Factors of mathematical aptitude

168 Pages·2015·2.68 MB·English

Iowa State University Capstones, Theses and
Retrospective Theses and Dissertations
Dissertations
1973
Factors of mathematical aptitude
Christine Leigh Taylor
Iowa State University
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Taylor, Christine Leigh, "Factors of mathematical aptitude " (1973).Retrospective Theses and Dissertations. 5052.
https://lib.dr.iastate.edu/rtd/5052
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TAYLOR, Christine Leigh, 1944-
FACTORS OF MATHEMATICAL APTITUDE.
Iowa State University, Ph.D., 1973
Education, psychology
University Microfilms, A XEROX Company, Ann Arbor, Michigan
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.
Factors of mathematical aptitude
by
Christine Leigh Taylor
A Dissertation Submitted to the
Graduate Faculty in Partial Fulfillment of
The Requirements for the Degree of
DOCTOR OF PHILOSOPHY
Major: Education (Evaluation)
Approved:
Signature was redacted for privacy.
In Charge of Major Work
Signature was redacted for privacy.
Signature was redacted for privacy.
For the Graduate College
Iowa State University
Ames, Iowa
1973
ii
TABLE OF CONTENTS
Page
INTRODUCTION 1
REVIEW OF LITERATURE 6
Theoretical Background 6
ATI Studies 8
Variables Related to Math Achievement 11
Studies Related to Algebra and Geometry 26
Summary 29
METHODS 31
Subjects 31
Instruments and Variables 32
Validation of the Problem Solving Test 36
Design and Analysis 38
Data Collection 40
Assumptions and Limitations 41
RESULTS 43
Data Reduction 43
Interrelationships of Variables 49
Design I. Factors of Mathematical Aptitude 49
Design II. Aptitude-Treatment Interaction 58
Summary 72
iii
Page
DISCUSSION AND CONCLUSIONS 73
Correlations Between Variables 73
Indicators of Success 75
Factors of Mathematical Aptitude 76
ATI 77
Implications for Education 78
Recommendations for Further Study 81
BIBLIOGRAPHY 82
ACKNOWLEDGMENTS 92
APPENDIX A.1; MULTI-APTITUDE TEST 93
APPENDIX A.2: TEACHER RATING FORM 109
APPENDIX A.3; EDWARDS PERSONALITY INVENTORY 110
APPENDIX A.4: PROBLEM SOLVING TEST 120
APPENDIX A.5: SEMANTIC DIFFERENTIAL INTEREST INVENTORY 128
APPENDIX A.6: CONTENT VALIDITY STUDY OF PROBLEM SOLVING TEST 134
APPENDIX B: TABLES 135
iv
LIST OF TABLES
Page
Table 1. Summary of studies with variables related
to math achievement 12
Table 2. Design I: Stars and nonstars 39
Table 3. Design II: Algebraic stars and geometric stars 40
Table 4a. EPI scale intercorrelations 44
Table 4b. EPI factor loadings 44
Table 5. Rotated EPI factor loadings 45
Table 6. Factor loadings from the SDII 47
Table 7. Order in which significant predictors entered
the regression 50
Table 8a. Legend for variables in study 54a
Table 8b. Mean differences among groups on predictor
variables 54b
Table 9. Relative contribution to regression and order
of predictors 59
Table 10. Mean differences between treatments on aptitude
measures 61
Table B.l. Description of sample by school and sex 136
Table B.2. Description of sample by parents' education level 136
Table B.3. Description of sample by parents' socioeconomic
status (SES) 137
Table B.4. Comparison of sample to nonparticipants 138
Table B.5. Distribution of sample by math grade point average
(MGPA) and. teacher rating (TR) 139
Table B.6. Distribution of sample by algebra grade point
average (AGPA) and geometry grade point average
(GGPA) 140
V
Page
Table B.7. Interrater correlations of content ratings on PST 141
Table B.8. Description of content of PST by item
(n = 17 raters) 142
Table B.9. Interrater correlations on item difficulty
of Problem Solving Test 143
Table B.IO. Raters estimation of item difficulty of PST 144
Table B.ll. Correlations and reliability coefficient of the
trial form of PST 144
Table B.12. Correlation and reliability coefficients of
PST of total presample 144
Table B.13. Algebra grades predicted by means of stepwise
regression 145
Table B.14, Geometry grades predicted by means of stepwise
regression 146
Table B.15. Mathematics grades predicted by means of
stepwise regression 147
Table B.16. Teacher Rating predicted by means of stepwise
regression 148
Table B.17. Semantic differential interest inventory 149
Table B.18. Correlation matrix of dependent and
independent variables 130
/
vi
LIST OF FIGURES
Page
Figure 1. Variables which discriminate between stars
and nonstars 57
Figure 2. Interaction of MVOC with algebra (A) and
geometry (G) 63
Figure 3. Interaction of MGENFO with algebra (A) and
geometry (G) 63
Figure 4. Interaction of EQUA with algebra (A) and
geometry (G) 64
Figure 5. Interaction of SCON with algebra (A) and
geometry (G) 64
Figure 6. Interaction of NSBK with algebra (A) and
geometry (G) 65
Figure 7. Interaction of EXPR with algebra (A) and
geometry (G) 65
Figure 8. Interaction of QUANT with algebra (A) and
geometry (G) 66
Figure 9. Interaction of SSREAD with algebra (A) and
geometry (G) 66
Figure 10. Interaction of NSREAD with algebra (A) and
geometry (G) 67
Figure 11. Interaction of LIT with algebra (A) and
geometry (G) 67
Figure 12. Interaction of VOCAB with algebra (A) and
geometry (G) 68
Figure 13. Interaction of USES with algebra (A) and
geometry (G) 68
Figure 14. Interaction of VOCAL with algebra (A) and
geometry (G) 69
Figure 15. Interaction of FED with algebra (A) and
geometry (G) 69
vii
Page
Figure 16. Interaction of EPI-IW with algebra (A) and
geometry (G) 70
Figure 17. Interaction of SDII-G with algebra (A) and
geometry (G) 70
Figure 18. Interaction of with algebra (A) and
geometry (G) 71