-Fort Worth metroplex have
both said that such a study would be valuable for evaluating
both curriculum and content of their physics courses and
pre-engineering programs (19,24). In particular, if
students exposed to statics courses solve problems better
than those exposed only to physics courses, then it would
seem desirable to include some engineering mechanics courses
m the physics department for pre-engineering majors and,
perhaps, as either required courses or electives for physics
majors.
Definitions of Terms
Definitions for the purpose of this study are as
follows:
1. Engineering student- This student is probably, but
not necessarily, an engineering major enrolled in a first
course in calculus-based statics. This student may or may
not have had a first course in calculus-based physics or may
be concurrently enrolled in a first course in calculus-based
physics.
2. Physics student- This student is probably, but not
necessarily, a physics, mathematics, or chemistry major
enrolled in a first course in calculus-based physics. This
student has never been enrolled in a first course in
calculus-based engineering mechanics in statics.
3. Problem solving- The ability to read a problem
stated in paragraph form in a textbook or on an examination
and, using general principles to translate it into
equations, diagrams, or graphs as required, through
mathematical manipulation, obtain the solution.
4. Formalism- A stating of general principles in
equation form which is appropriate for application to the
solution of particular types of problems.
^• Conventional physics and engineering instruction- A
lecture format with the possible use of demonstrations and
media to derive the principles and formalism required to
solve problems. Illustrative example problems are solved in
class.
6. Depth of coverage- The application of basic
equations to a wide variety of situations and circumstances.
Limitations
This study was limited to physics and engineering
students in beginning calculus-based statics and physics
courses at the northeast campus of Tarrant County Junior
College. Problem solving was limited to those kinds of
10
problems typically found in beginning calculus-based
textbooks in statics and physics, since these textbooks
determine the kinds of problems that are solved in these
courses (12, p. 1047) .
The examination problems used in this study came from
problems in both physics and engineering textbooks but were
limited to equilibrium problems in two and three dimensions
involving concurrent forces on particles and non-concurrent
forces on rigid bodies. More specialized applications such
as structures, trusses, frames, and machines were not
included since they are too specialized to be applicable to
physics.
If physics students are not able to solve two and three
dimensional equilibrium problems involving concurrent forces
on particles and non-concurrent forces on rigid bodies, it
seems doubtful that they could solve problems involving more
specialized applications such as structures, trusses,
frames, and machines. Thus, physics students without
exposure to the formalism and methods developed in
engineering mechanics courses would appear to be at a real
disadvantage compared to engineering majors in their ability
to solve problems related to engineering design and
practice.
Two year colleges usually offer no more than four of the
six engineering mechanics courses. Statics was the only
beginning engineering course offered for the 1985 fall term
11
at the northeast campus of Tarrant County Junior College.
The other two campuses in the district did not offer
engineering mechanics courses for the 1985 fall term.
Since specialized topics account for more than half of
the content in statics, less than half the course is common
to, or overlaps with, the physics course. The study was
also limited to one examination administered to both groups
of students. Aside from content limitations, administration
of more than one examination would probably be too much of
an imposition on the instructors involved.
Basic Assumptions
The validity of problem solving as practiced in physics
and engineering education is assumed to be fundamental to
both the acquisition of an understanding of the principles
and to the ability to move beyond the academic arena to the
more complicated solutions of real world problems involving
judgment, economics, and compromise. Because both courses
require the same calculus prerequisite, the students were
assumed to have the same overall intelligence and general
ability, particularly in problem solving. Instructors
generally regard the students as being comparable in their
background and in the skills necessary for success in these
courses. Therefore any difference in problem solving
ability would seem to be attributable to the difference in
emphasis on application and practice and to the difference
12
in the development of the formalism between physics and
engineering.
Summary
Problem solving is the cornerstone in the foundation of
engineering and physics education. Mastery in both areas is
based almost exclusively on problem solving ability. While
both disciplines place an equal emphasis on problem solving,
the formalism used to solve the problems is different.
Engineering formalism emphasizes applicability while physics
formalism aims toward generality. A question which appears
unanswered is whether or not this difference in formalism
results in a difference in problem solving ability.
The problem of this study is a comparison of the
problem solving ability of engineering and physics students.
The purpose of this study is to compare the problem solving
ability of these two groups of students in the normal ebb
and flow of their learning environment, and to determine
whether a difference exists.
To achieve the purpose of this study three hypotheses
were tested. First, the study hypothesized that engineering
students would solve engineering problems better than
physics students. The second hypothesis tested was that
there would be no difference in the ability of the two
groups to solve physics problems. Finally, it was
hypothesized that the overall problem solving ability of
13
engineering students would exceed that of physics students.
The study is significant for at least two major
reasons. If formalism does make a significant difference in
problem solving ability, then changes in instruction may be
indicated. Secondly, degree requirements and course
offerings may need to be changed or altered.
The study was limited to engineering and physics
students on the northeast campus of Tarrant County Junior
College. Problems were limited to two and three dimensional
statics problems involving concurrent forces on particles
and nonconcurrent forces on rigid bodies problems. The
problems were also limited to those kinds of problems found
in representative textbooks from each discipline.
Chapter II contains a review of related literature.
Chapter ill describes in detail the methods and procedures
used for the collection and analyses of data. In Chapter IV
the data is presented and analyzed and the hypotheses are
tested. The study is summarized in Chapter V. Chapter V
also presents a discussion of the findings, conclusions, and
recommendations for further research.
14
10
12,
CHAPTER BIBLIOGRAPHY
Adams, Forrest, Engineer, General Dynamics, Fort Worth, Texas. Interview with John R. Martin, February 12 t 1985.
Anderson, Miles E., Physics Department, North Texas State University, Denton, Texas. Interview with John R. Martin, April 9, 1985.
Arfken, George B. and others, University Phvsics. New York, Academic Press, 1984T"
Beer, Ferdinand P. and E. Russell Johnson, Jr., Vector Mechanics for Engineers, 3rd ed., New York, McGraw-Hill Book Company, 1977.
Eisberg, Robert M. and Lawrence S. Lerner, Physics Foundations and Applications, New York^ McGraw-Hill Book Company, 1981.
Feynman, Richard P., The Feynman Lectures On Physics 1963me lf R e a d i n g' Massachusetts, Addlson-Wesley,
' Surely You're Joking, Mr. ynman1, New York, W. W. Norton & Company,
Fox, Robert W. and Alan T. McDonald, Introduction to F l u i d Mechanics, 2nd ed., New York, John Wiley, 1978.
9. Ginsberg, Jerry H. and Joseph Genin, Statics, New York, John Wiley, 1977.
Goodchild, Peter, J. Robert Oppenheimer Shatterer of Worlds, Boston, Houghton Mifflin Company, 198X7
11. Halliday, David and Robert Resnick, Fundamentals of Physics, revised printing, New York, John WiTey, 1974. 2
Halloun, Ibrahim Abou and David Hestenes, "The Initial Knowledge State of College Physics Students "
w S f H ^ o T ^ f S r e . - 5 3 < N o v e m b e r ' '
15
13
14
15
16
17,
18.
20
21
22
23.
24.
Hibbeler, R. c . , Engineering Mechanics: Statics, 2nd ed., New York, Macmillian Publishing Co., Inc., 1978.
Higdon, Archie and others, Engineering Mechanics, Englewood Cliffs, New Jersey, Prentice-Hall, Inc.,
Kaplan, Herbert and Frederic Zweibaum, "The Invisible B.S.E.O. Degree: the Need for More Practical ndergraduate Training," Barnes Engineering
Company, Stamford, CT., nd.
Malvern, Lawrence E., Engineering Mechanics, Vol. 1 Englewood Cliffs, New Jersey, Prentice-Hall, Inc.,
Meriam, J. L., Engineering Mechanics, Vol. 1. n#*w vm-v John Wiley and Sons, 1978: '
Radin,^Sheldin H. and Robert T. Folk, Physics for Scientists and Engineers, Englewood Cliffs— New Jersey, Prentice-Hall, Inc., 1982. '
19. Redding, Rogers W., Physics Department Chairman, North
^ U n i v e r s i t y , Denton, Texas. Interview with John R. Martin, April 9, 1985.
Scott, Bruce L., "A Defense of Multiple Choice Tests," American Journal of Physics, 53 (November, ±yoo), 1035.
Sears, Frances W., Mark W. Zemansky, and Hugh D. Young, University Physics, 5th ed., Reading, Massachusetts, Addison-Wesley Publishing Company,
Shames, Irving H., Engineering Mechanics. Vol. l, 3rd
Inc.', 1980 e W°° d C l i f f s ' N e w J e r s e Y , Prentice-Hall,
Shelly, Joseph F., Engineering Mechanirs- Statics New York, McGraw-Hill Book Company, 19lKn '
Sybert, James R., Physics Department, North Texas State
M a S " 1 g r a e S r ? 9 8 5 ? X a S ' I n t e r v l e » John R.
25. T i p l e ^ c ^u J 9 A - , Physics, New York, Worth Publishers,
16
26. Zafiratos, Chris, Physics, New York, John Wiley, 19 76
CHAPTER II
REVIEW OF RELATED LITERATURE
An examination of representative textbooks used in
calculus-based engineering mechanics and physics courses
seems to reveal an attitude that the ability to solve
problems is better learned by example and practice than by
explicit development of problem solving skills (2,4,10,
H/13,15,18,19,24,25,26,34,37,.38,39,41,42) . This is
substantiated by at least one researcher whose studies have
led him to conclude that a knowledge of problem solving is
often taught implicitly by example rather than explicitly
(28, p. l) .
All of the texts, to various degrees, include numerous
solved problems as illustrative examples but none give a
comprehensive treatment of problem solving as such. Some
of the texts include a few brief comments intended to be of
help in actually solving problems (26, p. 12; 37, p. 12).
Typically, in engineering courses a handout is given showing
the form to be used in solving the assigned problems.
While little work has been done in textbooks on problem
solving per se, a great deal has been done and reported in
the journal literature. An Educational Resources
Information Center, ERIC, computer search showed over twenty
thousand articles with the words physics, engineering, or
17
18
problem solving in the titles. About two dozen articles
contained all three words. A computer search of
dissertation abstracts and titles showed that there are no
dissertations indexed which have conducted a study similar
to this study.
One article (23) presents several monographs dealing
with various aspects of problem solving such as training
patterns, taxonomy of activities, structure and process,
backward reasoning, learning and learner skills,
instructional variables, and human information processing.
The editor's motivation in assembling the monographs was
based on the conclusion that teaching problem solving was
not as simple as he had previously thought and that students
could not teach themselves (23, p. 7). He requested that
the papers be well-referenced to current literature and
focus on the less fashionable but fundamental starting point
of teaching problem solving (23, p. 7).
Among the conclusions reached by the editor was that
problem and problem solving must be carefully defined before
any meaningful methodology can result (23, p. 8). Both
terms are carefully defined in this study. The editor also
concluded that few science and engineering teachers have
been taught to teach, few students who reach science and
engineering courses have been taught to learn, and few
teachers have been taught to teach students how to learn
(23, p. 8). in his opinion, teaching students how to learn
19
is not a waste of time (23, p. 8). The final conclusion was
that teaching abstract reasoning and logical thinking is
extremely difficult (23, p. 8).
Other studies deal individually and in depth with these
aspects of problem solving. One paper, in trying to answer
the question of what makes problem solving so hard
identifies six steps used in solving problems (21, p. l).
These six steps, which are considered minimal, are:
Step (1): Read the problem and find out what is
given and what is required.
Step (2): Translate the given and required
quantities into symbols.
Step (3): Recognize the law which applies to the
situation.
Step (4): Identify which definitions are required
by analyzing the law and the given and
unknowns.
Step (5): Substitute the definitions into the law.
Step (6): Evaluate the formula obtained numerically
and check the validity of the results
(21, p. 18).
The paper also points out that the six steps correspond
to the six levels in Bloom's taxonomy. To reach a
particular level requires that all the previous steps at the
specified lower levels must have been completed (21, p.18).
Another discusses processes involved when problems are
20
solved by analogy (7). The two major processes involved are
matching key features or relationships and forming bridging
analogies (7, p. l). Three analogy generation mechanisms,
generation via an abstract principle, generative
transformations, and associative leaps, are also presented
(7, p. 7) .
The chosen content area to investigate problem solving
in physics and engineering seems to be mechanics
(14,17,28,29,30,31,35). One article gives two reasons for
restricting investigations to mechanics (16, p. 1043).
First, the first course in physics deals mainly with
mechanics and secondly because mechanics is an essential
prerequisite to almost all the rest of physics (16, p.
1043). The one exception to this use of mechanics involved
the use of thermodynamics to evaluate skills in problem
solving (32, p. 3). This study by Pilot, et al (32) also
evaluated theories of learning which were suitable and
relevant to an investigation of problem solving.
