the relationships between spatial ability, logical thinking, mathematics performance and kinematics

226 Pages·2006·2.07 MB·English

THE RELATIONSHIPS BETWEEN SPATIAL ABILITY, LOGICAL THINKING,
MATHEMATICS PERFORMANCE AND KINEMATICS GRAPH
INTERPRETATION SKILLS OF 12TH GRADE PHYSICS STUDENTS

DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University

By
Behzat Bektasli, M.S.
*****

The Ohio State University
2006
Dissertation Committee:
Professor Arthur L. White, Adviser Approved by
Professor Donna F. Berlin ____________________
Assistant Professor Karen E. Irving Adviser
College of Education
ABSTRACT

Graphs have a broad use in science classrooms, especially in physics. In physics,
kinematics is probably the topic for which graphs are most widely used. The participants
in this study were from two different grade-12 physics classrooms, advanced placement
and calculus-based physics. The main purpose of this study was to search for the
relationships between student spatial ability, logical thinking, mathematical achievement,
and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the
Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding
Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom
observations were made to acquire ideas about classroom environment and instructional
techniques. Factor analysis, simple linear correlation, multiple linear regression, and
descriptive statistics were used to analyze the quantitative data.
Each instrument has two principal components. The selection and calculation of the
slope and of the area were the two principal components of TUG-K. MIPT was
composed of a component based upon processing text and a second component based
upon processing symbolic information. The Purdue Spatial Visualization Test was
composed of a component based upon one-step processing and a second component
based upon two-step processing of information.
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Student ability to determine the slope in a kinematics graph was significantly
correlated with spatial ability, logical thinking, and mathematics aptitude and
achievement. However, student ability to determine the area in a kinematics graph was
only significantly correlated with student pre-calculus semester 2 grades. Male students
performed significantly better than female students on the slope items of TUG-K. Also,
male students performed significantly better than female students on the PSAT
mathematics assessment and spatial ability.
This study found that students have different levels of spatial ability, logical thinking,
and mathematics aptitude and achievement levels. These different levels were related to
student learning of kinematics and they need to be considered when kinematics is being
taught. It might be easier for students to understand the kinematics graphs if curriculum
developers include more activities related to spatial ability and logical thinking.

iii
Dedicated to my wife Filiz, my daughter Beliz, and my son Kaplan Emre

iv
ACKNOWLEDGEMENTS

I wish to thank my advisor Dr. Arthur L. White for his support, encouragement,
friendship, and patience. I appreciate his help and look forward to having a continued
relationship with him.
I also wish to thank Dr. Donna F. Berlin who provided particularly valuable
conceptual and technical advice. I appreciate her help and friendship, and look forward to
having a continued relationship with her.
I thank Dr. Karen E. Irving for her support and help during my study. I look forward
to having a continued relationship with her.
I am grateful to Karen Scott, the physics teacher, who let me use her students for my
study. Without her help it would be impossible to collect my data. I thank Valerie
Sharritts, the mathematics teacher, and Dan Garrick the principal who supported my
study.
I also wish to thank the students that participated in my study and their parents for
their permission.
I would like to express my deepest love and thanks to my wife for being with me and
supporting me all the time.

v
VITA
February 1, 1972 …………………………………………..Born-Hatay, Turkey

1995 ………………………………………………………. Bachelor of Science
Physics,
Cukurova University
Adana, Turkey

1995-1999 …………………………………………………Physics Teacher
Somuncubaba High School
Aksaray, Turkey

2002 ………………………………………………………..Master of Science
Science Education
The Ohio State University

2005……………………………………………………….. Lecturer
The Ohio State University
Mansfield, OH

FIELD OF STUDY

Major Field: Education

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TABLE OF CONTENTS

Page

Abstract..........................................................................................................................ii
Dedication......................................................................................................................iv
Acknowledgements.........................................................................................................v
Vita.................................................................................................................................vi
List of Tables..................................................................................................................x
List of Figures.............................................................................................................xiii

Chapters:

1. Visuospatial ability and learning by graphical displays.....................................1

Rationale.............................................................................................................1
Background.........................................................................................................1
Theoretical framework........................................................................................2
Introduction.............................................................................................2
Dual coding theory..................................................................................6
The relation of DCT to cognitive and neuroscience research.....7
The visual argument hypothesis..............................................................9
The conjoint retention hypothesis.........................................................10
Logical thinking....................................................................................12
Mathematics achievement.....................................................................15
Summary...........................................................................................................16
Problem statement.............................................................................................18
Hypotheses........................................................................................................19
Delimitations.....................................................................................................19
Limitations........................................................................................................20

2. Literature review...............................................................................................22

Introduction.......................................................................................................22
Kinematics and graphs......................................................................................23
Learning implication of DCT................................................................25
Learning by graphic organizers............................................................30
Difficulties with using graphs in kinematics........................................32
Microcomputer-Based Laboratory (MBL)...........................................37

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The relationship between visual and spatial abilities
and kinematics graphs...........................................................................41
Summary...........................................................................................................43

3. Methodology.....................................................................................................45

Kinematics graphs.............................................................................................45
Prerequisites......................................................................................................49
Classroom settings, activities and teaching strategies......................................50
Participants........................................................................................................51
Instruments........................................................................................................55
Plan for data collection and analysis.................................................................56
Instrumentation.................................................................................................57
Reliability..............................................................................................57
Principal component analysis...............................................................60
MIPT.........................................................................................63
MIPT: Principal Component 1......................................64
MIPT: Principal Component 2......................................67
Purdue Spatial Visualization Test.............................................71
Spatial: Principal Component 1....................................72
Spatial Principal Component 2.....................................76
TUG-K......................................................................................78
TUG-K: Principal Component 1...................................80
TUG-K: Principal Component 2...................................84
Definition of terms............................................................................................87
Variables...............................................................................................87
Dependent variables..................................................................87
Independent variables...............................................................87
Original subscales.................................................................................88
MIPT subscales.........................................................................88
Purdue Spatial Visualization Test subscales.............................89
TUG-K subscales......................................................................89

4. Results ...............................................................................................................90

Introduction.......................................................................................................90
Quantitative data analysis.................................................................................90
Descriptive statistics ...........................................................................90
Correlations...........................................................................................91
Significant relationships between dependent variables............93
viii
Significant relationships between dependent
and independent variables.........................................................93
Significant relationships between independent variables.........94
Forward multiple linear regression.......................................................95
TUG-K: Slope...........................................................................95
TUG-K: Area............................................................................96
TUG-K frequency analysis for selected specific choices.....................97
Research questions..........................................................................................100
Research question 1............................................................................100
Research question 2............................................................................105
List of findings................................................................................................106

5. Conclusions and implications.........................................................................110

Summary.........................................................................................................110
Conclusions.....................................................................................................113
Discussion and interpretation of findings...........................................116
Implications and recommendations................................................................122
Recommendation for physics teachers................................................122
Recommendations for further research...............................................123

References ...................................................................................................................126

Appendices:

A. Factor Analysis Rotated Matrices and Scree Plots.........................................131

B. Classroom Observations.................................................................................138

C. IRB Forms.......................................................................................................152

D. Instruments......................................................................................................159

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LIST OF TABLES
Table Page
1.1 Influence of the delimitations and limitations on internal
and external validity..........................................................................................21

3.1 Information about length of class period and textbooks...................................53

3.2 Gender distribution and mathematics background of participants...................54

3.3 Reliability statistics for MIPT, Spatial Visualization, and TUG-K..................57

3.4 Reliability statistics for MIPT subscales...........................................................58

3.5 Reliability statistics for Spatial Visualization test subscales............................59

3.6 Reliability statistics for TUG-K subscales........................................................60

3.7 Distribution of principal components for the MIPT responses.........................64

3.8 Reliability analysis of the MIPT principal components...................................64

3.9 Rotated matrix loading and mean of correct answer by item for
MIPT: Principal Component 1..........................................................................65

3.10 Rotated matrix loading and mean of correct answer by item for
MIPT: Principal Component 2.........................................................................67

3.11 Distribution of subscales for Purdue Spatial Visualization test responses.......71

3.12 Reliability analysis for Purdue Spatial Visualization test responses................72

3.13 Rotated matrix loading and mean of correct answers by item for
Spatial: Principal Component 1........................................................................73

3.14 Rotated matrix loading and mean of correct answer by item for
Spatial: Principal Component 2........................................................................76

3.15 Distribution of items by subscales for TUG-K responses................................79

x