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Orde r Number 91S0457
A concept learning and teaching approach to the instruction of linear motion in introductory college physics
Chyuan, Jong-pyng Michael, Ph.D.
The Ohio State University, 1991
U M I300 N. Zeeb Rd.Ann Aibor, MI 48106
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A CONCEPT LEARNING A N D TEACHING APPROACH TO THE
INSTRUCTION OF LINEAR MOTION
IN
INTRODUCTORY COLLEGE PHYSICS
DISSERTATION
Presented in Partial Fulfillment o f the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Jong-pyng Michael Chyuan, B.S., M.S .
* * * * *
The Ohio State Universi ty
1991
Dissertation Committee:
Dr. Arthur L. White
Dr. Wil li am D. Ploughe
Dr. Keith A. Hall
Approved by
Coll ege of Education
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To my parents, my wife, and my son
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ACKNOWLEDGMENTS
X wish to express my deep grati tude to Dr. Arthur L.
White for his enthusiastic and expert guidance throughout
this research project. Th e complet ion of this dissertation
would no t have been possible w ithout support.
Sincere appreciation and thanks is expressed to Dr.
Will iam D. Ploughe for sharing his knowledge and experience
teaching physics and for generously implementing the three
teaching methods in his physics 101 classes.
I would also like to thank Dr. Keith A. Hall fo r his
valuable counsel and thoughtful suggestions throughout this
research project.
Finally, my deep appreciat ion and thanks to a dear
friend and colleague, Evelyn Zei fman Becker, for her patience and help in edi ting manuscript.
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VITA
November 13, 1952 ........... Born - Taiwan,Republic of China
1974 ......................... B.S., National Taiwan NormalUniversity, Taiwan, Republic of China
1974-1975 ................... Teaching Assistant,Provincial Tainan Teachers Co11ege, Ta iwan, ROC
1979 ......................... M.S., National Taiwan NormalUniversity, Taiwan, Republic of China
1979-1980 ................... Instructor National Defense Medicine
College, Taiwan, ROC
1979-1987 ................... InstructorProvincial Taipei Teachers College, Taiwan, ROC
1987-present ................. Associate Professor,Taipei Teachers College,
Taiwan, ROC1987-1988 . . . Director of Computer Center
Taipei Teachers College Taiwan, ROC
1990-present ................. Graduate Research AssociateThe Ohio State University, Columbus, Ohio, USA
PUBLICATIONS
Chyuan, J. M. (1979). The growth and the analysis of Cu-Zn
alloy crystal . Unpublished mas ters thesis, National
Taiwan Normal University, Taipei, Taiwan, ROC.
Chyuan, J. M. (1980). Physics of Matter, Temperature and Heat (chapter 6, 7). In J. Chou (Ed.), Teachers College Phvsics (I). Taipei: Cheng-jong Book Company.
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Chyuan, J. M. (1981). Waves and sound, Optics, Electricity and Magnetism, Electromagnetism, Modern Physics (chapter 8, 9, 10, 11, 12). In J. Chou (Ed.), Teachers College Physics (II). Taipei: Cheng-jong Book company.
Chyuan, J. M. (1984). Water and energy. In T. Li (Ed.),Children Natural Science Research and Study Curriculum and Development (I). Taipei: Taipei Teachers College.
Chyuan, J. M. (1985). The analysis and research of primary school natural science learning adaptation's problem in Taipei area . Taipei: Jong-shing Publishing.
Chyuan, J. M. (1985). Energy and soil. In M. Kou (Ed.),Children Natural Science Research and Study Curriculum and Development (II). Taipei: Taipei Teachers College.
Chyuan, J. M. (1986). Energy and soil. In J. Chen (Ed.), Children Natural Science Research and Study Curriculum and Development (III). Taipei: Taipei Teachers College.
Chyuan, J. M. (1987). Energy and soil. In J. M. Chyuan(Ed.), Childrerr-i'Jatural Science Research and Study Curriculum and Development (IV^. Taipei: Taipei Teachers College.
Chyuan, J. M. (1988). Taipei teachers college entrance examination information system (EEIS). In J. M. Chyuan (Ed.), Computer Education Symposium of Teachers colleges in Taiwan Area (pp. 97 - 129). Taipei: Taipei Teachers College.
FIELDS OF STUDY
Major Field: Education
Studies in Science Education: Dr. Arthur White,Dr. Victor Mayer, Dr. Patricia Blosser.
Studies in Educational Research: Dr. Arthur White,Dr. Keith Hall, Dr. John Kennedy.
Studies in Technology in Science: Dr. William Ploughe.
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TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ...................................... iii
V I T A ..................................................... iv
LIST OF T A B L E S ........................................ viii
LIST OF FIGURES ....................................... xii
CHAPTER
I. INTRODUCTION .................................. 1
Need for Study ................................ 3Statement of the Problem ...................... 6Definition of Terms ............................ 8
A s s u m p t i o n s ....................................... 10Delimitations .. ................................ 10L i m i t a t i o n s .................................... 11
II. LITERATURE REVIEW ............................... 13
Misconception .................................. 13Concept Definition ............................ 20Concept Learning .............................. 22Concept M a p ....................................... 26Teaching Concept .............................. 32Concept Teaching Model ........................ 39General Instruction Model 4 6
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III. METHODS AND PROCEDURES ............................ 50
Design ............................................. 50Sample and Population ........................... 59Instrumentation .................................. 65Research Design .................................. 80
Analysis ........................................... 85Procedures ......................................... 86
IV. R E S U L T S ............................................. 90
Cognitive Learning Effect ....................... 90Cognitive Teaching Effect ....................... IllLearning Physics Attitude Effect ............... 116 Multivariate Regression Effect ................. 121S u m m a r y ............................................ 137
V. SUMMARY AND RECOMMENDATIONS .................... 139
Summary of Findings ......................... 139Discussion ........................................ 142Summary and Interpretation ..................... 149Specific Instructional Recommendations ........ 154Future Research .................................. 159
BIBLIOGRAPHY .......................................... 162
APPENDICES
A. Physics Concept Instruction Design ............. 169
B. Physics Concept Map T e s t .......................... 221
C. Physics Misconception T e s t ........................ 226
D. Physics Achievement T e s t .......................... 231
E. Physics Attitude Test ............................. 236
F. Course Copies for the Concept Teaching Method . . 246G. Students' Constructed Concept Maps ............. 255
H. Frequency Distribution for Items of the Physics Misconception Test and the Physics Att itude Test. 258
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LIST OF TABLES
Table Page1. Univariate ANOVA on the Physics Misconception
Pretest by Retained/Deleted Group ............. 61
2. Distribution by Gender among Three Classes . . . 62
3. Distribution by Program Areas among three Groups. 62
4. Distribution by Age among Three Classes . . . . 63
5. Distribution by High School Physics Chemistry Courseamong Three Classes ............................ 64
6. Items of the Achievement Test by Knowledge Level. 70
7. Means, Standard Deviations, and Item-TotalCorrelations for the Physics Learning Concept
Attitude Test .................................. 74
8. Means, Standard Deviations, and Item-TotalCorrelations for the Physics Misconception Attitude T e s t ............................................ 75
9. Means, Standard Deviations, and Item-TotalCorrelations for the Physics Teaching Concept