In their view only three theories of learning were
relevant to problem solving (32, p. 3); those of Ausubel
(3), Gagne (12), and Gal'perin (20, 40). Gal'perin's
instructional theory of problem solving, as supplemented by
Talyzina (20) and Lande (40), was chosen because in their
view it was the only one explicitly instructional in the
sense that it defines an optimal learning result by
prescribing the behavior of both the teacher and student
21
(32, p. 3). Gal'perin1s theory gives the mental actions of
problem solving in stage-by-stage procedures which the
student must master by practice to excel in problem solving
(32, p. 3) .
In Gal'perin's theory there are four characteristics in
the performance of an action (32, p. 3). The first
characteristic has to do with form, and states that an
action can be executed in three ways (32, p. 3). The first
form is material and involves manipulating actual objects,
such as an abacus, or manipulating symbolic representations
such as figures on paper (32, p.3). The second form in
which an action may be executed is verbal and involves
stating in words or formulating how the action is to be
executed (32, p. 3). The third form is mental and the
action is performed by mental operations such as speaking
silently or thinking without speaking (32, p. 3). The
second characteristic or parameter in the performance of an
action is generalization, where the action is directed to
one or more different sets of objects (32, p. 3). The third
characteristic involves completing the action links (32, p.
3). The action can be executed sequentially where the links
are carried one after the other or in a more compact form
where certain links are carried out at the same time (32, p.
3). The fourth and last characteristic is mastery which
measures how well the execution of the action has been
mastered and consequently rates the performance as high or
22
low (32, p. 3).
The classic work on problem solving theory in the
mathematical and physical sciences is the work of George
Polya (33). Polya's approach to problem solving involves
four steps:
I : UNDERSTAND THE PROBLEM.- What are the unknowns?
What is the data? What are the conditions? Can
the conditions be satisfied? Are the conditions
sufficient to determine the unknowns? Are the
conditions redundant or contradictory? Will a
figure help? What notation should be
introduced? Can the various parts of the
conditions be separated and written down (33, p.
xvi) ?
II : DEVISE A PLAN.— Has this problem or a similar
problem been solved before? What laws might be
useful? Are there connections between the data
and the unknowns? is there a simpler problem
whose solution is known and would help solve the
problem? Can the problem be restated? what
definitions are applicable? Is there a more
general or a more specialized problem which
could be solved? is there an analagous problem
which might be useful? Have all the essential
notions involved in the problem been taken into
account? what is the plan for the solution of
23
the problem and can it be carried out (33, p.
xvi) ?
Ill : CARRY OUT THE PLAN.— in carrying out the plan
check each step and make sure it is correct.
Can it be proven correct (33, p. xvii)?
IV : LOOKING BACK.— Can the result be checked? Can
the result be derived differently? is the
result reasonable and consistent with the
conditions? Could the result or method be used
for another problem (33, p. xvii)?
The impact and pervasiveness of Polya's work on problem
solving has been substantiated by the translation of How To
Solve rt (33) into fifteen languages (1, p. 13). p 0l y a was
influenced by earlier writers in physics and mathematics who
dealt with problem solving (1, p. 1 6, 17). Ernst Mach and
Rene' Descartes were two who had an influence on Polya (1,
p. 17).
Although he wrote principally on mechanics and the
theory of heat, Ernst Mach believed that you could not
really understand a theory until you knew how it was
discovered (1, p. 17). So Mach came to heuristics (1, p.
17). some of Mach's other books contain direct remarks on
problem solving (1, p. 17).
Theories of problem solving go back at least as far as
Rene' Descartes' Regulae (1, p. 17). This is not mentioned
m histories of philosophy because those historians didn't
24
know about problem solving (1, p. 17).
Although Polya's work on problem solving is regarded as
the classic work in the field (8, p. 285), it has not been
established whether his ideas work in the classroom (8, p.
291). Follow-ups of attempts to reduce his program to
practical pedagogies have been difficult to interpret (8, p.
291). Apparently, there is more to teaching problem solving
than a good idea from a master such as Polya (8, p. 291).
The hindrance to problem solving of prior miscon-
ceptions has also been studied (5,6,14). According to a
study by Halloun and Hestenes each student entering a first
course in physics has a common sense theory of beliefs and
intuition about physical phenomena derived from extensive
personal experience (16, p. 1043). It is claimed that since
the student uses this common sense theory to interpret what
he uses and hears in physics, it must be the major factor in
what he learns in the course (16, p. 1043).
This study by Halloun and Hestenes suggests that
conventional physics instruction failing to take these
common sense theories into account is largely responsible
for the legendary incomprehensibility of beginning physics
courses (16, p. 1043). These common sense theories are
generally incompatible with Newton's mechanics and as a
result students systematically misinterpret the material in
beginning physics courses (16, p. 1043). These common sense
theories are very strongly held and conventional physics
25
instruction does little to change them (16, p. 1043). The
discrepancy between the common sense theory and Newton's
theory best describes what the students need to learn (16,
p. 1043).
Various other studies have compared, profiled, and
identified several elements of problem solving. Student
problem solving ability has been compared with spatial
aptitudes (27), preexisting knowledge (36), and performance
against experts (28,29,36). Spatial aptitude was found to
determine the efficiency with which certain strategies could
be utilized (27, p. l).
Observations indicate that from preexisting knowledge,
students possess complex conceptual structures derived from
prior experience and from informal cultural transmission
(36, p. 5,6). While these conceptual structures are useful
in explaining and predicting phenomena encountered in every
day life, they tend to be vague, ambiguous, inconsistent,
and not accurately predictive when compared to scientific
conceptual structures (36, p. 6). A substantial
restructuring of preexisting knowledge and the acquisition
of a new mode of learning is required (36, p. 6). This new
mode of learning is quite difficult to acquire without
earfully designed instruction (36, p. 6).
Analysis of the problem-solving protocols of experts
and novices has been carried out. It has clearly shown that
problem solving does not consist of applying all the
26
applicable physical laws in the context of a specific
problem (28, p . 2).
The ability of lower level students in problem solving
has been compared with upper level students (5). Entering
freshmen engineering majors were compared before and after
their introductory physics course with upper level
engineering students who had just completed an introductory
mechanics course and it was determined that student learning
had been formula-centered (5, p. 1,4).
How student preferences for the concrete or the
abstract influence problem solving has also been studied
(9). The study showed that there was no significant
difference between science majors and non-science majors in
their preference for an abstract approach to problem solving
(9, p. 6). There was, however, a difference in abstract
ability between the two groups (9, p. 2). it was found that
students will change their preference from concrete to
abstract or vice-versa when faced with an actual problem
solving task (9, p . 21). This suggests the interpretation
that preference is task dependent (9, p. 21).
Entering students' cognitive skills have been profiled
using Piagetian measures, Scholastic Aptitude Test (S.A.T.)
scores, first semester grade point average (G.P.A.), and
level of math skill (22). The Piaget test indicated that
less than five percent of engineering freshmen were concrete
operational as compared with the non-engineering population,
27
where twenty-five to fifty percent of the students are
concrete (22, p. 8). There was no correlation between the
Piaget test results and the other measures leading to the
conclusion that Piaget-type tests are biased in favor of
scientific reasoning (22, p. 10).
Although there are differences in the formal reasoning
among engineering students, these differences are not
strongly related to scholastic performance indicating that
grades in engineering courses are primarily related to other
skills (22, p. 11). The low correlation between academic
performance and formal operational ability was attributed to
two factors (22, p . 11,. First, students most often learn
material and earn grades by rote which involves very little
understanding and reasoning (22, p . 11). Faculty teach and
test students in ways consistent with rote because they have
found other ways to be unrewarding (22, p. 11). Second,
adult reasoning is much more complex and involved than the
skills which are measured by the logical and intuitive
skills described by Piaget's concept of formal reasoning
(22, p. li).
Thus, students with little formal reasoning ability, as
measured by Piaget testing, perform well in many academic
and real-life situations (22, p . li). The fact that
non-formal thinkers.survive even in engineering does not
invalidate the importance of formal thinking as a construct
(22, p. 11). in a society where a.high percentage of adults
28
are non-formal in their thinking, one could certainly not
afford to require formal thinking as a prerequisite to
success (22, p. 11). on the other hand, it does not mean
that society might not be improved if the number of formal
thinkers were increased, especially if these increased
number of thinkers used this level of analysis in their
decision making (22, p. 11). in the field of engineering
there are countless failures caused by designers operating
from rote (22, p. 11).
The study concludes by saying that there is little
evidence to suggest that formal reasoning is necessary or
even helpful in obtaining a college education since
correlations between fromal reasoning and college grades are
low (22, p. 12). However, students in engineering and
Physics do seem to score significantly higher on any number
of tests measuring cognitive development than other groups
of students (22, p. 12). This evidence is consistent with
the debated claim that science, foreign languages,
mathematics in general, and physics in particular, are good
vehicles for the development of formal reasoning (22, p.
12). Assuming this claim to be true, the author concludes
that current trends in education would seem to reduce even
further the percentage of college students capable of formal
thought (22, p. 12).
Typical mistakes in problem solving have been
identified (5). One of the major findings of this study was
29
that students take an overly formula-centered approach to
learning physics in which they memorize formulas without any
understanding of what they mean (5, p. 4). Two major
aspects of this difficulty were isolated by clinical
interviews and written tests:
1. Students can mathematically manipulate equations
without a qualitative understanding of the physical
situation.
2. Students can mathematically manipulate equations
without being able to translate between the equations and
other symbol systems such as tables, verbal descriptions,
and diagrams (5, p. 4).
Two studies present evidence which indicates that
having students follow a rather rigid and methodical
prescriptive process in solving problems does improve their
ability to solve problems (17,35). The prescriptive process
involves a basic description which explicitly identifies the
information specified and required by the problem and
introduces useful symbols to specify the relevant
information in a convenient symbolic representation (35, p.
1). This basic description generates a theoretical
description which is a deliberate redescription of the
problem in terms of the specialized knowledge of the subject
area and then exploits the known properties in the
specialized subject area to obtain a solution (35, p. l).
These studies (17,35) report that in three groups of
3 0
students with one group adhering strictly to prescribed
procedures, one somewhat, and the third not at all, the
number of problems solved correctly diminished
correspondingly.
Summary
While problem solving has been considered from various
perspectives, apparently little or no study has been devoted
to comparing how well physics students and engineers, in the
context of their usual courses, solve problems. The only
comparisons made in these studies-are those of novices with
experts (28,29,36), and lower level with upper level
students in the same discipline (5).
31
CHAPTER BIBLIOGRAPHY
1. Alexanders™, G. L., "George Polya Interviewed on His Birthday," The Two-Year College
athematics Journal, 1 (January, 1979)t 13-19.
2. Arfken, George B. and others, University Physios.. KfoW York, Academic Press, 198T.— y ' N e w
3. Ausubel, D. p., Educational Psychology: A rooniUva View, New York, Holt, Rinehart aid W i n s S n * lies.
4' B e e r ' M ! ^ fi n a n d / - a n d E" R u s s e U Johnson, Jr., vector
Mechanics for Engineers, 3rd ed., New York McGraw-Hill Book Company, 1977. '
5. Byron, Fredrick, W., Jr. and John Clement, identify*™ Different levels of Understanding Attained by
FPTp 1n S n t s * F i n a l Report. Columbus,"Ohio-1980 raent ^Production Service, ED 214 755,
6. Champagne, Audrey B. and others, Effecting Changes in
ffiniK1V8 S ^ r u c t u r e s Amongst-Phiyilcs^Studenfs. lumbus, Ohio: ERIC Document Reproduction—
Service, ED 229 238, 1983. F^auction
7. Clement, John, Analogy Generation in sr.i*n + i Prnhlrm folvincj. Columbus^oETcT: ERTc DocumenF^ P£oblem Reproduction Service, ED 228 044, 1983.
8. D a v i s ^ Philip j. and Reuben Hersh, The Mathematical
198l! Boston, Houghton Mifflin Company,"
9. Dunlop, David L,, The Role of Student Preferpnrpc in
Problem-Solving Strategies. Columbus, Ohio: ~ERIC ocument Reproduction Service, ED 156 427, 1978.
10. Eisberg, Robert M. and Lawrence S. Lerner, Physics Foundations and Applications. New Y o r k — McGraw-Hill Book Company, 1981. '
u . Fox, Robert w and Alan T. McDonald, Introduction to Plui^ Mechanics, 2nd ed., Me» York, John wile?7
32
15
16
12. Gagne, R M., The Conditions of Learning, 3rd ed., New York, Holt, Rmehart and Winston, 1977.
13. Ginsberg, Jerry H. and Joseph Genin, Statics, New York, John Wiley, 1977.
14. Green, Bert E. and others, The Relation of Knowledge to Problem Solving, with Examples from — Kinematics. Columbus, Ohio: ERIC~Document Reproduction Service, ED 223 419, 1983.
Halliday, David and Robert Resnick, Fundamentals of Physics, revised printing, New York, John Wiliy,
Halloun, Ibrahim Abou and David Hestenes, "The Initial Knowledge State of College Physics Students,"
1043-1055 J° U r n a l — Ziiysics, 53 (November, 1985) ,
17. Heller, Jean I. and F. Reif, Cognitive Mechanisms Faci1itating Human Problem Solving in Physics: Empirical Validation of a Prescriptive Model. Columbus, Ohio: ERIC Document Reproduction Service, ED 218 077, 1982.
