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Nortti ZGGb Rosd Ann Arbor, Michigan 48106

74-580

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:

In

Charge

of Major Work For the

Graduate

College

Iowa

State University

Ames, Iowa

1973 Signature was redacted for privacy.

Signature was redacted for privacy.

Signature was redacted for privacy.

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 LISTquotesdbs_dbs14.pdfusesText_20