Attitude Test .................................. 76
10. Means, Standard Deviations, and Item-TotalCorrelations for the Physics Concept Map Attitude Test .......................................... 77
11. The Mode of Physics Instruction ............... 82
12. Sample Size, Means, and Standard Deviations of thePhysics Concept Map Pretest and Posttest, Physics
Misconception Pretest and Posttest, and Physics Achievement Test among Three Groups ........... 92
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13. Multivariate Tests of Regression Effect for theRelationship between Dependent Variables, Physics Concept Map Posttest, Physics Misconception Posttest, and Physics Achievement Test, and Covariates, PhysicsConcept Map Pretest and Physics Misconception P r e t e s t .......... 93
14. Multivariate and Univariate Analysis of Covariance: Treatment Effect on the Concept Map Posttest, the
Misconception Posttest, and the Achievement Test with the Concept Map Pretest and the Misconception
Pretest as Covariates ......................... 95
15. Bryant-Paulson Comparisons on Physics Concept Map T e s t ............................................ 96
16. Test of Significance for Discriminant Functions about Dependent Variables: Physics Misconception Posttest, Physics Concept Map Posttest, and Physics
Achievement T e s t ................................ 98
17. Canonical Discriminant Functions Evaluated at Group Centroids of the Physics Misconception Posttest, the Physics Concept Map Posttest, and the Physics Achievement Test ........................ 99
18. Standardized Discriminant Function Coefficients of Dependent Variables ............................. 100
19. Sample Size, Means, and Standard Deviations of the Proposition, Hierarchy, Cross-Link, and Example of the Concept Map Posttest among Three Groups . . 102
20. Multivariate Tests of Regression Effect for the Relationship between Dependent Variables, Four Parts of the Concept Map Test, and Covariates,Concept Map Pretest and Misconception Pretest . . 103
21. Multivariate and Univariate Analysis of Covariance:
Treatment Effect on the Concept Map Posttest with thePhysics Concept Map Pretest and the Physics Misconception Pretest as Covariates .......... 104
22. Bryant-Paulson Comparisons on the Proposition of thePhysics Concept Map T e s t .......................... 106
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23. Bryant-Paulson Comparisons on the Hierarchy of the Physics Concept Map T e s t .......................... 106
24. Test of Significance for Discriminant Functions about Dependent Variables: Proposition, Hierarchy,Cross-Link, and Example of the Concept Map Test . 107
25. Canonical Discriminant Functions Evaluated atGroup Centroids of the Concept Map Test . . . . 109
26. Standardized Discriminant Function Coefficientsof Dependent Variables ......................... 110
27. Mult ivariate Tests of the Effect of Concept Map and Misconception Pre-Post-Tests and the Effectof Group by Pr e- Po st -T es ts .................... 113
28. Within-Subject Effect on Misconception Test . . 114
29. Within-Subject Effect on Concept Map Test . . . 114
30. Means and Standard Deviations of Four AttitudeTests ............................................. 118
31. Multivariate Tests of Regression Effect for theRelationship between Dependent Variables, Four
Attitude Subtests, and Covariates, Concept Map Pretest and Misconception Pretest ............. 119
32. Multivariate Analysis of Covariance: Treatment Group Effect Test of Four Parts of the Concept
Map P o s t t e s t .................................. 119
33. Means of the Physics Attitude T e s t ............ 120
34. Correlation of the Dependent Variables and thePredictors for the Traditional Teaching Method (Group 1) 126
35. Canonical Correlation, Coefficients, and Componentsfor Each Canonical Variate for the Group 1 . . . 127
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36. Multivariate Regression Analysis of the Relation between the Concept Map Posttest, Misconception
Posttest, and Achievement Test, and the Four Attitude Subtests for the Traditional Teaching Method . . 128
37. Univariate F-Test of the Dependent Variables forthe Traditional Teaching Method ............... 128
38. Multiple Regression Test on the Traditional Teaching Method ................................ 129
39. Correlation of the Dependent Variables and the Predictors for the Example-NonexampleTeaching Method (Group 2) 130
40. Canonical Correlation Mult ivariate Regression Analysis of the Relation between the Concept Map
Posttest, Misconception Posttest, and Achievement Test, and the Four Attitude Subtests for the Example-Nonexample Teaching Method (Group 2) . . 131
41. Correlation of the Dependent Variables and the Predictors for the Concept Teaching Method (Group 3 ) ........................................... 132
42. Canonical Correlation, Coefficients, and Components for Each Canonical Variate for the Group 3 . . . 133
43. Multivariate Regression Analysis of the relation between the Concept Map Posttest, Misconception
Posttest, and Achievement Test, and the Four Attitude Subtests, for the concept Teaching Method . . . 134
44. Univariate F-Test of the Dependent Variables forthe Concept Teaching Method .................. 134
45. Multiple Regression Test on the Concept Teaching M e t h o d ............................................. 135
46. The Overall Significant Correlation of the Dependent Variables and the Predictors Relating Group 1, 2, and 3 136
47. Summary of the Significant Results in This Study. 137
48. Concepts Taught in the Three Lecture Sessions . . 156
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LIST OF FIGURES
Figure Page
1. Probabil ity Levels of Examples and Nonexamples . 36
2. A Concept Teaching-Model ( Tennyson and Cocchiarella, 1986) 47
3. General Instructional Model (Berlin & White,1987) 49
4. The Schema of the Physics Concept InstructionalDesign ........................................ 53
5. Physics Instructional Design Model ............. 54
6. The Teacher-Made Concept Map About Position . . 57
7. The Instructional Design for the Concept,P o s i t i o n ..................................... 58
8. The Name and Contents of Experiment Instruments . 79
9. The Concept Teaching Sequence among ThreeTreatments .............................. 81
10. Physics Concept Teaching and Learning ResearchD e s i g n ....................................... 83
11. Data Collection Procedure ...................... 88
12. Time T a b l e .................................... 89
13. The Three Group Centroids of the Physics Misconception Posttest, the Physics Concept Map
Posttest, and Physics Achievement Test in the Discriminant-Function Space ................... 99
14. The Three Group Centroids of the Concept MapPosttest in the Discriminant-Function Space . . . 109
15. Interaction between the Three Teaching Methodsand the Concept Map Pretest and Posttest . . . . 115
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concepts, Novak and Gowin (1984) illustrate an educational
tool referred to as concept mapping to help students learn
and to help teachers organize teaching material. A concept
map is a schematic device for representing a set of concept
meanings embedded in a framework of propositions which are
two or more concept labels linked by words in a semantic
unit.
As for teaching concepts in the classroom, Merrill and
Tennyson (1977), based on the conceptual model of
classification behavior (Woolley & Tennyson, 1972) and
experimental research studies (Tennyson, 1973; Tennyson,
Steve, & Boutwell, 1975), developed a concept-teaching model
in which a set of instructional design guidelines is
provided to enhance concept teaching. Tennyson and
Cocchiarella (1986) update and extend the concept-teaching
model which is composed of two fundamental components of
instructional design: (1) the content structure of a given
domain of information and (2) the organization of
instructional design variables related to the use of
specific content structures.