18. Hibbeler, R. c . , Engineering Mechanics: Statics, 2nd ed., New York, Macmillian Publishing Co Inc., 1978. y "
Higdon, Archie and others, Engineering Mechanics, Englewood Cliffs, New Jersey, Prentice-Hall, Inc.,
Lande, L. N., "Some Problems In Algorithmization and Heuristics In Instruction," Instructional Science, 4 (July, 1975), 99-TlT.
Hohly, Richard, A Concise Model of Problem Solving: A Report on its Reliability and Validity " ~~ Columbus, Ohio: ERIC Document Reproduction Service, ED 225 853, 1983.
L°ckheed Jack A profile Of the Cognitive Development Of Freshmen Engineering StudentsIAnn Arbor,
151 672n*1978IC D o c u i n e n t R eP r°duction Service, ED
19
20
21.
22
33
23
24,
26
27
29
30
32
L U b k i S ' ^ m e s L-'.Ed.f The Teaching of Elementary Problem Solving in Engineering and Related Fields. Columbus, Ohio: ERIC Document Reproduction Service, ED 243 714, 1984.
Malvern, Lawrence E., Engineering Mechanics, Vol. I Englewood Cliffs, New Jersey, Prentice-Hall, Inc.,1976.
25. McKelvey, John P. and Howard Crotch, Physics for Science and Engineering, New York, Harper and Row Publishers, 1978.
M e r i a r?' J-r7L!' Engineering Mechanics, Vol. I, New York,
John Wiley and Sons, 1978.
Mumaw, Randall J. and others, Individual Differences in Complex Spatial Problem Solving: Aptitude and Strategy Effects. Columbus, Ohio! ERIC Document Reproduction Service, ED 221 358, 1983.
28. Novak, Gordon S., Jr., Cognitive Process and Knowledge Structures Used in Solving Physics Problems. Final Technical Report. Columbus, Ohio: ERIC Document Reproduction Service, ED 232 856, 1983
ova , Gordon S., Jr., Goals and Methodology of Research on Solving Physics Problems. TR-58. Columbus, Ohio: ERIC Document ReproductTon-
Service, ED 232 857, 1983.
Novak, Gordon S., Jr and Agustin A. Araya, Physics Problem Solving Using Multiple Views. TR-173. Columbus, Ohio: ERIC Document Reproduction Service, ED 232 858, 1983.
31. Novak, Gordon S. Jr., Model Formulation in Physics Problem Solving. Draft. Columbus, Ohio: ERIC Document Reproduction Service, ED 232 859, 1983.
Pilot, A. and others, Learning and Instruction of S o l v i n q Science. Columbus, Ohio?
ERIC Document Reproduction Service, ED 201 536 19 84. '
33. Polya, G., How To Solve It, 2nd ed., Princeton, Princeton University Press, 1973.
34. Radin,^Sheldin H. and Robert T. Folk, Physics for Scientists and Engineers, Englewood Cliffs7~New Jersey, Prentice-Hall, Inc., 1982.
34
35,
36
37
38
39
40
R e i f ' F* and J ? a n I* Heller, Cognitive Mechanisms Facilitating' Human Problem Solving In Phvsi i-c • Formulation aHd~A^sessment of A Y • Prescriptive Model. Columbus, Ohio: ERIC Document Reproduction Service, ED 218 076, 1982.
Reif, F., how Can Chemists Teach Problem Solving' Suggestions Derived from Studies of Cognitive Processes. Working Paper ES-17. "Columbus,—
2 74°" 19 8 3 ^ Document Reproduction Service, ED 229
Sears, Frances W., Mark W. Zemansky, and Hugh D. Young, University Physics, 5th ed., Reading, Massachusetts, Addison-Wesley Publishing Company,
Shames, Irving H., Engineering Mechanics, Vol. I 3rd ed., Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1980.
Shelly, Joseph F., Engineering Mechanics; Statics, New York, McGraw-Hill Book Company, 1980.
Talyzina, N. F., "Psychological Bases of Instruction," instructional Science, 2 (November, 1973), 243-280
41. T i P l e r , Paul A Physics, New York, Worth Publishers, -Lnc • , iy /b .
42. Zafiratos, Chris, Physics, New York, John Wiley,
CHAPTER III
METHODS AND PROCEDURES FOR THE COLLECTION
AND ANALYSIS OF DATA
Research Design
This study, designed to compare the problem solving
ability of physics students with engineering students and
determine whether any difference exists, involved two
formalisms as treatments. Thus, the study can be considered
experimental in nature. As Borg and Gall point out, an
experimental study is the most powerful research method
known, and is the only one from which causality may be
established (1, p. 632). m a sense, this study is more
exploratory than experimental in that the purpose was the
determination of a difference in problem solving ability
rather than discovery of the causal factors to which the
difference may be attributable. Behavioral research is a
fully developed field and well-known experimental designs
which have become standard over the years are described in
detail in the classic text by Campbell and Stanley (3).
Recently, however, these traditional designs have been
criticized as being artificial and contrived, and as such,
the generalization of results is not valid (14). Another
author says that perhaps the greatest inhibitor of important
research in higher education has been the fallacious view
35
36
that research in higher education can and should be done
using the scientific method (10, p. 9-10). He also suggests
that phenomena in higher education cannot be explained by
law-like generalizations derived from controlled, rigorous
experiments and mathematical analysis resulting in
replicative situations providing predictive power for future
events, and that trying to do so should be abandoned as
unproductive in higher education (10, p. 9-10).
Typically, these simple systematic designs, as they are
called, utilize experimental and control groups studied in a
laboratory or in one or two school days with the
experimental group receiving a treatment that the control
group does not receive (14, p. 269). The two groups are
then compared using pretest and posttest criterion measures
(14, p. 269). The other variables, besides the treatment,
are either ignored or subjected to attempted control in some
manner (14, p. 269). Controlling out background variables
in certain research situations can produce artificial
situations and unnatural behavior (14, p. 266). it would be
safe to say that the bulk of educational research uses some
variation of these systematic designs.
These systematic designs can be problematic in that
they tend to produce artificial situations and unnatural
behavior in the subjects (14, p. 266). The well-known halo
effect, hall locker effect, John Henry effect, the Hawthorne
effect, and the placebo effect are all examples of this.
37
Snow (14) argues for what he calls representative design to
offset these problems and to increase the ability to
generalize from the results.
In this study, which should be regarded as exploratory,
the purpose is to determine whether there is any difference
in problem solving ability in the teaching-learning
environment as it exists rather than to try to attribute the
difference to a particular causal factor of factors. Hence,
generalizations will be made with some care. Representative
design is one which has been constructed to be an accurate
representation of the actual environment in which the
learning takes place and of the abilities of the learners.
According to Borg and Gall (1), Snow's (14) argument
for representative design is based on at least four
assumptions:
1. Educational environments are complex and
interrelated and need to be studied as such, in much the
same way ecosystems are considered symbiotic in biology.
2. Human learners, unlike rats in psychology and
electrons in physics, do not react passively when subjected
to systematic designs.
3. Humans have the capacity to adjust and adapt;
systematic designs are artifical because they may restrict
the behavior of the subjects and give results different from
those which might be obtained if the subjects were allowed
to act as they usually do.
38
4. Experimental intervention probably affects
the learner in a number of complex and interrelated ways (1,
P. 643,644).
Higher education may need to look to biology rather
than physics to find a model on which to base experimental
designs (14, p. 267). it has also been suggested that
research in higher education and the social sciences cannot
be modeled after the natural sciences, much less physics
(10, p. 10).
Interestingly enough, the idea that experimental
intervention affects what is being measured has been known
in physics for some time. Perturbation theory has been
developed to deal with this very problem, it has been said
that physicists, in studying elementary particles to try to
find the ultimate constituent of matter, try to find out
what is inside a watch by smashing it with a hammer and then
looking at what flies out. it would be preferable to do it
in some other, less perturbing way, but none is now known.
By way of analogy, traditional or systematic designs
could correspond to smashing the watch with a hammer, and
representative design could correspond to looking inside in
a less perturbing way. The state of the art in physics
today is that not only does the intervention of the
measuring device perturb what is being measured, it actually
creates the measurement (11, p. 38). m quantum mechanics
today, observations are properties of the interaction
39
between the system being measured and the observing
apparatus, thus, an object only has position, for example,
when the position is being measured (16, p. 178). A
parallel to this for educational research may be a long time
coming since it seems to be true, a priori, that IQ exists
whether it is being measured or not. A model which says
that IQ exists only when it is being measured and that the
measurement of IQ produces IQ does not appear to be a model
that behavioral science would be likely to adapt from
physics, at least not any time soon.
While recognizing that a truly representative design
may not be easily achievable in education, Snow (14)
suggests that experiments should be designed to more
accurately reflect the learners in their environment and
makes six recommendations to achieve representative design:
1. Conduct the research in an actual school
setting-the one to which the results will be generalized
(14, p. 274).
2. Use more than one teacher (14, p. 277)
3. Observe what the students actually do during
the experiment (14,. p. 278).
4. Observe other events which are occurring at
the same time which could affect the results (14, p. 278).
5. Adequately prepare the students prior to the
experiment (14, p. 280).
6. Choose a control treatment which allows the
40
students to utilize their usual approach to learning (14, p.
280) .
As Borg and Gall (1, p.645) note, the concept of
representative design is neither widely known nor used.
Traditional educational research designs make assumptions,
perhaps implicit, about the environment and about subjects
which may or may not be true. The effective use of
representative design should increase the ability of
educators to generalize from the findings of experimental
research in education, and allow them to apply those
generalizations to the real world of educational theory and
practice.
The design proposed here is to administer an
examination composed of a combination of problems taken from
standard textbooks in physics and engineering to classes of
physics and engineering students as one of their regular
examinations in the normal ebb and flow of their courses.
While the experimental design proposed here could be
considered simple, it does appear to be a representative
design when compared to Snow's six recommendations. Snow
says one of the most important factors in representative
design is to embed the experiment unobtrusively in the flow
of events (14, p . 274). The research in this study will be
conducted in the actual school setting, the teaching-
learning environment.
Although generalizations in this study are made
41
cautiously, the research was conducted in the setting within
which generalizations were appropriate. Four teachers were
used in this study (14, p. 277). other events, such as a
bomb scare, which could affect the results were observed by
the instructors and reported during the instructor
interviews (14, p. 278). There were no distractions during
the administration of the examinations in this study.
It was assumed that the instructors adequately prepared
the students for the examination. The preparation was
certainly more than the superficial preparation (14, p. 280)
of traditional designs where a few minutes are given to
instructions just prior to the administration of an
instrument which the students did not previously expect and
With which they are probably not familiar and which they may
not take seriously.
There was not a control treatment per se, but the
students were certainly utilizing their normal approach to
learning (14, p. 280). The treatment or independent
variable was the formalism, physics or engineering, and the
dependent variable was the examination score.
Extrapolating on Snow's ideas may mean that some of the
considerations in traditional designs such as validity and
reliability of instruments, instructor variables, and
comparability of students do not play as significant a role
as m representative designs, in fact, at least three
investigations (8, p. 1046; 4, p. 299; 17, p. 385) have
42
found that differences in age, gender, major, high school
mathematics, high mathematical competency, and academic
background have small effects on performance in introductory
physics.
It would seem that using more than one instructor would
require control of the instructor variable. Remarkably
enough, the control of the instructor variable may not be as
important as previously thought according to a recent study
(8). If the classes are conducted in a lecture format,
which is so common in physics and engineering instruction in
American universities that it is referred to as conventional
Physics instruction, and devoted to problem solving, then
the g a m in basic knowledge is essentially independent of
the professor (8, p. 1048).
This is even more remarkable when it is recognized that
within the format of conventional physics instruction wide
variations in instructional style are possible (8, p. 1047).
In this particular study the styles of the professors
differed considerably (8).
Professor A was a theoretical physicist whose lectures
emphasized the conceptual structure of physics with careful
definitions and orderly logical arguments (8, p. 1048). The
other three professors were experimentalists but with quite
different specializations (8, p. 1048).
Professor B spent a great deal of time and energy
preparing demonstrations for his lectures to help the
43
students develop physical intuition (8, p. 1048). Professor
C emphasized problem solving and taught by solving one
example problem after another (8, p. 1048). Professor D was
teaching the course for the first time and followed the book
closely (8, p. 1048).
All four had the reputation of being good instructors
according to informal peer opinion and student evaluations
(8, p. 1048). m fact, Professor B had received two awards
for outstanding teaching (8, P. 1048).
Representative designs determine, as best they can,
first how things really are and then proceed more slowly to
consider why they are that way and what it may mean. m
this study, this meant answering the question of which group
of students, physics or engineering, is better at solving
problems, at least statics problems, in their respective
environments as they currently exist.
