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Uni International 300 N INFORMATION TO USERS This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1.The sign or “target” for pages apparently lacking from the document photographed is “Missing Page(s)”. If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity. 2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image of the page can be found in the adjacent frame. If copyrighted materials were deleted, a target note will appear listing the pages in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of “sectioning” the material has been followed. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete. 4. For illustrations that cannot be satisfactorily reproduced by xerographic means, photographic prints can be purchased at additional cost and inserted into your xerographic copy. These prints are available upon request from the Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases the best available copy has been filmed. Uni International 300 N. Zeeb Road Ann Arbor, Ml 48106 8503988 Bowers, Francis Andrew Imaikalani, Jr. DISCRIMINANT ANALYSIS APPLIED TO PREDICT SUCCESS IN ADVANCED PLACEMENT MATHEMATICS: CALCULUS AB OR CALCULUS BC The Ohio State University Ph.D. 1984 University Microfilms International300 N. Zeeb Road, Ann Arbor, Ml 48106 Copyright 1984 by Bowers, Francis Andrew Imaikalani, Jr. All Rights Reserved PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V . 1. Glossy photographs or pages______ 2. Colored illustrations, paper or print ______ 3. Photographs with dark background ______ 4. Illustrations are poor copy ______ 5. Pages with black marks, not original copy____ 6. Print shows through as there is text on both sides of page ______ 7. Indistinct, broken or small print on several pages S 8. Print exceeds margin requirements ______ 9. Tightly bound copy with print lost in spine ______ 10. Computer printout pages with indistinct print ______ 11. Page(s)____________ lacking when material received, and not available from school or author. 12. Page(s)____________ seem to be missing in numbering only as text follows. 13. Two pages numbered ____________ . Text follows. 14. Curling and wrinkled pages ______ 15. Other_____________________________________________________ __________________ University Microfilms International DISCRIMINANT ANALYSIS APPLIED TO PREDICT SUCCESS IN ADVANCED PLACEMENT MATHEMATICS: CALCULUS AB OR CALCULUS BC DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Francis Andrew Imaikalani Bowers, Jr., B.A., M.A. it it it it it The Ohio State University 1984 Reading Committee: Approved By Professor F. Joe Crosswhite Professor Jon L. Higgins Professor Arthur L. White Department of Science and Mathematics Education © Copyright by Francis Andrew Imaikalani Bowers, 1984 All Rights Reserved DEDICATION: To the grandparents and mother of our six children, and to the indomitable six "We have met the enemy and he is us." Pogo "To be what we are, and to become what we are capable of becoming, is the only end in life." Robert Louis Stevenson "What is honored in a country will be cultivated there." Plato ACKNOWLEDGMENTS To the many individuals whose counsel, cooperation, and support made this study possible, I express my sincere thanks: mahalo nui loa. Specifically, recognition is due the following: The late Professor John W. Riner, Jr., Vice-Chairman of the Department of Mathematics, and the other dedicated members of my Dissertation Committee, Professors F. Joe Crosswhite, Jon L. Higgins, Harold C. Trimble, and Arthur L. White, have my appreciation for their guidance and professional counsel. Dr. Harlan P. Hanson, Director of the Advanced Placement Program, The College Board, for his prompt responses to my many queries; and to Dr. Carl H. Haag and Mariette Reed at Educational Testing Service for their five-year effort to keep me supplied with national data. Dr. Roderick F. McPhee, President of Punahou School, for my sab­ batical and years leave-of-absence to pursue my studies; and to Professor J. Philip Huneke, Vice-Chairman of the Department of Mathe­ matics, for the repeated offers of encouragement and employment in what I most enjoy— teaching mathematics. Robert L. Steele, Alan H. Price, and Beverly Bell O'Sullivan at Punahou and Lawrence S . Braden at Iolani for their long distance support in data collection; and to Dr. Winston Healy, Jr., Punahou Academy Principal, and Charles G. Proctor, Acting Headmaster at Iolani School for permission to use the data. Particularly, I owe more than can be expressed to my mentor and major advisor, Professor F. Joe Crosswhite, whose thoughtful profession­ alism and personal interest made the return to studies enjoyable and the absence of family at least bearable. And finally, to my wife and children, whose encouragement and support over five thousand miles never waivered, my love and gratitude; and to Mom and Dad, whose weekly letters over the past five years were an inspiration, what can I add but me ke aloha pumehana. iv VITA 20 October 1927 ........ Born - Honolulu, Territory of Hawaii 1950.....................B.A. in Economics, University of Hawaii, Honolulu, Territory of Hawaii 1951-53 ................ Mathematics Teacher, Punahou School, Honolulu, Territory of Hawaii 1953-56 Teaching Associate, Department of Mathematics, University of Kansas, Lawrence, Kansas 1956.....................M.A. in Mathematics, University of Kansas, Lawrence, Kansas 1956-68 ................ Mathematics Teacher and Department Chairman, Punahou School, Honolulu, Hawaii 1960.....................National Science Foundation Summer Institute, Stanford University, Stanford, California 1968-70 U.S. Army, Hawaii and Republic of Vietnam 1970-79 ................ Mathematics Teacher, Punahou School, Honolulu, Hawaii 1971-72 ................ U.S. Army War College, Carlisle Barracks, Carlisle, Pennsylvania 1979-81, Summers 1982-84. Instructor, Department of Mathematics, The Ohio State university, Columbus, Ohio FIELDS OF STUDlf Major Field: Mathematics Education Studies in Mathematics Education. Professor F. Joe Crosswhite Studies in Educational Research. Professor Arthur L. White Studies in Mathematics. Professor John W. Riner, Jr. Studies in Statistics, professor Douglas A. Wolfe TABLE OF CONTENTS Page EE HE CA T I O N ...................................................... ii EPIGRAMS........................................................ iii ACKNOWLEDGMENTS.................................................. iv VITA ............................................................ V LIST OF T A B L E S ..................................... ix LIST OF.............FIGURES...................................... xiii CHAPTER I . INTRODUCTION TO THE S T U D Y ................................. 1 Background of the P r o b l e m ...... 1 Statement of the Problem............................. 10 Design and Procedures ............................... 12 Delimitations of the Study........................... 17 Chapter Outline ...... ................. .... 22 II . REVIEW OF RELATED RESEARCH AND LITERATURE................. 23 Introduction: Bounds on Review....................... 23 General and Differential Predictors of Academic Success ............................. 25 S u m m a r y .............................................. 94 III . THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS: ITS GROWTH NATIONALLY AND ATPUNAHOU SC H O O L .......... 96 Historical Perspective............................... 96 The National Growth of Advanced Placement Mathematics as a College Board Program........... 110 The Growth of Advanced Placement Mathematics at Punahou S c h o o l ............................... 155 IV. DATA PRESENTATION AND EE SIGN OF THE S T U D * .............. 173 Data Presentation................................... 173 Design of the S t u d y ................................. 188 vi TABLE OF CONTENTS— Continued CHAPTER Page V. DATA REDUCTION, PREDICTION, AND ANALYSIS.............. 195 Reducing the Number of Class Variables.............. 195 Deriving the Prediction Equations .... .......... 223 The Discriminant Analysis ......................... 227 Internal Validity Application ..................... 234 External Validity Application ..................... 235 VI . SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS............ 236 S u m m a r y ..........................................
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