In classroom teaching, the organization of teaching
materials and activities is closely concerned with concept teaching. Berlin and White (1987) present an instructional
model which provides for the infusion and integration of
teaching technology into the instructional process, and it
also assists teachers in effectively promoting the learning
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of concepts in the classroom.
Need for Study
Understanding of kinematical concepts is the ability to
apply them successfully in learning and interpreting simple
motions of real objects. However, certain conceptual
difficulties occur frequently and predictably among
introductory physics students in college. Student
understanding of physical concepts has been subject to
descriptive analysis (Trowbridge & McDermott, 1980). Physics
instructors generally share a common interpretation of the
kinematical concepts based on operational definitions and
precise verbal and mathematical articulation. On the other
hand, students are likely to have a wide variety of somewhat
vague and undifferentiated ideas about motion based on
intuition, experience, and their perception of previous
instruction. Thus students often have insufficient
qualitative understanding of position, velocity, and
acceleration (Trowbridge & McDermott, 1981). Moreover, in
introductory physics teaching, Ploughe (1990, private
communication) indicates that many college students have
verbal problems in explaining the phenomena of motion and
incorrectly use physics definitions to discriminate the
concepts of motion.
Frequently, many students taking introductory physics
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cannot apply what they have learned about graphs from their
study of mathematics to physics. The difficulties
experienced by students in connecting graphs to physical
concepts includes the indecision as to whether to extract
the desired information from the slope or the height of a
graph. Students also find it more difficult to interpret
curved graphs than straight-line graphs (McDermott,
Rosenquist & Zee, 1987; White, 1987; Mokros & Tinker, 1987).
Furthermore, many students are unable to translate back and
forth from a position versus time graph to a velocity versus
time graph (McDermott et al., 1987).
Prior to the instruction of introductory college
physics, many students have a set of protoconcepts for
interpreting motion in the rea l world (Trowbridge &
McDermott, 1980). McCloskey (1983) indicates that the
protoconcepts, misconceptions, appear to be grounded in a
systematic, intuitive theory of motion and they are not
consistent with fundamental principles of Newtonian
mechanics. Halloun and Hestenes (1985) also explain that a
system of beliefs and intuitions about physical phenomena
are possessed by each college student entering a first
course (motion) in physics and the system is derived from extensive personal experience. This system functions as a
common sense theory of the physical world which the student
uses to interpret what he uses and hears in the physics
course. Yet conventional physics instruction fails almost
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completely to take this into account. Moreover, the level of
mathematical competence is not sufficient for high
performance in physics. McDermott, Rosenquist, and Zee
(1987) express that students who have no trouble making
physics graphs and computing slopes of graph cannot apply what
they have learned about graphs from their study of
mathematics to physics. Differences in gender, age, academic
major, and high school mathematics showed no effect on
physics achievement. Conventional instruction had little
effect on the student's basic knowledge state and the basic
knowledge gain under conventional instruction is essentially
independent of the professor (Halloun & Hestenes, 1985).
Thus, Clement (1982) suggests that development of innovative
instruction techniques that emphasize rigorous understanding
of qualitative physics principles should be encouraged.Based on using the conceptual model of classification
behavior (Woolley & Tennyson, 1972), the example and
nonexample teaching strategy had significant results for
instructional procedures on the cognitive level of behavior
in non-science areas (Tennyson, Woolley, & Merrill, 1972;
Tennyson, 1973; Tennyson, Steve, & Boutwell 1975; Tennyson &
Tennyson, 1975) and in a study of crystal structure
(Tennyson, et al., 1975; Merrill & Tennyson, 1978). But,
this teaching strategy has not been used for instructional
procedures in the physics area.
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The concept-teaching model originally derived by
Merrill and Tennyson (1977) and updated and extended by
Tennyson and Cocchiarella (1986) is based on the theory of
cognitive learning processes and presents strategies of
concept instructional design. However, this model does not
clearly infuse and integrate teaching technology in its
strategies. On the other hand, the general instructional
model designed by Berlin and White (1987) relates to
organizing teaching materials and activities to combine with
the concept-teaching model.
Therefore, there is a need to (1) develop an
instructional design, in accordance with a physics concept
teaching model derived from learning theories and teaching
models, that is related to the motion topic in introductory
physics for college level students, (2) test whether the
design can improve students' concept learning about motion,
and (3) learn if it can be used as an instructional system
for introductory college physics.
Statement of the Problem
The major tasks of this study are to : (1) develop and
analyze a physics unit of physics instructional design
derived from the physics concept teaching model for college
non-science students, (2) test the design in regard to the
students' learning physics concepts, students' physics
misconceptions, students' physics achievement, and students'
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attitude toward learning physics, (3) compare whether the
design is better in helping students' concept learning than
the teaching strategy using example and nonexample or the
traditional teaching strategy, and (4) identify what should
be done to further improve the design.
Problems
According to the statement of the main tasks in this
study, three groups of college non-science students are
randomly assigned to three teaching methods: physics concept
teaching method, physics example-nonexample teaching method,
and physics traditional teaching method. Thus the problems
related to the major tasks are stated as follows:
(1) Are there significant differences among the three
groups of non-science students on measures of their learning
physics concepts, their physics misconceptions, and their
physics achievement after three teaching methods are
implemented?
(2) Are there significant difference in physics concept
learning and physics misconception between before and
after three different teaching methods being implemented by
three groups of non-science students?(3) Are there significant differences among three
groups of non-science students on measures of their
attitudes toward learning physics concepts after three
teaching methods are implemented?
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(4) What is the predictive contribution of such
variables to learning physics concepts, physics
misconceptions, physics achievement, and attitude toward
learning physics concepts for each of the three teaching
methods?
Definition of Terms
Physics traditional teaching method An approach to
physics concept instruction that involves the teaching of
(1) definition and label of a concept, (2) example or
examples about the concept, and (3) phenomena description or
demonstration to a large group of students.
Physics example-nonexample teaching method An
approach to physics concept instruction that involves the
use of example and nonexample after teaching of the definition of a concept in the traditional teaching method.
Physics concept teaching method An approach to
physics concept instruction that involves the presentation
of a concept map designed by Novak (1984), the teaching
technology of the general instructional model designed by
Berlin and White (1987) , and the instructional strategy of
the concept-teaching model designed by Tennyson and
Cocchiarella (1986).
Concept map A concept map is a schematic device for
representing a set of concept meanings embedded in a
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framework of propositions (Novak & Gowin, 1984).
Misconception Misconception is the term commonly
used to describe an unaccepted (but not necessarily "wrong")
interpretation of a concept illustrated in the statement in
which the concept is embedded (Novak & Gowin, 1984).
Concept teaching Concept teaching contains five
procedures: (1) present a definition, (2) provide an
expository presentation, (3) provide attribute isolation,
(4) provide an inquisitory practice presentation, and (5) provide a test of classification (Merrill & Tennyson, 1977).
Concept learning Learning the meaning of a concept,
tha t is, learning the meaning of its criteria attributes;
includes concept formation and concept assimilation
(Ausubel, Novak & Hanesian, 1978).
Physics 101 Nature of Physical World An
undergraduate physics course which is an elementary
description of the physical world emphasizing scientific
method and contemporary viewpoints. This course is the first
quarter of two quarters sequence. Laboratory work and
demonstrations are included in it.