Since a difference was established in this study,
subsequent studies which control or manipulate different
variables in a more traditional sense may be conducted to
possibly determine what causal factors, if any, are
responsible for the observed difference in problem solving
ability. Certainly validity and reliability of instruments,
general overall intelligence, and instructor variables would
be included among the variables to be controlled. To assume
that all examinations have reliability and validity and that
all students have the same overall intelligence may not be
44
justified without experimentation.
The instrument used in this study does appear to
contain both content validity, as established by a panel of
experts, the items being selected from standard texts and
concurrent validity, since three of the four engineering
students who took the examination a second time in their
physics course made identical scores the second time.
The two groups of students did not appear to be
significantly different at the 0.05 level in overall ability
based on statistical analyses of their cumulative overall
grade point average and mathematical background. in fact, a
probability-value for the level of significance of 0.215
indicates very little, if any, difference in overall ability
based on a comparison of cumulative overall grade point
average.
The two groups of students also did not appear to
differ significantly at the 0.05 level of significance in
mathematical background based on a statistical anylysis of
the number of semesters of mathematics completed as either
prerequisite or corequisite. The probability-value of
0.0698 indicates more difference in mathematical background
than in cummulative overall grade point average but again it
should be pointed out that even though the two groups of
students do not appear to differ significantly at the 0.05
level on these two measures, both of these measures seem to
have small effects on performance in introductory physics
45
courses (8, p. 1046) .
Also, as mentioned previously, the instructor variable
•nay be of minor significance (8, p. 1048). However, to
control for these variables before determining the actual or
representative situation would seem to be an incorrect order
of experimentation. m fact, controlling for the variables
first may actually produce the difference (14, p. 286). The
experimental design of this study was an attempt to deter-
mine whether the actual teaching and learning environment
produces a difference in problem solving ability rather
than using intervention and manipulation of variables to
control the environment to establish causal factors for
generalization.
Instrument
The instrument was a six problem, five choice, multiple
choice examination taken from representative calculus-based
textbooks in physics and engineering. These textbooks,
whether they are regarded as standard, typical, or
representative, determine course content and organization as
well as the kinds of problems that are considered in the
courses (8, p. 1043) .
Major examinations in physics and engineering usually
consist of four problems. This allows the student some
fifteen or so minutes for each problem. By using a multiple
choice examination rather than requiring the solutions to be
46
written out in detail, the number of problems on the
examination can be increased by fifty percent over what is
typical.
Since physicists generally agree that being able to
solve problems is almost synonymous with understanding, the
preferred type of examination in physics and engineering has
been a few problems requiring the student to write out
detailed solutions (13, p. 1035). The grader interprets the
solution and assigns a grade attempting to evaluate each
paper in the same manner (13, p. 1035). This works so well
that it is employed universally (13, p . 1035).
A recent paper (5, p . 407) which included a multiple
choice examination, was replied to in several articles (2,
12, 13, 15), and rebutted in another article (6, p. 392).
The sentiment was four (2, 9, 12, 15) to one (13) against
the use of multiple choice examinations in physics.
Criticisms of multiple choice examinationss included:
1. Poor wording penalizes the better student (13,
p. 1035)
p. 1035)
Correct answers can be guessed (2, p. 873; 13,
3. Fortuitous combinations of errors can cancel
and give the correct answer (12, p. 299).
4. Multiple choice can contain biases against
students for which English is a second language (12, p.
300) .
47
5. Writing good and fair multiple choice
questions is extremely difficult (2, p. 874). However, it
has been pointed out that these faults are not inherent in
multiple choice exams (13, p. 1035).
The objection to poor wording can be eliminated by
putting the questions in a problem oriented or problems-only
form, with the answers consisting entirely of numbers (13,
P- 1035). The instrument used in this study follows both of
these guidelines.
Finally, scoring of multiple choice examinations
eliminates unfair subjective evaluations which plague
reader-graded examinations (13, p. 1035). In practice, the
subjective factor is assumed to be constant for a given
grader and differences between sections are eliminated by
curving the grades, since more than one section is being
considered in this study and since only one examination was
given, a multiple choice examination seemed more appropriate
than reader-graded examinations. There is evidence to show
that multiple choice examinations which have been
extensively tested and for which validity and reliablity
have been established measure the same thing as written
examinations, but more efficiently (8, p. 1044).
Half of the problems on the instrument used in this
study came from each of the two disciplines involved.
Selection of the problems from representative texts served
to help establish content validity of the items. Problems
48
were included only if all four instructors teaching the
courses agreed that the item was an appropriate problem for
inclusion on a major examination in their course.
By accepting the problem the instructors were saying,
in effect, that based on the content and context of their
course, the student could be expected to solve the problem,
in other words, it would be a fair examination problem in
Physics or engineering based on the course content. The
instructors, all of whom had at least a master's degree and
some fifty years of combined teaching experience, would also
be verifying, as a panel of experts, the content validity of
the instrument. The instructors were not told which
problems came from which discipline as they did their
evaluation. A university physics professor also evaluated
the items on the examination as being fair problems for
inclusion on a major examination in a calculus-based physics
course at the university level (7). This further served to
established content validity. The problems were edited so
as to achieve common terminology. The instrument, a
discussion of the instrument, and the solutions to the
examination problems can be found in the Appendix.
Population
The population was all physics and engineering students
m beginning calculus-based statics and physics courses at
the northeast campus of Tarrant County Junior College. These
49
students were enrolled in two day and two night sections o£
Engineering Mechanics, ENR 2603 Mechanics I (Statics), and
Engineering Physics I (Mechanics and Heat), PHY 2614, during
the Fall term of 1985.
The total number of students involved in the study was
forty-nine, consisting of twenty-six engineering students
and twenty-three physics students. These students were all
required to have previously met the same calculus
prerequisite and were regarded by the instructors as
comparable in overall intelligence and problem solving
ability.
The study was confined to the northeast campus because
it was the only one of the three campuses in the Tarrant
County Junior College District offering sections in both
Physics and statics for the fall term of 1985. The south
campus did not offer statics or physics for the fall term of
1985. The northwest campus did not offer statics; physics
was offered on the northwest campus but the material on
statics was omitted by the instructor teaching the course.
Procedures for Collection of Data
The four instructors involved in the study agreed to
administer the instrument in class as a regular major
examination to the two groups of students as described
above. The instructors were given complete freedom to
handle the administration of the examination in their class
50
in a manner consistent with the ebb and flow of their normal
course routine. The only instruction given to the
instructors was that the students were to regard the
examination as one of the major examinations in the course
which would be used to determime their course grade. It
would thus seem that they took the examination more
seriously than they would a questionnaire or an examination
which obviously had nothing to do with the course grade.
Instructor A gave the examination in two, back-to-back,
fifty minute periods with three problems each period. It
was his observation that most students finished the
examination in about eighty minutes. The examination was
open book and open notes, but it was the instructor's
observation that neither were needed nor used. Calculators
were used.
Instructor B gave the examination in a three-hour
laboratory period. All students completed the examination
in less than two hours. The examination was closed book and
closed notes, and calculators were allowed.
Instructor C gave the examination in a regular one-hour
and twenty minute class period and considered this time
adequate for the students to finish the examination. The
examination was closed book and closed notes and calculators
were allowed.
Instructor D had a larger lecture class which was
divided into two smaller laboratory sections on two separate
51
days. He used half of the three hour laboratory period to
give the examination. The students all finished in the time
allowed. It was his observation that no interaction between
the groups occurred. The examination was given as closed
book and closed notes, and calculators were used.
Treatment of Data
Since the instrument was administered to two different
groups, they were considered independent or unrelated for
purposes of statistical analysis. The means and standard
deviations were required for the inferential statistics so
they were calculated for each group of students for the
engineering problems, the physics problems, and the
composite examination. The inferences concerned differences
between the means of the two groups whose parent populations
were assumed to have normal distributions with unknown
variances.
An F-test was used to determine whether or not the
variances of the parent populations were equal. For equal
variances the means were compared using a t-test computed
from a pooled estimate for the standard deviation. The
means for unequal population variances were compared using a
t-test computed from the means and standard deviations of
the two groups.
Summary
This study compares the problem solving ability of
52
engineering and physics students. Since a representative
design was used rather than a more traditional systematic
design, this study should be regarded as exploratory in that
the purpose was the determination of a difference in problem
solving ability rather than the attribution of the
difference to particular causal factors.
The multiple choice instrument was administered to all
the engineering and physics students at the Northeast Campus
of Tarrant County Junior College during the fall term of
1985. The mean scores of the two independent groups were
compared using the appropriate descriptive and inferential
statistics. The overall cummulative grade point average and
number of semester hours of mathematics of the two groups
were also compared.
53
CHAPTER BIBLIOGRAPHY
1. Borg, Walter and Meredith Gall, Educational Research: An Introduction, 4th ed., New York, Longman, Inc., 1983.
2. Bork, Alfred, "Letter To The Editor," American Journal of Physics, 52 (October, 1984), 873-874.
3. Campbell, Donald and Julian Stanley, Experimental and Quasi-Experimental Designs for Research, Chicago, Rand McNally, 1973.
4. Champagne, A. B. and L. E. Klopper, "A Causal Mode of Students' Achievement In A College Physics Course," Journal of Research in Science Teaching, 19 (March, 1982), 299.
5. Cohen, R., B. Eylon, and U. Ganiel, "Potential Difference and Current In Simple Electric Circuits: A Study of Students' Concepts," American Journal of Physics, 51 (May, 1983), 407-412.
6. Cohen, R., B. Eylon, and U. Ganiel, "Answer to Letter by M. Iona," American Journal of Physics, 52 (May, 1984), 392.
7. Deering, William D., Physics Department, North Texas State University, Denton, Texas. Interview with John R. Martin, November 19, 1985.
8. Halloun, Ibrahim Abou and David Hestenes, "The Initial Knowledge State of College Physics Students," American Journal of Physics, 53 (November, 1985), 1043-1055.
9. Iona, Mario, "Multiple Choice Questions," American Journal of Physics, 51 (May, 1984), 392.
10. Keller, George, "Trees Without Fruit," Change, 17 (January/February, 1985), 7-10.
11. Mermin, David, "Is The Moon There When Nobody Looks? Reality and Quantum Theory," Physics Today, 38 (April, 1985), 38-47.
54
12. Sandin, T. R., "On Not Choosing Multiple Choice Questions," American Journal of Physics, 53 (April, 1985), 299-300.
13. Scott, Bruce L., "A Defense of Multiple Choice Tests," American Journal of Physics, 53 (November, 1985), 1035.
14. Snow, Richard E., "Representative and Quasi-Representative Designs for Research on Teaching," Review of Educational Research, 44 (Summer, 1974), 265-291.
15. Varney, Robert N., "More Remarks On Multiple Choice Questions," American Journal of Physics, 52 (December, 1984), 1069.
16. Villars, C. N., "Observables, States, and Measurements In Quantum Physics," European Journal of Physics, 5 (March, 1984), 177-183.
17. Wollman, W. and F. Lawrenz, "Identifying Potential 'Dropouts' From College Physics Classes," Journal of Research in Science Teaching, 21 (April, 1984), 385.
CHAPTER IV
DATA ANALYSIS, PRESENTATION OF DATA,
AND HYPOTHESIS TESTING
Introduction
This chapter presents an analysis of the data collected
from the instrument, student transcripts and questionnaire,
and instructor interviews. The data is presented in tabular
form. The methods of data analysis are described as they
relate to the testing of hypotheses. Instructor and student
profiles are followed by a summary of the major findings of
the study.
Data Analysis
The examinations were hand graded as being either
correct or incorrect; no partial credit was given in
determining the scores for the purposes of this study. The
scores were reported to the instructors so they could use
the solution sheets the students turned in with the
examinations to give partial credit and determine the
examination score for the purpose of determining the course
grade.
Since the mean and standard deviation are required for
inferential statistics, they were calculated for each group
of students for the physics problems, the engineering
problems, and for the composite exam. The appropriate
55
56
inferential statistical procedures are described by Johnson
(1, p. 350). The inferences concerned differences between
the means of two independent or unrelated groups where the
population variances were unknown and the groups were small.
Each of the four classes was less than thirty in size.
The parent populations were assumed to have normal
distributions for the purpose of comparing the means of the
independent groups. Since the variances of the parent
populations were unknown, there were two possible cases: 1)
the variances of the two populations are equal or 2) the
variances of the two populations are unequal. An F test was
used to differentiate between the two cases. The null
hypothesis for the two-tailed F test of the variances is
that the variances are equal (no difference) or that their
ratio is one.
If the null hypothesis is retained (the variances are
equal), then the standard error of estimate is given by
sp(l/n1 + l/n2)1//2
where s^ is the pooled estimate for the standard deviation
and is calculated from
sp = (((^ - 1)S;L2 + (n2 - l)s2
2)/(n1 + n2 - 2))1/2
where s^ and s2 are the sample standard deviations and n^
and n2 are the sample sizes. The number of degrees of
freedom, df, is n^ + n2 - 2. The difference between the
sample means is then tested using a t test where the test
statistic for t is given by
57
t = ( (x1 - x2) - (m1 - m2))/(Sp(l/n1 + l/n2)1/2)
where x.̂ and x2 are the sample means and m^ and m2 are the
population means (1, p. 350).
