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.