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Factors of mathematical aptitude PDF

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Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1973 Factors of mathematical aptitude Christine Leigh Taylor Iowa State University Follow this and additional works at:https://lib.dr.iastate.edu/rtd Part of theEducational Psychology Commons Recommended Citation Taylor, Christine Leigh, "Factors of mathematical aptitude " (1973).Retrospective Theses and Dissertations. 5052. https://lib.dr.iastate.edu/rtd/5052 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please [email protected]. INFORMATION TO USERS This material was produced from a microfilm copy of the original document. 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Xerox University D/iicrofiims SCO 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: 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

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etry); differential abilities (verbal reasoning, numerical ability, abstract be alone, being a perfectionist); general aptitude test scores (verbal, mathematical) .. achievement frequently occurs in studies on aptitude. "There is a large.
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