If the null hypothesis for the variances is rejected,
that is, the populations have unequal variances, then the
hypothesis test for the sample means is performed using a t
test where t is given by
t = ( (xx - x2) - (m1 - m2) ) / ( (s12/n1) + (s^
and the number of degrees of freedom for the critical value
is the smaller of n^ - 1 and n2 - 1 (1, p. 353).
Each hypothesis was restated in the null form and
tested at the 0.05 level. In the null form, the hypothesis
are as follows:
I: On statics problems typical of those in
engineering texts, there will be no significant
difference at the 0.05 level between the mean
scores of engineering students and physics
students. This is a one-tailed test with the
alternate hypothesis being that the engineering
students score higher than the physics students.
II: On statics problems typical of those in physics
texts, there will be no significant difference
at the 0.05 level between the mean scores of
physics students and the mean scores of
engineering students. This is a two-tailed test
with the alternate hypothesis being that one
58
group scores higher than the other.
Ill: There will be no significant difference at the
0.05 level between the means of the composite
scores of physics and engineering students.
This is a one-tailed test where the alternate
hypothesis is that the engineering students
score higher.
The research questions associated with the hypotheses are as
follows:
1) Do engineering students solve engineering
problems better than physics students?
2) Is there any difference between the ability
of physics and engineering students to solve
physics problems.
3) Are engineering students better overall
problem solvers?
To answer the first research question in the
affirmative requires the rejection of null I, to answer the
second question in the affirmative requires null II be
rejected, and to answer the third question affirmatively
means the rejection of null III.
Presentation of The Data
Table I shows the results of the experiment and also
contains the descriptive statistics. The table shows both
the mean and standard deviation for the number correct of
59
three physics problems, the number correct of three
engineering problems, and the total number correct of six
for both groups of students.
TABLE I
RESULTS OF EXPERIMENT AND DESCRIPTIVE STATISTICS
Number Correct
of 3 of 3 of 6
Student Engineering Problems
Physics Problems Total
Engineer n^ = 26
1.692 0.844
2.577 0.504
4.269 1.002
Mean Standard Deviation
Physics n 2 = 23
1.130 0.920
1.609 1.270
2.739 1.864
Mean Standard Deviation
Table II contains the values for the inferential
statistics. All values are shown for each of the three
hypotheses being tested in the study. The degrees of
freedom for each group is one less than the number in the
group. The individual degrees of freedom are then added to
obtain the degrees of freedom for the experiment. The
critical values for F and t were determined using an
interval-halving technique in conjunction with a
commercially available software package for a hand-held
electronic calculator. The value for the pooled estimate of
the standard deviation and the test values for F and t were
60
calculated from the appropriate expressions earlier in this
chapter.
TABLE II
INFERENTIAL STATISTICS FOR TESTING OF HYPOTHESES
Hypothesis
Statistic I II III
nl 26 26 26
n2 23 23 23
d f l 25 25 25
df2 22 22 22
df 47 47 47
F critical
<0.440;>2.320 <0.440;>2.320 <0.440;>2.320
Ftest 0.842 0.157 0.289
s P
0.880 NA NA
^"critical >1.650 <-2.070;>2.070 >1.720
fctest 3.366 3.425 3.513
Hypothesis Testing
The following discussion is based on Table I and Table
II. The value of Ffc t for null hypothesis I is not in the
critical region (0.440 < 0.842 < 2.320), requiring the null
hypothesis for the population variances to be retained.
This is case 1 with equal variances and a pooled estimate
(s ) for the standard deviation is used. The calculated P
value for s p is 0.880 from which t t e s t is found to be 3.366,
a value in the critical region (3.366 > 1.650). Thus, the
61
null of hypothesis I for the study is rejected and the
alternate hypothesis, engineering students solve engineering
problems better than physics students, is retained.
Null hypothesis II for the study has a value for F LCD L
of 0.157, which is in the critical region (0.157 < 0.440).
The null hypothesis for population variances is rejected;
the variances are not equal (case 2). Since the value of
ttest' 3 * 4 2 5 ' i s i n t h e critical region (3.425 > 2.07), the
null of hypothesis II for the study is rejected with the
interpretation that engineering students solve physics
problems better than physics students.
The null of the third hypothesis for the study has a
value for F t e s t of 0.289 which is also in the critical
region (0.289 < 0.440). As with the second hypothesis of
the study, the population variances are not equal and case 2
is used to calculate a value for t t e g t of 3.513, which is in
the critical region (3.313 > 1.720). So the null for the
third hypothesis of the study is rejected and the alternate
retained, with the interpretation that engineering students
are better overall problem solvers than physics students.
Table III summarizes the results of the testing of the
hypotheses. Hypotheses I and III as stated in the study
were retained while the study statement of hypothesis II was
rejected. The null statement of all three hypotheses was
rejected. The research questions associated with all three
hypotheses were answered in the affimative.
62
TABLE III
SUMMARY OF HYPOTHESIS TESTING
Hypothesis Study Statement
Hypothesis Stated As Null
Answer To Associated Research Question
I Retain Reject Yes
II Reject Reject Yes
III Retain Reject Yes
The three hypotheses are stated in detail below for
comparison:
Hypothesis I;
Each hypothesis may be described as stated in the
study, as a null statement, or as an associated research
question.
Study. On problems typical of those in engineering
texts, engineering students will score significantly higher
than physics students.
Null statement.—On statics problems typical of those
in engineering texts, there will be no significant
difference at the 0.05 level between the mean scores of
engineering students and the mean scores of physics
students.
Research question.—Do engineering students solve
engineering problems better than physics students?
63
Hypothesis II:
Study.—On problems typical of those in physics texts,
there will be no significant difference between the scores
of engineering students and physics students.
Null statement.—On statics problems typical
of those in physics texts, there will be no significant
difference at the 0.05 level between the mean scores of
engineering students and the mean scores of physics
students.
Research question.—Is there any difference between the
ability of engineering students and physics students to
solve physics problems?
Hypothesis III;
Study.—The composite scores of the engineering
students on statics problems typical of those in engineering
and physics texts will be significantly higher than the
composite scores of the physics students.
Null statement.—On statics problems typical of those
in engineering and physics texts, there will be no
significant difference at the 0.05 level between the means
of the composite scores of engineering students and physics
students.
Research question.—Are engineers better overall
problem solvers than physics students?
64
The hypotheses testing indicates experimental
confirmation for two of the three hypotheses. The rejection
of the second hypothesis seems to show that engineering
students solve statics problems better than physics
students, even when the problems are from a physics text.
The rejection of the second hypothesis indicates an
incorrect choice of hypothesis rather than a failure of the
study to confirm the hypothesis. The rejection of the
second hypothesis actually strengthens the results of the
study since it indicates that engineering students are
better problem solvers than physics students regardless of
whether the problems being solved are engineering problems,
physics' problems, or a combination of the two.
Finally, it should be noted that not only are the
results of this study significant at the 0.05 level of
testing but also significant at much lower levels. Using
the probability-value, also called the prob-value and
p-value, approach the results shown in Table IV are obtained
(1, p. 281).
Table IV contains the probability values for each of
the three hypotheses, and a comparison to the 0.05 level of
significance. The comparison is the factor by which the
probability-value must be multiplied to give the 0.05 level.
For example, 65(0.000764) = 0.04966, 20(0.0024) = 0.048, and
50(0.001) = 0.05. If the second hypothesis had. been chosen
differently, the numbers in parentheses would apply and the
65
calculation would be 42(0.0012) = 0.0504, a factor more than
twice as great.
TABLE IV
PROBABILITY-VALUES OF HYPOTHESES COMPARED TO 0.05 LEVEL
Comparison to Hypothesis Probabi1ity-Value 0.05 Level
I 0.000764 65
II 0.0024 (0.0012) 20 (42)
III 0.001 50
These probability-values are the smallest values for
the level of significance for which the results are
significant. These are not borderline results, in the sense
that compared to the 0.05 level they are lower by factors of
65 for the first hypothesis, 20 for the second hypothesis,
and 50 for the third hypothesis. If the study had
hypothesized that engineering students would solve physics
problems better than physics students (rather than
hypothesizing no difference), then the second hypothesis
would have been significant at the 0.0012 level, as shown in
parentheses in Table IV, rather than the 0.0024 level. Also,
as shown in parentheses in Table IV, this is lower by a
factor of 42.
Instructor Profiles
Instructor A has a bachelor's and master's degree in
66
civil engineering and has completed all the requirements for
the doctorate except the dissertation. He is a certified
professional engineer and was employed by the Texas Highway
Department for seven years and was a full-time consultant
for one year (he still consults part-time) before entering
teaching, where he has been for the last nine years. He
uses mainly the lecture format with two slide shows. He
does not use demonstrations. There is no formal development
of the theory in class; it is simply taken as stated in the
text. The theory is illustrated by solving two or three
example problems from the text each class period. He
follows the book and tries to be more practical and
intuitive than rigorous. In a lecture observed in this
study he referred to welds and rivets on particular bridges
in Fort Worth, Texas.
Instructor B has a bachelor's degree in physics, a
master's in secondary education, and a doctorate in higher
education and administration. He has no industrial
experience but has taught for fourteen years, including four
years in Air Force vocational-technical, and one year in
high school, together with five years in two year colleges
and four years at the university level. He uses primarily
the lecture with about five percent of class time for
demonstrations. About one-half of class time is devoted to
derivations and development of formalism and one half to
solving illustrative example problems. In statics the
67
number of example problems solved is greater than the number
of solved problems for other topics. He follows the book
rigidly and emphasizes physical reasoning and intuition
along with a low to medium level of rigor in derivations, in
his development of the theory he is teaching.
Instructor C has a bachelor's and master's degree in
mechanical engineering and is a certified professional
engineer. He also has a master's degree in program
management and extensive experience in the aerospace
industry. He has never taught full-time but has taught
part—time for the past fifteen years. He uses the lecture
format with frequent references to an industrial setting.
He continually makes reference to the tools of statics and
how they are used in practice. He does few derivations but
gives an indication of where the equations come from. He
does numerous example problems. He follows the book closely
but does make an occasional departure. He does not care
about definitions and stresses intuition.
Instructor D has both a bachelor's and master's in
physics and with the completion of the dissertation will
have a doctorate in higher education. He has no industrial
experience but has taught for five years full-time in high
school. For the past ten years he has taught one physics
course each semester at the university level where he has
one third academic and two thirds administrative
responsibilities. He also uses the lecture format as his
68
primary method of instruction. About ten percent of class
time is used for demonstrations. He uses some media, mostly
overheads, and shows four films during the semester. He
devotes about forty percent of class time to derivations and
sixty percent to problem solving. Sticking closely to the
book, he stresses correctness on details such as units. He
is not mathematically formal or rigorous but stresses
physical insight and tries to develop physical intuition.
Student Profiles
A questionnaire was administered to each of the two
groups of students to determine age, sex, and personal
problem solving strategy. The students were to state
whether they had been taught a systematic approach to
problem solving or had been expected to develop their own.
they had a personal problem solving strategy they were to
describe it. The results are shown in Table V.
TABLE V
AGE, SEX, AND PERSONAL PROBLEM SOLVING STRATEGY
Student. Response
S« 2X
Age
Problem Solving Strategy
Student. Response Male Female Age Taught Develop Personal
Engineer
Physics
73% 19/26
78% 18/23
89% 17/19
83% 15/18
11% 2/19
17% 3/18
27.8 Mean 5.0 Standard
Deviation
27.0 Mean 5.2 Standard
Deviation
83% 15/18
53% 9/17
28% 5/18
47% 8/17
94% 16/17
83% 15/18
69
The percent response to the questionnaire was seventy-
three for the engineering students and seventy-eight for the
physics students. The male to female ratio was 89 to 11
percent for the engineering students and 83 to 17 percent
for the physics students, which does not appear to be
substantially different. The mean age and standard
deviation were almost identical at 27.8 and 5.0 for the
engineering students and 27.0, and 5.2 for the physics
students.
There does appear to be some difference in the way the
students perceive problem solving instruction in their
courses. Eighty-three percent of the engineering students
felt they had been taught a systematic approach to problem
solving while only fifty-three percent of the physics
students felt they had been taught a systematic approach to
problem solving. Two of the engineering students felt they
had been taught a systematic approach to problem solving but
had also been expected to develop their own approach to
solving problems. Consequently the eighty-three and
twenty-eight percent for this entry in Table V do not add to
one hundred percent..
A high percentage of both groups, ninety-four for the
engineering students and eighty-three for the physics
students, said they had developed a personal strategy for
problem solving. The eighty-three percent for the physics
students is interesting in view of the fact that only fifty-
70
three percent felt they had been taught problem solving in
their course. In reading through these student strategies
the impression is received that not only are they remarkably
similar to each other but also to the classic four-step
approach given by Polya (3, p. xvi,xvii). As mentioned in
Chapter II, Polya's four steps are:
I: Understand the Problem
II: Devise a Plan
III: Carry Out the Plan
IV: Looking Back
The students did not elaborate on their strategies to the
extent that Polya does, but for the most part they contain
the essentials of the four steps. O'Neil has succinctly
stated that problem solving consists of listing what is
known, being clear on what is to be found, and setting about
to find it (2, p. 270).
