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The Effect of a Modified Moore Method on Conceptualization of Proof Among College Students

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The Effect of a Modified Moore Method on Conceptualization of Proof Among College Students THE EFFECT OF A MODIFIED MOORE METHOD ON CONCEPTUALIZATION OF PROOF AMONG COLLEGE STUDENTS A dissertation submitted to the Kent State University College and Graduate School of Education, Health, and Human Services in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Yaser Y. Dhaher December 2007 © Copyright by Yaser Y. Dhaher 2007 All Right Reserved ii Dissertation written by Yaser Y. Dhaher B.S., Yarmouk University, 1985 M.S., Yarmouk University, 1989 M.Ed., Kent State University, 1996 Ph.D., Kent State University, 2007 Approved by __________________________________, Co-Director, Doctoral Dissertation Genevieve Davis Committee __________________________________, Co-Director, Doctoral Dissertation Michael Mikusa Committee __________________________________, Member, Doctoral Dissertation Ulrike Vorhauer Committee Accepted by __________________________________, Chairperson, Department of Teaching, J. David Keller Leadership and Curriculum Studies __________________________________, Dean, College and Graduate School of Donald L. Bubenzer Education, Health, and Human Services iii Dhaher, Yaser Y., Ph.D., December 2007 TEACHING, LEADERSHIP AND CURRICULUM STUDIES THE EFFECT OF A MODIFIED MOORE METHOD ON CONCEPTUALIZATION OF PROOF AMONG COLLEGE STUDENTS (701 pp.) Co-Directors of Dissertation: Genevieve Davis, Ph.D. Michael Mikusa, Ph.D. Research projects have long indicated incompetence in justification of mathematical arguments among students of high school as well as college level. This research sought to understand the mental proof schemes that students possess, and to determine if these schemes progress when the Moore method is used in teaching a mathematics course. This study is significant in two major ways: First, it confirmed the mental schemes of proofs proposed by Harel & Sowder. Second, the study examined the effect of the Moore method on students’ learning and appreciation of proofs. Using a qualitative analysis design the study showed that the Moore method has positive affects on students’ conceptualization of mathematical proof, their self-confidence in their abilities, their appreciation of the relevance of proofs, and their ability to think autonomously. The Moore method allowed students to experience mathematics first hand. They built a coherent body of knowledge in which they created their own proofs. In memory of my mother Aminah and my father Yousef ACKNOWLEDGMENTS This dissertation could not have been written without Drs. Genevieve Davis and Michael Mikusa who not only served as my advisers but also encouraged and challenged me throughout this research project. They and Dr. Ulrike Vorhauer patiently guided me through the process, never accepting less than my best efforts, and for that I thank them. I would like to acknowledge the Foundation for the Advancement of Education and the Moore’s Legacy Project for the great resources they provided about R. L. Moore and his teaching method. This project would not have been possible without the help of John Neuzil for allowing me to collect the data from the course he taught. I am also thankful to the participants in this study --- Shannon, Ryan, Zack, and Chris. Their willingness to participate and donate their time was invaluable. My much gratitude and appreciation goes to my wife, Iktimal Alamin, for her support and encouragement. I am thankful for the moral support and encouragement that my sister Khadijeh and my brothers Yacoub and Yasin have provided throughout my educational career. In addition, I am thankful for the support of my close friend Waleed Abukhaled and the support and encouragement of fellow educator Paul Baiotto, M.A. iv TABLE OF CONTENTS Page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF FIGURES ........................................................................................................... ix CHAPTER I. INTRODUCTION......................................................................................................... 1 Focus and Rationale for the Study ............................................................................ 1 Statement of the Problem .......................................................................................... 6 Research Questions ................................................................................................... 6 Major Goals of This Study ........................................................................................ 6 Significance of the Study .......................................................................................... 6 Definition of Terms................................................................................................... 7 Organization of the Study ....................................................................................... 13 II. LITERATURE REVIEW............................................................................................. 15 Jean Piaget and Genetic Epistemology ................................................................... 16 Constructivist Theory of Learning .......................................................................... 20 History of Proof....................................................................................................... 23 Meaning of Proof .................................................................................................... 25 Function of Mathematical Proof ............................................................................. 26 Moore Method......................................................................................................... 26 v Van Hiele and the Obstacles to Learning Proofs .................................................... 29 III. RESEARCH DESIGN AND DATA COLLECTION ................................................ 31 Selection of Research Design.................................................................................. 31 Rationale.................................................................................................................. 32 Description of Teaching Experiment Design .......................................................... 32 Methodological Considerations............................................................................... 35 Sample......................................................................................................... 35 Procedure..................................................................................................... 36 Preliminary Work........................................................................................ 37 Setting and Data Collection......................................................................... 37 Validity and Reliability ............................................................................... 38 IV. DATA AND RESULTS ............................................................................................ 41 September................................................................................................................ 44 Summary ................................................................................................................. 87 October.................................................................................................................... 89 Summary ............................................................................................................... 104 November .............................................................................................................. 104 Summary ............................................................................................................... 119 V. RESULTS ................................................................................................................ 122 Discussion ............................................................................................................. 122 Implications........................................................................................................... 130 Implications for Further Research............................................................. 135 vi Limitation of the Study ............................................................................. 136 APPENDICES ................................................................................................................ 138 APPENDIX A. RECRUITMENT......................................................................... 139 APPENDIX B. AUDIOTAPE CONSENT ........................................................... 141 APPENDIX C. NOTE TAKING PROTOCOL .................................................... 143 APPENDIX D. VIDEOTAPE CONSENT ........................................................... 145 APPENDIX E. PROJECT DESCRIPTION.......................................................... 147 APPENDIX F. RYAN AND ZACK, FIRST PRESENTATION ......................... 149 APPENDIX G. SHANNON, FIRST INTERVIES ............................................... 178 APPENDIX H. RYAN, FIRST INTERVIEW...................................................... 216 APPENDIX I. RYAN AND ZACK, SECOND PRESENTATION ..................... 229 APPENDIX J. SHANNON AND CHRIS, FIRST PRESENTATION................. 275 APPENDIX K. SHANNON, SECOND INTERVIEW ........................................ 327 APPENDIX L. RYAN, SECOND INTERVIEW ................................................. 358 APPENDIX M. RYAN AND ZACK, THIRD PRESENTATION......................
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