Physics 111 General Physics: Mechanics and Heat
An undergraduate course in mechanics and heat for students majoring in the life sciences and in architecture. This
course is the first of a series of three courses which
presents major physical principle and concepts from a
contemporary point of view. The sequence includes laboratory
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work and demonstrations.
Physics 131 Introductory Physics: Particles and
Motion An undergraduate physics course that presents the
major concepts of physics from a contemporary point of view,
for students majoring in physical sciences, mathematics, or
engineering. This course is the first quarter of three
quarters sequence.
Assumptions
The assumptions of this study are stated as follows:
1. The non-science students in this study, before
attending the Physics 101 course, have at least studied
Mathematics 075 (previously Math 102) or placement in
mathematics course code R or higher.
2. The non-science students over the duration of this
study do not get any private physics tutorial except
classroom teaching and recitation and appointments with the
teaching professor and teaching assistant.
3. The non-science students responses to the
instruments in this study are a valid indication of their
physics concepts, physics achievement, and physics attitude
about motion.
Delimitations
1. The subjects of this study are college non-science
students studying non-calculus (algebra only) physics
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(Physics 101).
2. The total of three sections of Physics 101 will be
included in this study.
3. The concept map test for assessing students'
learning of physics concepts is related to Novak's learning
theory. The scoring criteria of the test are from Novak's
rules and include: (a) relationships, (b) hierarchy, (c)
cross lines, and (d) specific examples. Also, the content of
the concept map pretest and posttest is the same.
4. The content of the items of the misconception test
related to the specific physics topic in the design unit are
concerned with position, velocity, acceleration, and graph,
and the item sources of the misconception test are from
research results. Also, the content of the misconception
pretest and posttest is the same.
5. The items of the physics achievement test are based
on the objectives of Physics 101.
6. The item sources of the learning attitude test are
from the research results, students' written responses,
classroom observation, and personal interview. The contents
of the test are concerned with: (a) learning concepts, (b)
misconception beliefs, (c) teaching concepts, and (d)
concept mapping.
Limitations
1. The classroom teaching time of this study was
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determined by the schedule of Physics 101.
2. Results of this study apply only to the Physics 101
course, not to Physics 111 and 131 series physics courses.
3. Out-of-class physics learning is undetermined.
4. Results of this study cannot be generalized to other
units of study in the Physics 101 course, without further
testing.'
5. The tested results of any subject who misses one of
the implemented cognitive tests will not be considered in
this study.
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CHAPTER II
LITERATURE REVIEW
The relevant literature for this study encompasses
seven main topics: misconception, concept definition,
concept learning, concept map, teaching concept, concept
teaching model, and general instruction model.
Misconception
Recent studies have indicated that many students
construct their own informal theories to interpret a number
of physics events. Those students7 intuitive ideas often
conflict with Newtonian theory and so interfere with physics
learning and teaching. The ideas are always labeled as
misconceptions. Trowbridge and McDermott (1980) indicated
that students have a set of "protoconcepts" before
instruction which are a repertoire of procedures,
vocabulary, associations, and analogies for interpreting
motion in the real world. Students often fail to make connections between the protoconcepts and the concepts of
kinematics. Some students are even remarkably persistent in
certain preconceptions and they depend strongly upon the
establishment of satisfactory connection between the new
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motion concepts and the protoconcepts.
In observing a large number of college students taking
introductory physics, Clement (1982) found that "conceptual
primitives" which include key physics concepts and
fundamental physics principles and models are misunderstood
by many physics students at the qualitative level in
addition to any difficulties that might occur with
mathematical formulation. He explains that Newtonian ideas
are more likely misperceived or distorted by students so as
to fit their existing preconceptions; or they may be
memorized separately as formulas with little or no
connection to fundamental qualitative concepts.
McCloskey (1983) indicates that many students have
striking misconceptions about the motion of objects in
apparently simple circumstances and the misconceptions are
apparently grounded in a systematic, intuitive theory of
motion which is not consistent with basic principles of
Newtonian mechanics.
Halloun and Hestenes (1985) also found that each
student entering a first course in physics possesses a
system of beliefs and intuitions about physical phenomena
derived from extensive personal experience. These systems are referred to as a "common sense belief" of the physical
world which the student uses to interpret his experience,
including what he uses and hears in the physics course. The
common sense beliefs about motion are generally incompatible
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with Newtonian theory and they are very stable, and
conventional physics instruction does not .successfully
correct them. Halloun and Hestenes (1986) indicate that the
common sense beliefs which are incompatible with established
scientific theory are dismissed by most scientists, but
students are not so easily disabused of the beliefs because
their own beliefs are grounded in long personal experience.
They also express that Aristotle was the first to
systematically develop explicit formulations for the common
sense beliefs about physical phenomena and organize them
into a coherent conceptual system, and the beliefs systems
of students untutored in physics are sometimes characterized
as "Aristotelian." McClelland (1985) used "pre-Galilean
ideas" to characterize these views of the world which differ
from those ideas held by "scientists". Hewson (1985) indicated that students bring to the science classroom
surprisingly extensive "student theories" or "alternative
conceptions" about how the natural world works.
Misconception about motion
In learning introductory college physics, many students
have misconceptions in studying the kinematical concepts, the first subject of classical mechanics. Trowbridge and
McDermott (1980) found that college students with no
previous study of physics thought of the word 'speed' as a
relation between the distance traveled and the elapsed time
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16
but not necessarily as a ratio; 'accelerate ' was used to
indicate that an object 'speeded up'. From many exploratory
interviews and a number of preliminary trials, Trowbridge et
al. (1980) developed two speed comparison tasks and asked
student to compare the simultaneous motions of two identical
balls rol ling on parallel U channels. As a result, they
found that failure on the speed comparison tasks was almost
invariably due to improper use of a position criterion to
determine relative velocity. Moreover, they also found
evidence that some students' certain preconceptions may be
remarkably persistent.
About the understanding of the concept of acceleration
among college students, Trowbridge and McDermott (1981)
designed acceleration comparison tasks to find how students
apply their concepts of acceleration in interpreting simple motions of real objects. They found that many students use
different concepts as the criterion to compare accelerations
and these concepts are position, speed, relative velocity,
and average velocity.
In the real world experience, it is illustrated that
some students have the misconception in separating the
concepts of velocity and position at a particular instant.
Trowbridge and McDermott (1980) and Halloun and Hestenes
(1985) reported that some students believe that if two cars,
on the freeway, reach the same position at the same time,
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then they must have the same speed at that instant.
Misconception about motion graphs
Graphing is a powerful and key symbol system for
representation of data and scientific communication.
McDermott, Rosenquist, and Zee (1987) point out that many
undergraduates taking introductory physics seem to lack the
ability to use graphs either for imparting or extracting
information. The analysis of graphing errors identified in
their study indicates that many are a direct consequence of
an inability to make connections between a graphical
representation and the subject matter it represents. For
example, students frequently do not know whether to extract
the desired information from the slope or the height of a
graph, and many are unable to translate back and forth form
a position versus time graph to a velocity versus time graph.