The two groups of students do not appear to differ
significantly when compared to each other using their
overall cumulative grade point average, based on a 4.0
system, or on the basis of mathematical background as
measured in terms of the number of semesters completed as
either prerequisite or corequisite. The number of semesters
could range from one (calculus I) to four (three semesters
of calculus and one of differential equations). Table VI
contains the data for the comparison of overall cumulative
grade point average.
TABLE VI
STATISTICS FOR COMPARISON OF OVERALL CUMULATIVE GRADE POINT AVERAGE
71
Student
Statistic Engineer Physics Composite
n 26 23 NA
Mean 2.777 2.618 NA
Standard Deviation
0.662 0.736 NA
d fi 25 NA NA
d f 2 NA 22 NA
df NA NA 47
F . . critical NA NA <0.44;>2.32
F test NA NA 0.809
s P
NA NA 0.698
t ... .. critical NA NA > 1.650
fctest NA NA 0.796
p-value NA NA 0.215
Since the value for Ft e s t is not in the critical region
(0.44 < 0.809 < 2.32) , the hypothesis that the population
variances are equal is retained and testing proceeds
according to case 1. The calculated value for the pooled
estimate of the standard devations (s ) is 0.698. This P
value of s p gives a value for t t e g t of 0.796, and since this
is less than o f 1.650, the hypothesis that
72
engineering students have a higher overall cumulative grade
point average can be rejected at the 0.05 level. In fact,
since the probability-value is 0.215, it seems reasonable to
conclude that there is essentially no difference between the
two groups based on a comparison of overall cumulative grade
point average.
Caluclus I and physics are both prerequisites for
engineering mechanics. All twenty-six of the engineering
students had met the calculus prerequisite and twenty-two
had met the physics prerequisite. Two apparently had not,
and for two it could not be determined either from
transcript analysis or questionnaire whether or not they had
met the physics' prerequisite.
Calculus is recommended as a prerequisite for physics
but enrollment in the course is allowed with calculus as a
corequisite. Twenty of the twenty-three physics students
had met this requirement, two had not, and for one it could
not be determined whether the requirement had been met.
Thus in terms of meeting the required prerequisites there
seems to be no essential difference between the two groups.
A more detailed look at mathematics background also
seems to bear out the conclusion that in overall ability and
intelligence the two groups appear to be comparable. There
certainly appears to be no difference based on grade point
average and mathematics background. Table VII contains the
data for the comparison of the two groups based on
73
their mathematical background.
TABLE VII
STATISTICS FOR COMPARISON OF MATHEMATICS BACKGROUND
Student
Statistic Engineer Physics Composite
n 26 20 NA
Mean 2.654 2.200 NA
Standard Deviation
1.056 0.951 NA
d fl 25 NA NA
df2 NA 19 NA
df NA NA 44
F . . critical NA NA <0.431;>2.460
F test NA NA 1.233
s P
NA NA 1.012
t critical NA NA >1.650
fctest NA NA 1.508
p-value NA NA 0.0694
Ftest ^ a s a v a * u e (1.233) between the values of
Fcritical (< ° - 4 3 1 ' > 2.460) which indicates the population
variances are equal and, thus, case 1 with a pooled estimate
of the standard deviations is used. The value for s is P
1.012 and gives a value for t t e g t (1.508) which is less than
Critical ( 1- 6 5°) with the interpretation that there is no
difference in mathematical background between the two groups
74
at the 0.05 level. The probability-value of 0.0694 shows
that of the comparisons done in this study this is the only
one which could be considered close in the sense that the
probability-values are close to the level of significance.
Table IV and Table VIII show these comparisons.
TABLE VIII
COMPARISON OF PROBABILITY-VALUES FOR GRADE POINT AVERAGE AND MATHEMATICS BACKGROUND
Comparison Prob-Value Comparison with
0.05 Level
Grade Point 0.215 4 Average
Mathematics 0.0694 1.4 Background
The probability-value of 0.215 for grade point average
differs from the 0.05 level by a factor of four, and the
probability value for mathematics background differs from
the 0.05 level by a factor of 1.4. While these results are
not as conclusive as the results for the testing of the
study hypotheses where the results differed from the 0.05
level by factors ranging from twenty to sixty-five,
nevertheless, they are not borderline results.
While there are significant differences in problem
solving abililty between engineering students and physics
students which appear to be conclusive, the differences do
75
not seem to be attributable to general overall ability or
intelligence as measured by grade point average or
mathematics background. Assuming the instructor variable is
negligible as indicated in Chapter III, the significant
difference in problem solving ability would seem to be due
to a difference in formalism between physics and engineering
instruction.
Summary
The following are the major findings of this study:
1. The mean score for the engineering students (1.692) on
the engineering problems on the instrument was higher than
the mean score for the physics students (1.130).
2. The mean score for the engineering students (2.577) on
the physics problems on the instrument was higher than the
mean score for the physics students (1.609).
3. The mean score for the engineering students (4.269) on
the composite exam was higher than the mean score for the
physics students (2.739).
4. There was no significant difference at the 0.05 level in
the overall cumulative grade point average of engineering
and physics students.
5. There was no significant difference at the 0.05 level in
the mathematical background of engineering and physics
students.
6. The male to female ratio was approximately the same for
76
engineering (89:11) and physics (83:17) students.
7. The mean age of engineering (27.8) and physics (27)
students was almost the same and the standard deviations
were even closer, 5.2 and 5, respectively.
8. Eighty-three percent of the engineering students felt
they had been taught a systematic approach to problem
solving as compared to 53 percent physics students.
9. Approximately the same percentage of engineering and
physics students, 94 percent and 83 percent, respectively,
said they had a personal strategy for solving problems.
77
CHAPTER BIBLIOGRAPHY
1. Johnson, Robert, Elementary Statistics, 4th ed.. Boston, Duxbury Press, 1984
2. O'Neil, Peter, "Calculus and Analytic Geometry," Unpublished Calculus Manuscript, Englewood Cliffs, N. J., Prentice-Hall, 1986.
3. Polya, G., How To Solve It, 2nd ed., Princeton, Princeton University Press, 1973.
CHAPTER V
SUMMARY, DISCUSSION OF FINDINGS, CONCLUSIONS, IMPLICATIONS
OF FINDINGS, AND RECOMMENDATIONS
FOR ADDITIONAL RESEARCH
Introduction
The problem with which this study was concerned is a
comparison of problem solving ability of engineering and
physics students. The purpose of this study was to
determine whether a difference exists between the problem
solving ability of the two groups of students. The
hypotheses of the study were that engineering students would
solve engineering problems better, and be better overall
problem solvers, than physics students, whereas no
difference would exist between the two groups of students in
their ability to solve physics problems.
The study was experimental in nature but used a
representative design rather than a more traditional,
systematic design. Thus, the study was considered
exploratory since it addressed the question of determining
whether or not there exists a difference in problem solving
ability between the two groups of students, rather than the
determination of the causal factor responsible for the
difference.
Representative designs attempt to take measurements in
78
79
the least perturbing manner possible. In studies like this
one involving a teaching-learning environment, the most
appropriate manner to make measurements is in the normal ebb
and flow of events. This study attempted to accomplish this
by the administration of a six-item instrument, consisting
of three items from each discipline, to the entire
population under study. Each group of students completed
the instrument as one of the major examinations in their
respective courses.
These data were analyzed using standard methods of
inferential statistics. The mean scores of the two
independent groups were compared at the 0.05 level of
significance with a t-test. The t value was calculaated
using either a pooled estimate for the standard deviation or
the individual means and standard deviations of the two
groups as determined by an F-test comparing the population
variances.
Data for student profiles were obtained from a
questionnaire administerd to both groups of students.
Additional data for student profiles came from transcript
analyses. Instructor profiles were based on interviews with
each of the four instructors.
Summary
The following are the major findings of this study:
1. The mean score for the engineering students (1.692) on
80
the engineering problems on the instrument was higher than
the mean score for the physics students (1.130).
2. The mean score for the engineering students (2.577) on
the physics problems on the instrument was higher than the
mean score for the physics students (1.609).
3. The mean score for the engineering students (4.269) on
the composite exam was higher than the mean score for the
physics students (2.739).
4. There was no significant difference at the 0.05 level in
the overall cummulative grade point average of engineering
and physics students.
5. There was no significant difference at the 0.05 level in
the mathematical background of engineering and physics
students.
6. The male to female ratio was approximately the same for
engineering (89:11) and physics (83:17) students.
7. The mean age of engineering (27.8) and physics (27)
students was almost the same, and the standard deviations
were even closer, 5.2 and 5, respectively.
8. Eighty-three percent of the engineering students felt
they had been taught a systematic approach to problem
solving as compared to 53 percent of the physics students.
9. Approximately the same percentage of engineering and
physics students, 94 percent and 83 percent, respectively,
said they had a personal strategy for solving problems.
81
Discussion of Findings
Statistical analysis of data showed that at the 0.05
level of significance there is a difference in problem
solving ability between engineering students and physics
students. The engineering students solved engineering
problems better than physics students, and were also better
overall problem solvers, as hypothesized. The engineering
students also solved physics problems better than physics
students in disagreement with the second hypothesis of this
study.
The rejection of the second hypothesis actually makes
the results of the study stronger, in that engineering
students are better problem solvers no matter how the
comparison is made. What this actually indicates is an
incorrect choice for the second hypothesis. If the second
hypothesis had been reversed the study would have
substantiated all three of the hypotheses.
The probability-values for the test statistics of
0.000764, 0.0024, and 0.001, respectively, for the three
hypotheses indicates that the results may be considered
conclusive rather than borderline in nature. These values
are greater than the 0.05 level by factors of 20 to 65,
implying that the results of this study are highly
significant.
Statistical analysis of student profiles showed no
82
significant difference at the 0.05 level in overall ability
based on a comparison of overall cumulative grade point
average and mathematical background. There was less
difference in mathematical background than in grade point
average. The probability-values for these differences,
0.215 and 0.0694, are not as great as the differences in
problem solving. However, they are neither marginal nor
borderline, compared to the 0.05 level, since they are
greater than the 0.05 level by factors of 4 and 1.4,
respectively.
Student response to questionnaires was almost
identical, 73 percent for engineering students and 78
percent for the physics students. Evaluation of the
questionnaires showed approximately the same male to female
ratio, with 89 to 11 for engineering students and 83 to 17
for physics students. The mean ages were almost identical
at 27.8 for engineering students and 27 for physics
students, with standard deviations of 5 and 5.2,
respectively.
Students seemed to differ in their perception of
whether problem solving was taught explicitly in their
courses. Eighty-three percent of the engineering students
felt it was compared to 53 percent of the physics students.
In spite of this, a high percentage of both groups, 94 in
engineering and 83 in physics, said they had a personal
strategy for solving problems. These strategies were
83
remarkably similar to each other and to the general approach
of deciding what the knowns and unknowns are and then
setting about to find the unknowns and evaluating the
solution.
Conclusions
Based on the findings of this study the following
conclusions appear to be warranted. Given the conditions
and limitations of this study, the findings seem to indicate
that engineering students are better problem solvers than
physics students. It does not matter whether the problems
are engineering problems, physics problems, or a composite
of both types.
The difference does not appear to be due to the two
characteristics of the two groups measured in this study.
There was no difference between the groups in terms of grade
point average or mathematical background. The groups were
almost identical in terms of age and male to female ratio.
Prior misconceptions could have been different between the
two groups but without the measurement of this
characteristic it cannot be concluded that it is responsible
for the difference.
Hestenes (4) argues that prior misconceptions are the
most determinative factor for performance in introductory
physics. Factors such as age, gender, major, high school
mathematics, high mathematical competency, and academic
84
background seem to have little effect (2,4,8). The gain in
basic knowledge is even independent of the instructor
variable (4, p. 1048).
If prior misconceptions are the dominant factor in
determining performance and since there appears to be no
reason to conclude a difference between the misconceptions
of the two groups, especially in view of the fact that there
is no significant change in misconceptions even after an
introductory physics course (4, p. 1048) , it would seem to
follow that the highly significant difference in problem
solving ability is conclusive and attributable to some other
factor. It is a major conclusion of this study that this
factor is the difference in formalism between engineering
instruction and physics instruction.
Implications of Findings
The findings of this study imply that physics formalism
should be changed to aim more toward applicability than
generality. The principles should be written in terms of
equations which are more directly applicable to solving
problems. This means, for example, that physics instruction
should be less abstract and more detailed about the various
kinds of supports and connections involved in statics
problems.
These implications run counter to current calls for
reform in the university physics curriculum (7, p. 120).
85
Pressure for reform seems to be coming from three directions
(7, p. 120). First is the role of the computer in
instruction (7, p. 120). Second, there is current learning
theory research, which is suggesting new instructional
strategies (7, p. 120). Third, there is the movement to
include more contemporary topics in introductory courses (7,
p. 120) .
