University of New Hampshire University of New Hampshire Scholars' Repository Doctoral Dissertations Student Scholarship Winter 2000 Mathematics and socio -cultural behavior: A case study of the enculturation of a new mathematician Timothy Byron Gutmann University of New Hampshire, Durham Follow this and additional works at: https://scholars.unh.edu/dissertation Recommended Citation Gutmann, Timothy Byron, "Mathematics and socio -cultural behavior: A case study of the enculturation of a new mathematician" (2000). Doctoral Dissertations. 2146. https://scholars.unh.edu/dissertation/2146 This Dissertation is brought to you for free and open access by the Student Scholarship at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. 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MATHEMATICS AND SOCIO CULTURAL BEHAVIOR A CASE STUDY OF THE ENCULTURATION OF A NEW MATHEMATICIAN BY TIMOTHY BYRON GUTMANN BA, Bowdoin College, 1989 MA, The Pennsylvania State University, 1992 DISSERTATION Submitted to the University of New Hampshire in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics Education December, 2000 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number 9991557 UMI* UMI Microform9991557 Copyright 2001 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This dissertation has been examined and approved. (? 19 oJ acl-^ _______________________ Dissertation Director. Karen J. Graham. Professor of Mathematics Thomas H. Schram. Associate Professor of Education Lee L. Zia. Program Director. Division of Research. Evaluation, and Communication. National Science Foundation Gertrud L. Kraut. Facultv-in-Residence. Instructor in Mathematics vn/«~cc~u? Donovan H. Van Osdol. Professor of Mathematics - Iif I - c < '7 t C Date Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS This project has taken the better part of two years to complete and I must gratefully acknowledge the support, suggestions, encouragement, and patience of many. In particular, my advisor, Dr. Karen Graham has been vital. Her expertise in constructing and evaluating research initiated me into and guided me through the complex process of taking my ideas, data, and theories from outside mathematics education and making from them a credible study and research product. She made it possible to pursue the questions of interest to me, even when those questions seemed to take me beyond the established research domain, beyond sure contributions to the academy. I wish to thank the members of my committee: Dr. Thomas Schram who led me through not only the initial methodological training, but who also asked questions rather than answered them when I came to him with raw data needing a direction; Dr. Lee Zia who has been enthusiastic about my work and its value to mathematics departments in a measure I am sometimes unable to muster, Dr. Gertrud Kraut who brought her own experience as a newcomer in a department to the analysis of my work, pointing out several aspects of my work that might resonate differently in different departments; and Dr. Donovan Van Osdol who wrote scathing comments on my first draft, all valid and useful, and who was then still willing to adjust to a new style of research and support it. I am a proud recipient of a dissertation fellowship from the Graduate School at the University of New Hampshire. This fellowship allowed me to conduct iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. research for an extended period of time away from the campus in Durham and this study would not have been possible without that opportunity. There is a mathematics department faculty at a state university in the Appalachian Mountains to which I will always be indebted. The individuals there who opened their lives to me to make this possible are a truly remarkable bunch. The chair said more than once he did not believe there is a better group of friends and colleagues constituting a mathematics department anywhere. He has been there for over 20 years. He ought to know. Without hesitation these people answered my questions, responded to my ideas, and explained their world to me. They told me what they liked and what they disliked. Knowing I would be there for only a few short months, they made me feel a colleague. They offered me friendship. I must particularly thank Beth who gave me a temporary home in her guestroom. Having a quiet, clean, safe place to return to was a great aid. It made onsite work comfortable and productive. Rick Kaminski, my primary informant, took a great risk. Having never met me and on the basis of only a few brief telephone calls, Rick risked his first semester experience as a new faculty member, quite probably a time that would set the stage for the remainder of his career. He risked his personal reflections about his situation, speaking openly to me of his pleasurable and his not so pleasurable experiences. In doing so, Rick gave me a chance to pursue my own future. For research purposes, I hoped not to affect Rick’s enculturation process any more than absolutely necessary. Still, Rick has affected my path. He made it possible to progress. I am most deeply and permanently indebted to him. Thank you, Rick. iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Finally I thank my family. They have always quietly assumed I would finish some day and that assumption has made finishing a realistic goal, even when it became, for a time, a rather tedious one. Along the way they have believed. That was enough. v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS ACKNOWLEDGEMENTS...............................................................................................iii LIST OF FIGURES.............................................................................................................ix ABSTRACT..........................................................................................................................x CHAPTER PAGE CONFUSION........................................................................................................................ 1 I. INTRODUCTION............................................................................................................3 n. LITERATURE REVIEW AND THEORETICAL FRAMEWORK .........................10 Theoretical Framework—Background for the Research ................................................ 10 Additional Literature Supporting Analysis ......................................................................32 IB. METHODOLOGY.......................................................................................................39 Identifying the Informant .................................................................................................. 39 Data Collection .................................................................................................................. 41 Methods of Analysis ..........................................................................................................45 Agreement with Conclusions ............................................................................................49 Two Research Concerns ..................................................................................................