Mokros and Tinker (1987) in their Microcomputer-Based
Lab (MBL) project identified that two major types of
graphing misconception are: (1) a strong graph-as-picture
confusion, and (2) a weaker indication of slope/height
confusion. White (1987) also indicates that students tend to
confuse the picture of an event with the graph of an event.
Implications for Instruction about Motion
Because many undergraduate students are unable to
discriminate between position and velocity and some students
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seem to depend strongly upon the establishment of
satisfactory connections between new physics concepts and
the protoconcepts with which the student is already
familiar, Trowbridge and McDermott (1980, 1981) suggest that
a conscious effort should be made to try to help students
relate physical concepts to their experience. For example,
the relationship between the use of technical vocabulary and
the understanding of physical concepts needs to be examined
carefully and more attention at the introductory level might
be devoted to the basic kinematical concepts. They also
suggest more attention to the detailed information about
conceptual understanding that can usefully help some college
students overcome deficiencies in studying introductory
college physics.
Clement (1982) thinks that it is important to find
teaching strategies that encourage students to articulate
and become conscious of their own preconceptions by making
predictions based on them and also encourage them to make
explicit comparisons between preconceptions, accepted
scientific explanations, and convincing empirical
observations. Furthermore, class discussions and arguments
between students are especially helpful in their qualitative
understandings about the Newtonian point of view.
Halloun and Hestenes (1985) from their diagnostic test
results argue that a student's initial knowledge has a large
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effect on his performance in physics, but conventional
instruction produces comparatively small improvements in his
basic knowledge. However, Hewson (1985) describes the use of
a microcomputer program designed to diagnose students who
use a position criterion for judging when two objects are
moving with the same velocity and the program is effective
in changing students' alternative conceptions of velocity.
Rosenquist and McDermott (1987) have developed an
approach to the teaching of kinematics. By means of specific
examples, instruction based on the direct observation of
motion can help students recognize key features of
definitions, distinguish related concepts from one another,
and make explicit connections among concepts, their
graphical representation, and the real world. For example,
Rosenquist and McDermott (1987) apply a limiting process of
a curved position versus time graph to have a conceptual
criterion at the limit. From the concrete experience of the
magnified sections of a curved graph, students can deepen
their understanding of both instantaneous velocity and the
slope of a curved graph.
When interpreting a graph in physics, McDermott,
Rosenquist, and Zee (1987) express that the ability to draw and interpret graphs is perhaps one of the most important in
the study of physics. They believe that facility with
graphing can play a critical role in helping students deepen
their understanding of the kinematical concepts.
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McDermott (1990) and Trowbridge (1990) introduce the
use of a computer software package, Graphs and Tracks, as
one way for students to deepen their understanding by having
a direct experience making connections between motion and
its graphical representation.
Concept Definition
In science teaching and learning, concepts are always
the important results of scientific processes. Pella (1966)
indicates that concepts may be viewed initially as a summary
of the essential characteristics of a group of ideas and
facts that epitomize important common features or factors
from a large number of ideas. Because of the comprehensive
nature of concepts, Pella states that concepts are useful to
the individual in order to gain some grasp of a much larger field of knowledge than he has personally experienced.
The most fundamental meaning of concept is exhibited in
individual behavior by responding to a class of observable
objects or object qualities such as those implied by the
names "color," "shape," "size," "heaviness," and so on, or
by common objects such as "cat," "chair," "tree," and
"house." Those concepts are concrete and they are concepts
by observation. Then, abstract concepts can be described and
even defined; [e.g., mass, temperature, and prime number.
(Gagne, 1970)].
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Shumway (1971) suggests a concept is a partitioning of
a class X, universal class over which the concept is
defined, into two disjoint classes X1# positive instances,
and X2 , negative instances of the concept. The class X is
the union of the class X1 and the class X2 and the classes
X1 and X2 are disjoint. To say that a student knows the
concept over the class X is to say that given any object
from the class X the student is able to identify the object
as a member of the class X^ or the class X2 associated with the concept over the class X. Thus their relationships can
follow from the above results:
X = xi x2 , X = X - X2, and X2 = X - X ^
According to the empirical research results by Merrill
and Tennyson (1977), a concept can be defined as "a set of
specific objects, symbols, or events which are grouped
together on the basis of shared characteristics and which
can be referenced by a particular name or symbol." Novak and
Gowin (1984) simply define concept as a regularity in events
or objects designated by some label. Gagne et al. (1988)
defines "a concept is a capability that makes it possible
for an individual to identify a stimulus as a member of a
class having some characteristic in common, even though such stimuli may otherwise differ from each other markedly." He
also identifies a concrete concept as an object property or
object attribute and a defined concept as an individuals
ability to demonstrate the meaning of some particular class
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of objects, events, or relations.
Concept Learning
An important type of learning is cognitive learning,
which is Ausubel's primary theory in cognitive processes.
Cognitive learning results in organized storage of
information in the learner's brain and this organized
complex is referred to as cognitive structure. The most
important concept in Ausubel's theory is what he describes
as meaningful learning. Meaningful learning occurs when new
information is linked to existing relevant concepts in the
learner's cognitive structure. Rote learning, on the other
hand, is also possible to learn new information with little
or no linkage to existing elements in cognitive structure
(Thorsland & Novak, 1974; Novak, 1976).
In the course of meaningful learning, individuals must
choose to relate new information to relevant concepts and
propositions they already know. The existing relevant
concept in cognitive structure is called the subsuming
concept or subsumer. The linkage of new information with a
relevant subsumer in the process of meaningful learning is
the course of subsumption. For a period of time, the new
information learned will no longer be dissociable from the
subsuming concept. This case is called obliterative
subsumption. After obliterative subsumption, the residual
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concept remains and much of the growth that occurred during
subsumption is retained. Therefore, the remaining concept is
strengthened and more capable of facilitating new meaningful
learning in the future (Novak,1976).
As the subsumption process proceeds, existing concepts
become more elaborated or more differentiated; that is,
meaningful learning is a continuous process wherein new
concepts gain greater meaning as new relationships with
previously learned, relevant concepts are acquired. Thus,
concepts are always being learned, modified, and made more
explicit and more inclusive as they become progressively
differentiated (Novak,1976; Novak & Gowin, 1984).
In the process of learning and concept differentiation,
conflicting meanings may arise and the process by which
conflicting meanings between concepts are clarified is
known as integrative reconciliation (Novak 1976, 1979; Novak
& Gowin 1984).
Meaningful learning incorporates new knowledge into the
cognitive structure of our minds non-arbitrarily and
substantively (Novak, 1979). However, each student will form
his/her own idiosyncratic meaning for the concept, and most
of the new concepts will be achieved through reception learning (Ausubel et al., 1978). If the reception learning
is to be meaningful, the learner must form unique linkages
between the concepts s/he already has and the new
descriptions of regularities that are to be learned. Thus,
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meaningful learning is always idiosyncratic, and in this
sense the learner "discovers" the meaning of all concepts by
the nonarbitrary way in which s/he learns the new concepts.
As the study of human learning has proceeded, Gagne
(1988) indicates that a whole set of factors that influence
learning may be called the conditions of learning. Some of
these conditions pertain to the stimuli that are external to
the learner. Others are internal conditions that are sought
within the individual learner.