The implications of the findings of this study, to
include different formalisms of some classical topics, run
counter to the third suggestion to include more contemporary
topics from modern physics in the introductory courses in
university physics (7, p. 120). One of the questions in the
new reform proposals is how much of the new body of
contemporary physics should be included in the introductory
courses (7, p. 120). It follows that to include topics from
contemporary physics would mean that topics from classical
physics must be abbreviated or omitted.
One obvious way to do this is to continue with the
traditional physics formalism aimed at generality rather
than change to an engineering formalism aimed more toward
application. This, leads to an interesting standoff. On the
one hand, introductory physics as it is now taught contains
nothing of modern physics, no hint of what physicists do or
how they think about the world today (7, p. 120). While on
the other hand, how can students cope with subjects
requiring an understanding of quantum physics when they do
86
not even understand Newton's laws (7, p. 120)? But as this
study implies, to gain a better understanding of Newton's
laws, that is to improve problem solving ability, may mean
going to a different formalism which leaves even less time
for modern physics topics than the current formalism.
An alternative to changing the formalism in
introductory physics would be to have physics students take
one or more of the six engineering mechanics courses as
either an elective or as prescribed. In universities
without engineering colleges this would mean offering
engineering courses in the physics department. This would
seem to make the pre-engineering curriculum of these
departments more attractive to pre-engineering students than
presently. It might also make physics degrees more
attractive in the market place.
Recommendations for Additional Research
Borg and Gall (1) list literal, operational, and
constructive as three types of replication. Literal
replication involves exact duplication of every aspect of
the research (1, p. 383). It is recommended that this study
be repeated under identical circumstances as nearly as
possible with additional subjects not only on the northeast
campus of Tarrant County Junior College but also on the
south and northwest campuses. The study should also be
repeated at four year colleges and universities which offer
87
both engineering and physics.
Operational replication attempts to duplicate the
experimental design exactly while varying the methods and
procedures to determine if the same result will be produced
(1, p. 384). It is recommended that operational replication
be achieved by keeping the same representative design used
in this study while varying the content of the instrument.
Rather than one examination of six statics problems with
three each from engineering and physics, include one
engineering problem from the appropriate area (statics,
dynamics, fluids, thermodynamics, circuits) with the three
or four physics problems on each examination. This could be
done on all of the major examinationss in the physics
course.
Constructive replication avoids deliberate imitation of
design, methods, or procedures (1, p. 384). It is
recommended that additional studies be conducted with
traditional or systematic experimental designs, procedures,
and methods significantly different from those used in this
study to determine whether the difference in problem solving
ability between engineering and physics students found in
this study can be replicated. It is recommended that these
studies be designed to establish causality and provide for
generalizations. It is also recommended that these studies
be designed and conducted in such a way as to eliminate
Snow's (6) objections to these more traditional designs.
88
It is recommended that these replicative studies
compare engineering and physics students in a university
which has an engineering college. A comparison of
engineering students in a university which has an
engineering college with physics students in a university
without an engineering college is also recommended. It is
recommended that the prior misconceptions of engineering and
physics students be compared to determine whether a
significant difference in their prior misconceptions exists.
Studies should also be conducted to compare upper level
engineering students with upper level physics students. A
university physics professor has suggested that perhaps the
observed difference in problem solving abililty for statics
would probably also be observed in dynamics, mechanics of
materials, and fluid mechanics, but not in thermodynamics
and circuits, since prior misconceptions are less likely in
these latter courses than in the former. Studies should be
conducted to investigate this hypothesis.
Finally, it is recommended that studies be conducted to
determine whether Polya's (5) problem solving methods can be
reduced to a program of practical pedagogies (3, p. 291).
It is also recommended that these studies be designed to
determine how this program works out in the classroom (3, p.
291) .
89
CHAPTER BIBLIOGRAPHY
1. Borg, Walter and Meredith Gall, Educational Research: An Introduction, 4th ed., New York, Loncrman, Inc.. 1983.
2. Champagne, A. B. and L. E. Klopper, "A Causal Mode of Students' Achievement in A College Physics Course," Journal of Research in Science Teaching, 19 (1984), 299.
3. Davis, Philip J. and Reuben Hersh, The Mathematical Experience, Boston, Houghton Mifflin Company, 1981.
4. Halloun, Ibrahim Abou and David Hestenes, "The Initial Knowledge State of College Physics Students," American Journal of Physics, 53 (November, 1985). 1043-1055.
5. Polya, G., How To Solve It, 2nd ed., Princeton, Princeton University Press, 1973.
6. Snow, Richard E., "Representative and Quasi-Representative Designs for Research on Teaching," Review of Educational Research, 44 (Summer, 1974), 265-291.
7. Wilson, Jack M., "Toward a New University Physics," AAPT Announcer, 4 (December, 1985), 120.
8. Wollman, W. and F. Lawrenz, "Identifying Potential 'Dropouts' From College Physics Classes," Journal of Research in Science Teaching, 21 (April, 1984) , 385.
90
APPENDIX A
Examination Instrument
EXAMINATION
Name:
INSTRUCTIONS; Write your name on this sheet. Work out your solutions on separate sheets. These solution sheets will be used to give partiaL credit. In the blank to the left of the problem write the letter of one of the answers listed below the problem that you feel is the best answer to the problem
1. The homogeneous rod AB has a mass of m kg and is supported as shown by the horizontal cable BC. Determine the tension in the cable (8, p. 131).
A. 3/2 mg B. 2/3 mg C. 1/2 mg D. 5/2 mg E. 3/4 mg
2. The uniform horizontal boom has a mass of 240 kg and is supported by the two cables anchored at B and C and by the ball-and-socket joint at 0. Calculate the tension T in the cable AC (II, p. 114).
A. 866 N B. 707 N C. 1312 N D. 1440 N E. 500 N
91
The beam AC is part of the roof structure of a small building. It is supported at C by a riveted connection and at B by the cable BDF. If the tension in the cable is 39 lb, determine the reaction at the riveted connection C (2, p. 140).
A. R = B. RX = C. RX = D. RX = E. RX =
x
36 lb, R = 5 lb 5 lb, R
Y = 36 lb 15 lb, R
Y = 20 lb 36 lb, R
Y = 5 lb, C = = 30 5 lb, R
y = y
36 lb, C = = 30
iSLQ, VgLl-VSLB YjfUg
7, $Pr
MPT
A wire supports a uniform beam as shown. The mass of the beam is 130 kg. How much mass can be hung at the end of the beam without exceeding the 2800 N strength of the wire (17, p. 250).
A. B. C. D. E.
143 kg 126 kg 13 kg 78 kg
182 kg
-Pivor W£/WT-*[j
92
Find the tension in cord B if the suspended weight is 200 N (13. p. 30) .
A. 283 N B. 200 N C. 141 N D. 173 N E. 244 N
A weightless beam 4 m long is perpendicular to a wall. The beam, in equilibrium, is supported by the wall, a cable at 30 to the horizontal and is pulled down by a 500 N weight hanging at the end as shown. Find the tension in the cable ( 1. p. 58).
A. B. C. D. E.
866 N 1000 N 500 N 732 N 288 N
o / B
Ov/
Discussion of Instrument
The six-item instrument was taken from representataive
text books in physics and engineering. Three items were
taken from each discipline. The items were sequenced using
a random number generator which generates random numbers
between 00 and 99.
Six random numbers were generated for each of the six
test items and if the number was even, then the problem
assigned to that position was an engineering problem and if
the number was odd, then a physics problem was assigned to
that position. The sequence of random numbers generated was
93
60, 90, 36, 63, 93, and 11 which resulted in the first three
problems being engineering problems and the last three being
physics problems.
Actually, when the first three numbers were even
resulting in the first three problems being engineering
problems, the last three problems were physics problems by
default. It is interesting to note that the next three
numbers were odd. The macroscopic ordering of this
sequence, E,E,E,P,P,P, may seem more ordered than some other
sequence such as E,P,P,E,P,E but both have the same
microscopic probability and thus the same mathematical
o^der. is just that, macroscopically, one appears more
ordered than the other because of a subjective notion of
order which may or may not coincide with the mathematical
definition of order. Here the two do not coincide.
The answers to the individual problems were also
selcted using a random number generator. The correct answer
was chosen as A if the random number was between 00 and 19,
B if between 20 and 39, C if between 40 and 59, D if between
60 and 79, and E if between 80 and 99. The answers chosen
for the six problems using this method were B,C,D,D,A,B.
The first problem is a three—force body problem and is
treated in all the representative engineering texts
(2,4,5,7,8,9,11,14,15) and is not treated in any of the
representative physics texts (1,3,6,10,12,13,16,17).
Because the direction of the reaction at A is unknown in
94
general, the problem would appear to be insoluble. But once
it is recognized as a three-force body the direction of the
reaction at A is determined, since for a three-force body
all three forces must intersect at a common point and the
directions of the other two forces are known. The problem
is then solved quite easily.
The second problem is a problem in three dimensions.
Although all of the physics texts (1,3,6,10,12,13,16,17)
develop the necessary vector algebra for this problem in
three dimensions, none of them give any three dimensional
problems in the problem section on statics. All of the
engineering texts (2,4,5,7,9,11,14,15) cover this in detail.
In order to solve this problem, a physics student would have
to go from two dimensionsal problems to three dimensional
problems without the help of any formal development in class
or text. This is not to say that it couldn't be done but
why re-invent the wheel?
The third problem contains a riveted or fixed support.
All of the engineering texts (2,4,5,7,9,11,14,15) give
considerable attention to several different kinds of
supports and connections. No mention is made about any
difference between the various types of supports and
connections in any of the physics texts (1,3,6,10,12,
13,16,17). A fixed or riveted connection is capable of
supplying a moment or torque whereas a pivot,
ball-and-socket, or roller connection cannot supply a
95
torque. None of the physics texts (1,3,6,10,13,16,17) deal
with the fixed support in any way. Thus, even if a physics
student did recognize that a fixed support was involved,
which seems unlikely since fixed supports are never seen in
physics books, and is different from other types of supports
in that it can supply a couple (which is also seldom, if
ever, mentioned in physics texts) in addition to reaction
forces, he would again have to solve the problem without
the help of any formal development of methods in class or
text.
The fourth and sixth problems are similar in appearance
but differ in what is given and what is to be determined.
Also, they illustrate that in some older physics texts (17,
p. 250) some thought, even though slight, is given to the
type of support involved whereas in newer physics texts (1,
p. 58) there is ambiguity about the exact nature of the type
of support. The student is left to decide on his own what
the nature of the support is and since the only types of
connections considered in the physics texts always exclude
fixed supports, it seems probable that since solving
problems where the reactions never supply a moment always
gives the answer in the back of the book, a fixed support
could be overlooked in a real world problem and an incorrect
solution obtained.
The fifth problem, which appears in both physics and
engineering texts, is a straight forward problem which
96
should be easily solved by both physics and engineering
students.
FBD: AB -
Solutions to Examination
- THREE FORCE BODY: R, T, and mg are concurrent
0 - PL
OAL. OM l. GEOMETRY: a
Y
2.
tan 0< = (0.4L) / (0.6L) : < * = 3 3 . 7 °
EQUILIBRIUM CONDITIONS
^ Z px = 0 : R(cos 56.3°) = T
Z Fy = 0 : R(sin 56.3°) = mg
Dividing (1) by (2) gives T = mg(cot 56.3°) =
(32 + 5 2 + 62)1/'2 = (70)1/2
^AB = ( ta b/(70)
1 / 2) (3i + 5j - 6k)
T A C = (T A C/(70)1 / 2)(-3i + 5j - 6k)
mg = - (240) (9.8)j = -2352j
£ M q = 6kXT A B + 6kXTAC + 4kXmg = 0
6kX((T A B)/(70)1 / 2)(3i + 5j - 6k) +
6kX ( (Tac) / (70) 1/'2) (-3i +5j -6k) + 4kX(-2352k) =
2mg/3
97
2. (continued)
(( TAB) 7 ( 7°)
((Tac)/(70)
1/2
1/2
) (18j - 3 0 i) +
)) (-18j - 30i) + (9408i) = 0
Equating coefficients of like components,
i: "30T a b/(70)1 / 2 - 30T A C/(70)
1 / 2 + 9408 = 0
j: 18T A B/(70)1 / 2 - 18TAC/ (70)
1/2 = 0
From j component, TftB = T A C so that from the
i component,
60TAB/(70)
FBD: ABD
1/2 = 9408 from which T A B = T A C = 1311.88 N
Tso^f tan = 7.5/18
°< = 22.6°
I 'Y
EQUILIBRIUM CONDITIONS:
Z ? x = o
Z Fy - 0
S " c = 0
Letting T
" Rx + T B D ( c o s 2 2 - 6 ) = 0
R y - 20 + T B D(sin 22.6°) = 0
5(6) + 5 (12) + 5 (18) +5(24)
- 39(18)(sin 22.6°) + C = 0
B D = 39 in (1) gives R x = 36 lb < —
(1)
( 2 )
(3)
4.
Letting T g D = 39 in (2) gives R y = 5 lb/J.
From (3), C = -30 so that C = 30 lb-ft CW
FBD : BEAM 2.QOO
3 0 ^ Rx V — >
t Ry 12"? f
4
98
4. (continued)
£ m q = o : -1274 (L/2) - W(L) + 2800 (sin 30°) (L) = 0
5.
From which W = 763 N or m = 77.86 kg
FBD : KNOT
r w ~zoo
£ F X = 0 : -T a + TB(cos 45°) =
£ F y = 0 : -200 + Tg(sin 45q) =
From (2) Tg = 283 N
6. FBD : BEAM —
0 (1)
0 (2 )
30 J ***
£ M q = o : -500(4) + T (sin 30°) (4) = 0
From which T = 1000 N
99
APPENDIX B
Bibliography of Examination Instrument
1« Arfken, George B. and others, University Physics, New York, Academic Press, 1984.
2. Beer, Ferdinand P. and E. Russell Johnson, Jr., Vector Mechanics for Engineers, 3rd ed., New York, McGraw-Hill Book Company, 1977.
3. Eisberg, Robert M. and Lawrence S. Lerner, Physics Foundations and Applications, New York^ McGraw-Hill Book Company, 1981.
4. Fox, Robert W. and Alan T. McDonald, Introduction to Fluid Mechanics, 2nd ed., New York, John WilevT 1978.
5. Ginsberg, Jerry H. and Joseph Genin, Statics, New York, John Wiley, 1977.
6. Halliday, David and Robert Resnick, Fundamentals of Physics, revised printing, New York, John Wiley, 1974.
7. Hibbeler, R. C., Engineering Mechanics: Statics, 2nd ed., New York, Macmillian Publishing Co., Inc., 1978.
8. Higdon, Archie and others, Engineering Mechanics, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1976.
9. Malvern, Lawrence E., Engineering Mechanics, Vol. 1, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1976
10. McKelvey, John P. and Howard Grotch, Physics for Science and Engineering, New York, Harper~and Row Publishers, 1978.
11. Meriam, J. L., Engineering Mechanics, Vol. 1, New York. John Wiley, 1978.
100
12. Radin, Sheldin H. and Robert T. Folk, Physics for Scientists and Engineers, Englewood Cliffs,New Jersey, Prentice-Hall, Inc., 1982.
13. Sears, Frances W., Mark W. Zemansky, and Hugh D. Young, University Physics, 5th ed, Reading, Massachusetts, Addison-Wesley Publishing Company, 1976.
14. Shames, Irving H., Engineering Mechanics, Vol. 1, 3rd ed, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1980.
15. Shelly, Joseph F., Engineering Mechanics: Statics, New York, McGraw-Hill Book Company, 1980.
16. Tipler, Paul A., Physics, New York, Worth Publishers, Inc., 1976.
17. Zafiratos, Chris, Physics, New York, John Wilev, 1976.
BIBLIOGRAPHY
Books
Arfken, George B. and others, University Physics, New York, Academic Press, 1984.
Ausubel, D. P., Educational Psychology: A Cognitive View, New York, Holt, Rinehart and Winston, 1968.
Beer, Ferdinand P. and E. Russell Johnson, Jr., Vector Mechanics for Engineers, 3rd ed., New York, McGraw-Hill Book Company, 1977.
Borg, Walter and Meredith Gall, Educational Research: An Introduction, 4th ed., New York, Longman, Inc., 191T3.
Campbell, Donald and Julian Stanley, Experimental and Quasi-Experimental Designs for Research, Chicago, Rand McNally, 1973.
Davis, Philip J. and Reuben Hersh, The Mathematical Experience, Boston, Houghton Mifflin Company, 1981.
Eisberg, Robert M. and Lawrence S. Lerner, Physics Foundations and Applications, New York, McGraw-Hill Book Company, 1981.
Feynman, Richard P., The Feynman Lectures On Physics, Vol. I, Reading, Massachusetts, Addison-Wesley, 1963.
Surely You're Joking, Mr. Feynman1, New York, W. W. Norton & Company, 1985
Fox, Robert W. and Alan T. McDonald, Introduction to Fluid Mechanics, 2nd ed., New York, John WileyT 1978.
Gagne, R. M., The Conditions of Learning, 3rd ed., New York. Holt, Rinehart, and Winston, 1977.
Ginsberg, Jerry H. and Joseph Genin, Statics, New York, John Wiley, 1977.
Goodchild, Peter, J. Robert Oppenheimer Shatterer of Worlds, Boston, Houghton Mifflin Company, 1981.
101
102
Halliday, David and Robert Resnick, Fundamentals of Physics, revised printing, New York, John Wiley, 1974.
Hibbeler, R. C., Engineering Mechanics; Statics, 2nd ed., New York, Macmillian Publishing Co., Inc., 1978.
Higdon, Archie and others, Engineering Mechanics, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1976.
Johnson, Robert, Elementary Statistics, 4th ed., Boston, Duxbury Press, 1984.
Malvern, Lawrence E., Engineering Mechanics, Vol. I, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1976.
McKelvey, John P. and Howard Grotch, Physics for Science and Engineering, New York, Harper and Row~Publishers, 1978.
Meriam, J. L., Engineering Mechanics, Vol. I, New York, John Wiley, 1978.
Polya, G., How To Solve It, 2nd ed., Princeton, Princeton University Press, 1973.
Radin, Sheldin H. and Robert T. Folk, Physics for Scientists and Engineers, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1982.
Sears, Frances W., Mark W. Zemansky, and Hugh D. Young, University Physics, 5th ed., Reading, Massachusetts, Addison-Wesley Publishing Company, 1976.
Shames, Irving H., Engineering Mechanics, Vol. I, 3rd ed., Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1980.
Shelly, Joseph F.,.Engineering Mechanics: Statics, New York, McGraw-Hill Book Company, 1980.
Tipler, Paul A., Physics, New York, Worth Publishers, Inc., 1976.
Zafiratos, Chris, Physics, New York, John Wiley, 1976.
103
Articles
Alexanderson, G. L., "George Polya Interviewed on His Ninetieth Birthday," The Two-Year College Mathematics Journal, 1 (January, 1979), 13-19.
Bork, Alfred, "Letter To The Editor," American Journal of Physics, 52 (October, 1984), 873-874"!
Champagne, A. B. and L. E. Klopper, "A Causal Mode of Students' Achievement In A College Physics Course," Journal of Research in Science Teachincr. 19 (Marrh. 1982), 299. ~
Cohen, R., B. Eylon, and U. Ganiel, "Potential Difference and Current In Simple Electric Circuits: A Study of Students' Concepts," American Journal of Phvsics, 51 (May, 1983), 407-412. *
Cohen, R., B. Eylon, and U. Ganiel, "Answer to Letter by M. Iona," American Journal of Physics, 51 (May, 1984), 392.
Halloun, Ibrahim Abou and David Hestenes, "The Initial Knowledge State of College Physics Students," American Journal of Physics, 53 (November. 1985^. 1043-1055": ' '
Iona, Mario, "Multiple Choice Questions," American Journal of Physics, 52 (April, 1985), 392.
Keller^ George, "Trees Without Fruit," Change, 17 (January/February, 1985), 7-10.
Lande, L. N., "Some Problems In Algorithmization and Heuristics In Instruction," Instructional Science. 4 (July, 1975), 99-112.
Mermin, David, "Is The Moon There When Nobody Looks? Reality and Quantum Theory," Physics Today, 38 (April, 1985), 38—47.
Sandin, T. R., "On Not Choosing Multiple Choice Questions," American Journal of Physics, 53 (April, 1985), 299-300.
Scott, Bruce L., "A Defense of Multiple Choice Tests," American Journal of Physics, 53 (November, 1985), 1035.
104
Snow, Richard E., "Representative and Quasi-Representative Designs for Research on Teaching," Review of Educational Research, 44 (Summer, 1974), 265-291.
Talyzina, N. F., "Psychological Bases of Instruction," Instructional Science, 2 (November, 1973), 243-280.
Varney, Robert N., "More Remarks On Multiple Choice Questions," American Journal of Physics, 52 (December, 1984), 1069.
Villars, C. N., "Observables, States, and Measurements In Quantum Physics," European Journal of Physics, 5 (March, 1984), 177-183.
Wilson, Jack M., "Toward a New University Physics," AAPT Announcer, 4 (December, 1985), 120.
Wollman, W. and F. Lawrenz, "Identifying Potential 'Dropouts' From College Physics Classes," Journal of Research in Science Teaching, 21 (April, 1984), 385.
Reports
Byron, Fredrick, W., Jr. and John Clement, Identifying Different Leve1s of Understanding Attained by Physics Students. Final Report. Columbus, Ohio: ERIC Document Reproduction Service, ED 214 755, 1980.
Champagne, Audrey B. and others, Effecting Changes in Cognitive Structures Amongst Physics Students. Columbus, Ohio: ERIC Document Reproduction Service, ED 229 238, 1983.
Clement, John, Analogy Generation in Scientific Problem Solving. Columbus, Ohio: ERIC Document Reproduction Service, ED 228 044, 1983.
Dunlop, David L., The Role of Student Preferences in Problem-Solving Strategies. Columbus, Ohio: "~ERIC Document Reproduction Service, ED 156 427, 1978.
Green, Bert E. and others, The Relation of Knowledge to Problem Solving, with Examples from Kinematics. Columbus, Ohio: ERIC Document Reproduction Service, ED 223 419, 1983.
105
Heller, Jean I. and F. Reif, Cognitive Mechanisms Facilitating Human Problem Solving in Physics: Empirical Validation of a Prescriptive Model. Columbus, Ohio: ERIC Document Reproduction Service, ED 218 077, 1982.
Heller, Jean and F. Reif, Prescribing Effective Human Problem-Solving Processes: Problem Description in Physics. Working Paper ES-19," Columbus, Ohio: ERIC Document Reproduction Service, ED 229 276, 1983.
Hohly, Richard, A Concise Model of Problem Solving: A Report on its Reliability and Validity. Columbus Ohio: ERIC Document Reproduction Service, ED 225 853, 1983.
Kaplan, Herbert and Frederic Zweibaum, "The Invisible B.S.E.O. Degree: the Need for More Practical Undergraduate Training," Barnes Engineering Company, Stamford, CT., nd.
Lockheed, Jack, A Profile of the Cognitive Development of Freshmen Engineering Students. Ann Arbor, Michigan: ERIC Document Reproduction Service, ED 151 672, 1978.
Lubkin, James L., Ed., The Teaching of Elementary Problem Solving in Engineering and Related Fields. Columbus, Ohio: ERIC Document Reproduction Service, ED 243 714, 1984.
Mumaw, Randall J. and others, Individual Differences in Complex Spatial Problem Solving: Aptitude and Strategy Effects. Columbus, Ohio: ERIC Document Reproduction Service, ED 221 358, 1983.
Novak, Gordon S., Jr., Cognitive Process and Knowledge Structures Used in Solving Physics Problems. Final Technical Report. Columbus, Ohio: ERIC Document Reproduction Service, ED 232 856, 1983
Novak, Gordon S., Jr., Goals and Methodology of Research on Solving Physics Problems. TR-58. Columbus, Ohio: ERIC Document Reproduction Service, ED 232 857, 1983.
Novak, Gordon S., Jr. and Agustin A. Araya, Physics Problem Solving Using Multiple Views. TR-173• Columbus, Ohio: ERIC Document Reproduction Service, ED 232 858, 1983.
106
Novak, Gordon S. Jr., Model Formulation in Physics Problem Solving. Draft. Columbus, Ohio: ERIC Document Reproduction Service, ED 232 859, 1983.
Pilot, A. and others, Learning and Instruction of Problem Solving in Science. Columbus, Ohio: ERIC Document Reproduction Service, ED 201 536, 1984.
Reif, F. and Joan I. Heller, Cognitive Mechanisms Facilitating Human Problem Solving in Physics: Formulation and Assessment of A Prescriptive Model. Columbus, Ohio: ERIC Document Reproduction Service, ED 218 076, 1982.
Reif, F., How Can Chemists Teach Problem Solving? Suggestions Derived from Studies of Cognitive Processes. Working Paper ES-17. Columbus, Ohio: ERIC Document Reproduction Service, ED 229 274, 1983.
Unpublished Documents
Adams, Forrest, Engineer, General Dynamics, Fort Worth, Texas. Interview with John R. Martin, February 12, 1985.
Anderson, Miles E., Physics Department, North Texas State University, Denton, Texas. Interview with John R. Martin, April 9, 1985.
Deering, William D., Physics Department, North Texas State University, Denton, Texas. Interview with John R. Martin, November 19, 1985.
O'Neil, Peter, "Calculus and Analytic Geometry," Unpublished Calculus Manuscript, Englewood Cliffs, N. J., Prentice-Hall, 1986.
Redding, Rogers W., Physics Department Chairman, North Texas State University, Denton, Texas. Interview with John R. Martin, April 9, 1985.
Sybert, James R., Physics Department, North Texas State University, Denton, Texas. Interview with John R. Martin, April 9, 1985.