Advance Organizer
Advance organizers are introductory material at a high
level of abstraction, generality, and inclusiveness and they
facilitate meaningful verbal learning and retention
(Ausubel, 1960; Ausubel & Fitzgerald, 1961).
Two different ways that advance organizers facilitate
the incorporability and longevity of meaningful verbal
material: (1) the organizers explicitly draw upon and
mobilize whatever relevant subsumers are already established
in the learner's cognitive structure and make them part of
the subsuming entity, (2) the organizers at an appropriate
level of inclusiveness provide optimal anchorage. Thus, the more unfamiliar the learning material, the more inclusive or
highly generalized the subsumers must be in order to be as
proximate as possible to the degree of conceptualization of
the learning task. If appropriately relevant and proximate
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subsuming concepts are not available, the most dependable
way of helping retention is to introduce the appropriate
subsumers and make them part of cognitive structure before
the actual presentation of the learning task. The introduced
subsumers become advance organizers for the reception of new
material (Ausubel, 1960). Moreover, the organizer better
enables the learners to put their background knowledge to
effective use in structuring the unfamiliar new material
(Ausubel & Fitzgerald, 1962).
By using Ausubel's theory about the ideas of
subsumption as a promising base for research formulation,
Novak (1971) found that advance organizers can facilitate
learning before students have the available subsumers, and
effective instruction for meaningful reception learning
could benefit by use of advance organizers in sequences with
instruction. Thus, a hierarchical series of organizers would
be planned into the instructional sequence. Novak (1976)
also uses "cognitive bridges" to emphasize the "linking" or
"bridging" function of "advance organizers". Short segments
of learning material can be used to provide guidance to the
student by establishing appropriate subsuming concepts so
that new concepts can be assimilated in the cognitive
structure for meaningful learning. Moreover, the key
concepts in the new material and their subordinate or
superordinate relationship to concepts the learner already
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has can be helpful as cognitive bridges.
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Concept Map
Concept mapping is a model to demonstrate the nature of
concept learning to students (Novak, 1980, 1981; Novak,
Gowin & Johansen, 1983). Concept maps are intended to
represent meaningful relationships between concepts in the
form of propositions, which are two or more concept labels
linked by words in a semantic unit (Novak & Gowin, 1984). A
simple method for constructing concept maps is to supply
students with a list of related concepts and have them
construct a map, placing the most inclusive, most general
concept at the top and then showing successively less
inclusive concepts at lower positions on a hierarchy. Novak
et al. (1984) indicate that this idea of hierarchical
structure incorporates Ausubel's concept of subsumption,
namely that new information often is relatable to and
subsumable under more general, more inclusive concepts. The
hierarchical structure can also show the set of
relationships between a concept and other concepts
subordinate to it. If sections of a concept map are too
general or too specific, the hierarchical structure of it indicates either misunderstanding or the need for more
careful integration of superordinate and subordinate
concepts.
Concepts are always being learned, modified, and made
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more explicit and more inclusive as they become
progressively differentiated. Novak et al. (1984) state when
concept maps for one topic are cross linked to concept maps
for other related topics, progressive differentiation of
concepts is enhanced. Because the positive emotional
experience that derives from meaningful learning is a major
source of sustained intrinsic motivation for learning, Novak
et al. (1984) state that progressive differentiation of
concepts through concept mapping can provide emotional as
well as cognitive rewards, both in the short term and,
especially, in the long term.
When the learner recognizes new relationships between
related sets of concepts or propositions, integrative
reconciliation in the process of meaningful learning is
occurring. Novak et al. (1984) suggest that concept maps
that show valid cross links between sets of concepts that
might otherwise be viewed as independent, can suggest
learners' integrative reconciliation of concepts.
Concept Mao and Misconception
Because concept maps are an explicit, overt
representation of the concepts and propositions a person
holds, they allow teachers and students to exchange views on
checking propositional linkage or recognizing missing
linkages between concepts. More importantly, because concept
maps contain externalized expressions of propositions, they
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are effective tools for showing misconceptions.
Misconceptions are usually signaled either by a linkage
between two concepts that leads to a clearly false
proposition or by a linkage that misses the key idea
relating two or more concepts (Novak & Gowin, 1984) .
Concept Map and Evaluation
Concept mapping is a technique which allows the student
to demonstrate what he or she know in a visual form. Concept
maps help learners identify the key concepts to be learned,
and show links between what is to be learned and what he or
she already knows. Thus scoring systems have been designed
for concept maps, and the basis for the systems is the
quantification of meaningful learning relative to some
discipline area. Credit is given not only for the number of
valid propositions or concept linkages, but even more
importantly, for the number of valid hierarchical levels
(Novak & Gowin, 1984; Ridley & Novak, 1988).
Concept Map and Teaching
Using concept mapping techniques, in an introductory
biology course for biology majors, Arnandin, Mintzes, Dunn,
and Shager (1984) trained students to map, tested their pre
instruction maps and post-instruction maps, and assessed
their maps. They advanced the following claims made on behalf of
concept mapping: (1) concept mapping helps students
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understand what meaningful learning is, (2) concept mapping
facilitates meaningful learning, (3) concept mapping is an
effective study technique, (4) concept mapping provides a
useful evaluation tool, and (5) concept mapping is a useful
tool for organizing and sequencing instruction.
Ault (1985) introduced concept mapping as a study
strategy in an earth science course and indicated that
concept mapping is one strategy for solving the problem of
why students often learn so little. Judiciously used by
either instructors planning lectures or students preparing
for an examination, concept mapping enhances opportunities
for meaningful learning. However, in nonsupportive settings,
Ault indicates that students' tolerance for mapping
exercises will fade rapidly. And, grading practices can
thoroughly undermine the value of concept mapping by
reinforcing rote learning. Ault cautions that students
should not be asked to memorize instructor-prepared maps.
Moreover, students often do not feel comfortable working
within highly interconnected systems of thought and some
believe they must remember information precisely in the form
presented or be penalized. Thus the rote knowledge in novel
contexts becomes painfully evident. Ault suggests that meaningful learning requires uncompromising commitment by
both teachers and students to an understanding of structure
in knowledge, and concept mapping skill leads in this
direction.
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In order to actively promote meaningful learning,
Cliburn (1986, 1990) uses teacher-made concept maps as
potential applications of the advance organizer. He uses
whole-unit maps to represent the unit's conceptual framework
and then forms this large-scale map. A series of more
specific, higher-resolution maps can be drawn to show more
detail, result ing in a nested set of conceptual maps for the
unit. Furthermore, he makes a color-coded composite map
joining all the individual concept maps and posts it on the
classroom bulletin board. After the formal study of the
concept map, Cliburn found students who were taught by using
concept maps learned better and retained the material
better. Thus the effectiveness of concept maps promoting
long-term retention is strongly confirmed.
Some Alternate Assessments of Cognitive Structure
Shavelson (1974) presents a model of human information
processing which can be divided into two general components:
perception and memory. In the memory component, long-term
memory (LTM) and a retrieval and decision process serve to
define the cognitive structure. Two measurement methods that
retrieve the student's representation of a subject-matter
structure from his cognitive structure are Word-Association
Method and Graph-Construction Method.
In the Word-Association Method, the student's list of
responses to each stimulus word in a test are scored through
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their number, type (Shavelson, 1973), or overlap (Shavelson,
1974). Garskof and Houston (1963) provided a method of the
Relatedness Coefficient (RC) to define the relatedness of
each two words in a set of associates. This method was used
to judge the physics concepts in the subject matter
(Johnson, 1967); Preece, 1976). Then the observed
coefficients of all pairs of concepts can be analyzed by
using factor analysis, multidimensional scaling (Kruskal,
1964; Davison, 1983), or hierarchical cluster analysis
(SPSS, 1990) to present the student's cognitive structure.
Gussarsky and Gorodetsky (1988) use the method of
constrained word associations to gain knowledge on the
chemical equilibrium concept.
In the Graph-Construction Method, the student is given
a list of key words and asked to build a linear tree graph by connecting pairs of words. The distances between all
pairs of words on the graph are analyzed by various scaling
techniques the same as in the word-association method, in
order to examine the student's cognit ive structure (Waern,
1972; Shavelson, 1974).
Diekhoff and Diekhoff (1982) state that an instructor's
numerical judgments of all possible pairs of key concepts
selected from a knowledge domain should be useful in
conveying structural information to students. The
instructor's judgments can be analyzed through principal
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components analysis (SPSS, 1990) to translate relationship
judgments into distance. These distances are used in
creating a graphic array of concept-points in space, called
a "cognitive map".
Jonassen (1984) develops a technology, Pattern Notes,
for analyzing and classifying the relational links between
concepts. To construct a pattern note, a primary subject is
first identified and written in block letters in the center
of a blank sheet of paper, and a box drawn around it. Next,
the student free associates about the subject, thinking
about the key related concepts, and writes them on lines
connecting them to the box. The number of lines between two
concepts may be summarized in a distance matrix and then
they are analyzed by using the method of multidimensional
scaling. As a result, the structure of conceptual
relationships derived by the Pattern Notes test and the Word
Associat ion test are statistically and visually very similar
(Jonassen, 1987).
Teaching Concept
Concept Classification
Most studies of conceptual behavior have dealt mainly with the characterization of the specific concept to be
learned. The general form of solution (rule) has been simple
and familiar, e. g., a conjunction of attributes, and has
been described for the learner during preliminary
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instructions and/or practice problems. Under these
circumstances, the learning task can be described as
attribute identification and the rule relating the relevant
attributes given has received little attention. Thus, a rule
learning (RL) task based on the conceptual rules which are
conjunction, inclusive disjunction, joint denial, and
conditional is constructed and concerned with separable and
unique behaviors. In the RL task, changes in rule difficulty
are a function of the acquisition by learners of a stimulus-
coding strategy, and the strategy reduces a large and
potentially unlimited stimulus population to four classes:
(a) both, (b) the first but not the second, (c) the second
but not the first, and (d) neither of the two given relevant
attributes. In general, these classes are referred to as TT,
TF, FT, and FF in a bidimensional truth table. Each bidimensional rule can map the stimulus classes uniquely
into the two categories of a concept, positive and negative
instances. Once the strategy is mastered, learners are
merely required to learn the assignment of these four
classes to two response categories. Moreover, the
acquisition of a stimulus-coding strategy could reduce
differences in rule difficulty and produce apparent positive
interrule transfer effects (Haygood & Bourne, 1965).
In the study of the relationship between unknown
relevant attributes which are conjunctive, inclusive
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a concept class, and a nonexample (item) does not belong to
the class. Then the items in a class are normally
distributed based upon the ease in recognizing an item as
being either an example or a nonexample.
Example and Nonexample
During the process of concept learning, Woolley et al.
(1972) define three independent variables concerned with the
distribution to the examples: probability, matching, and
pairing. Probability levels of examples and nonexamples
presented are determined by their ease of recognition. The
relationships between high/low probability and examples/
nonexamples can be found in Figure 1. That the relationship
between examples and nonexamples is presented continuously
is called matching; that is, an example and nonexample are
matched when they share vir tually all of the same irrelevant
attributes, and differ only in some relevant attributes.
Pairing has two different types: divergent pairing refers to
the case when two examples presented in a sequence differ as
much as possible in their irrelevant attributes; convergent
pairing means two sequential examples differ only slightly
in irrelevant attributes.There are four concept learning outcomes specified in
relationship to the independent variables. If the
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High probability Low probability
Examples An example would be
recognized as belonging to a specified concept class.
An example would be incorrectly classified as belonging to a specified concept class
Nonexamples
A nonexample would be easily rejected as
belonging to a specified concept class.
A nonexample would be incorrectly accepted as belonging to a specified concept class.
Figure 1. Probability Levels of Examples and Nonexamples
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respondents would correctly classify previously
unencountered examples of all probability levels, it is the
case of correct classification. However, when previously
unencountered examples are correctly identified but some low
probability nonexamples are also included as being examples
is called overgeneralization; i. e. a respondent cannot
discriminate between examples and nonexamples and indicates
that the learner's range of acceptance is too great. On the
other hand, when the range of rejection is too great is
called undergeneralization. If the learner variously accepts
or rejects examples and nonexamples of all probability
levels based on their irrelevant attributes, it is
misconception (Woolley & Tennyson, 1972).
In investigating the relationship among examples and
nonexamples, concept learning is most effectively
facilitated as examples present a range from easy to
difficult, subsequent examples are divergent in variable
attributes (irrelevant attributes) from previous examples,
and examples are matched to nonexamples on the basis of
similarity of variable attributes (Tennyson, Woolley &
Merrill, 1972; Tennyson, 1973; Tennyson & Park, 1980).
Moreover, organized sequence of a presentation of examples is more effective than random presentation. (Tennyson, Steve
& Boutwell, 1975).
In a classroom study, Shumway (1971) found that
nonexamples discouraged overgeneralization errors by eighth
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grade students for concepts involving the properties of
mathematical binary operations.
In the study of the effects of an instructional
sequence of all examples and a sequence of examples and
nonexamples on the acquisition of the mathematical concepts
of commutativity, accociativity, distributiv ity , and
homomorphism, Shumway (1973, 1974) found that a sequence of
examples and nonexamples was superior to a sequence of all
examples for the acquisition of these concepts. The results
of these studies are consistent with Tennyson, Woolley, and
Merril l (1972) and Shumway (1972).
Instructional research on concepts in mathematics
(Shumway, 1974, 1977), Poetry (Tennyson, Woolley & Merrill,
1972; Tennyson, Steve & Boutwell, 1975), sentence (Tennyson,
1973), and chemistry crystal structure (Merrill & Tennyson,
1978) suggests that mixtures of examples and nonexamples are
favored over all examples in learning school-related
concepts. In order to identify important variables
influencing the role of nonexamples on logical thinking in
conjunctive feature identification tasks, the all example
treatment was favored over the mixed example and nonexample
treatment with the 1:1 feature frequency condition; the
mixed example and nonexample treatment was favored over the
all example treatment where the frequency of one feature of
the irrelevant dimensions was 9:1 compared to the other
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feature (Shumway, White, Wilson & Brombacher, 1983) . By
using Apple II microcomputer to design a program including
graphics animated to represent chemical and physical changes
which are often observed in qualitative chemical analysis,
White, Wilson, and Shumway (1981) also found the same
results.
In addition to organizing examples and nonexamples in
teaching concepts, additional improvements are suggested to
include: (1) the use of attention focusing devices
(attribute isolation) to focus the student's attention on
the critical attributes, (2) the use of a step-by-step
(algorithmic) presentat ion of the definition, and (3) the
combination of expository presentations with feedback-
accompanied practice (Merrill & Tennyson, 1978).
As to the question of how many examples and nonexamples
in concept teaching should be presented, Tennyson and Park
(1980) indicated that the appropriate number of examples
differs according to the learning characteristics of
individual students.
Concept Teaching Model
In carefully controlled experimental research studies, Merrill and Tennyson (1977) express that most concepts do
not exist in isolation but rather as part of a set of
related concepts. Thus " a concept taxonomy is a diagram
which is constructed to indicate the subordinate,
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superordinate, and coordinate relationships among a set of
related concepts." "When a superordinate concept is divided
into subordinate concepts, the subordinate concepts for a
single superordinate concept are called coordinate
concepts." Using the coordinate concepts selected from
psychology as a task wi th junior and senior high students,
Tennyson, Tennyson and Rothen (1980) examined three
presentation orders of sequencing examples of coordinate
concepts: (1) Simultaneous order, all of the coordinate
concepts were presented concurrently by grouping one example
from each concept in a rational set. Within a rational set
the representative examples had matched variable attributes
and different critical attributes, while between rational
sets the examples had divergent variable attributes; (2)
Collective order, the coordinate concepts are clustered according to shared critical attributes. That is, certain
critical attributes may be identical in various concepts,
with differences between these concepts based on subordinate
concepts; (3) Successive order, there were no groupings;
instead, each concept was presented independently. In terms
of concept learning, the results indicate that students
learn generalization behavior when they are given a range of
variable attributes between rational sets, and that they
learn discrimination behavior when given examples of each
concept within rational sets.
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In the research of concept learning, Tennyson, Chao,
and Youngers (1981) suggest that what is stored in memory is
a bes t example (prototype or clear case) and that learners
match newly encountered examples with that best example.
Thus they used three presentation methods to test concept
attainment: (1) expository, with labels and statements
clearly identifying examples and nonexamples; (2)
interrogatory, with questions requiring students to identify
examples and nonexamples; and (3) expository-interrogatory,
a combination of the first two. Data analyses showed that
learning was facilitated for fourth-grade students by a
presentation method that combined expository statements of
best examples with interrogatives over presentations that
were expository or interrogatory only.
From the extensive research on concept learning in
psychology and education, two processes should be involved
in the concept learning: first, formation in the
individual's memory of a best example and second,
development of the skill to recognize specific attributes of
similarity and difference between and among newly
encountered examples. As to the teaching concept, a good
concept lesson should include the following elements (Jassal & Tennyson, 1982):
1. a concept definition;
2. a best example;
3. an expository set of examples;
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4. an interrogatory set of examples;
5. a classification test.
For purposes of instructional design, the research
presented above have shown that concept learning involves
development of classification skills in generalization and
discrimination and that learners can learn most effectively
if the learners are presented with best examples of the
concept in both expository and interrogatory presentation
forms. In order to test (1) whether formation of conceptual
information may be learned by an instructional presentation
form that focuses attention on a best example or that
clarifies the relationship of the critical attributes, and
(2) the effect of expository examples in facilitat ing the
transition between the encoding of conceptual information
and the development of the classification skill, Tennyson,
Youngers, and Suebsonthi (1983) used the concept of a
regular polygon as a task with third-grade students. The
results of the study show (a) that presentation of best-
examples along with the definition facilitated prototype
formation more than did a presentation of the definition
along with a statement clarifying the relationship of the
critical attributes, and (b) that classification skill was
facilitated more by presentation of both expository and
interrogatory examples compared to an interrogatory-only
presenta tion .
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Based on a programmatic line of research that has
focused on the improvement of concept-learning through the
enhancement of instructional design variables, Tennyson and
Cocchiarel la (1986) present a concept-teaching model which
extends the earlier version of a model presented by Merrill
and Tennyson (1977). In this model, Tennyson et al. (1986)
use current theory and research findings from instructional
systems, cognitive science, and developmental psychology to
indicate two cognitive processes in a concept-learning
model: (a) formation of conceptual knowledge which is formed
in memory by the integrated storage of meaningful dimensions
selected from known examples and the connecting of this
enti ty in a given domain of information; and (b) development
of procedural knowledge which is developed by using
conceptual knowledge to solve domain-specific problems.
Based on this two-phase theory of concept learning, the
concept-teaching model is composed of two fundamental
components of design: (1) the content structure of a given
domain of information and (2) the organization of
instructional design variables related to the use of
specific content structures.
In the content structure variables of the concept-
teaching model, Tennyson et al. (1986) suggest that they
should be analyzed according to two conditions: (1) the
relational structure between concepts in a given domain of
information and (2) the variability of the attribute
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characteristics of each concept in the domain. The
relational structure of concepts are associated with two
classification skills: generalization and discrimination.
When engaging in a content analysis, successive and
coordinate are determined as the basic relations of the
domain's structures. With successive relationships, learning
is limited primarily to the development of generalizations
within a concept class. With coordination relationships,
learning includes the development of skills to generalize
within a concept class and discriminate between concepts.
The second condition, attribute characteristics, affects the
design of an instructional strategy for either coordinate or
successive concepts. Attributes can be thought of as having
constant or variable dimensions. When the definition of a
concept does not change with the context in which it is learned, the concept may be considered as having constant
attributes. On the other hand, a concept may be considered
as having variable dimensions when its definition and
examples tend to change with the context of instruction.
The instructional design variables for concept-teaching
suggested by Tennyson and Cocchiarella (1986) are directly
related to specific cognitive processes in concept-learning.
They are explained in the following:
(1) Label, definition, and context. Labels and
definitions seem to help the learner establish in memory the
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possible connection between existing necessary knowledge and
the to-be-learned concepts, but definitions play a secondary
role in concept learning because learners rarely learn well
from only definitions and most often verbatim definitions
are not encoded in memory. The relationship between a label
and the concept represented by a label often in an
unhelpful, arbitrary association established by cultural
convention. However, concept labels can assist learners in
conjuring up the concept in memory by relat ing the concept
to what is already known. A concept may have one label but
several definitions, a specific context for the presentation
of a problem within the appropriate situation or domain can
provide information to establish critical attributes of the
concept.
(2) Best examples. The best example represents an
average, central, or prototypical form of a concept, but it
is not necessarily a quantitative value. Because a best
example sets up the initial encoding of conceptual
knowledge, it should be an example that can conjure up in
memory existing knowledge structures.
(3) Expository examples. Expository examples provide
the dimensionali ty or richness of conceptual knowledge. In the process of teaching the examples, learners also acquire
the initial procedural knowledge for using the conceptual
knowledge.
(4) Interrogatory examples. Interrogatory examples
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further enhance the development of procedural knowledge.
(5) Attribute elaboration. This des ign variable assists
the learner in establishing the conceptual knowledge
structure of a given concept and its relationship in a
schematic network. There are two devices used for attribute
elaboration: (1) attribute prompting which is a tool to help
learners establish the conceptual knowledge by focusing