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UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48I06-I346 USA 313/761-4700 800/521-0600 MATHEMATICS PEDAGOGY IN THE POSTSTRUCTURAL MOMENT: A RHIZOMATIC ANALYSIS OF THE ETHOS OF SECONDARY MATHEMATICS TEACHING IN AN URBAN SETTING DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ferdinand Dychitan Rivera, B.S., M.A., M.A. ***** The Ohio State University 1998 Dissertation Committee Approved By Professor Suzanne Damarin, Adviser Professor Patricia Brosnan Professor Douglas Owens Adviser Educational Policy and Leadership College of Education DMI Number: 9900900 Copyright 1998 by Rivera, Ferdinand Dychitan All rights reserved. UMI Microform 9900900 Copyright 1998, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Copyright by Ferdinand Dychitan Rivera 1998 ABSTRACT This ten-week ethnographic research deals with the structure of complexity of four secondary mathematics teachers’ work and lives in an urban setting. It is argued that a mathematics teacher’s work and culture, in general and in its multiplexity, is wed to a plurality of competing factors and changing contexts that redound from the various contradictions, conflicts, assimilated contraries, and double binds that a teacher negotiates daily. Provisional findings and interpretive analyses were obtained through interviews, document analysis, survey and grounded questionnaires, persistent observations, and the rhizomatic attitude of working not for or with the teachers but “between” them. Two research questions were investigated: 1. What does it mean to teach high school mathematics in an urban setting at the present time? 2. To what extent do pedagogical practices subjectify students into a way of thinking about/acting/doing mathematics in the classrooms? The methodological framework employed is poststructural ethnography in that it seeks a critical ontology of “how things are,” problematizing the acritical status quo of everyday ideas in the current regime of mathematics pedagogy. The innocence of mathematics teaching is problematized. Recent reform rhetorics including the rhetoric of the Curriculum and Evaluation Standards with its promise of utopia and i i the rhetoric of meaningful (and authentic) learning of mathematics in the constructivist movement are (re)assessed vis-a-vis the constraints of urban mathematics teaching. Underlying the theoretical position that is pursued in this work is Deleuze and Guattari’s rhizome. The rhizomatic framework has a teacher’s regime of tmth disjunctively synthesized with many factors such as the social context of teaching, her/his personal epistemologies, beliefs and practices, the (implicit) meta­ revolutionary changes in school mathematics, and poststructural readings of the discourse of mathematics teaching. Findings of this study include: (1) the social context serves as a mediating difference between a mathematics teacher’s espoused and enacted theories and beliefs; (2) there exists a “gendered” deployment of school mathematics teaching based on relational and impersonal modes of epistemology; (3) teachers with few or narrow meaningful mathematical experiences tend to constrain the meaningfulness of learning and teaching; (4) teachers’ low clientele perception leads to the underestimation of their students’ mathematical power and needs; (5) a conflict seems to exist between the ethos of mathematics teaching and the “new” ethos of schooling; (6) patterns of absenteeism make it extremely difficult for teachers to implement curriculum innovation, and; (7) teachers tend to develop a sense of isolation. The study also includes ways in which a student’s math subjectivity is constructed through a Foucauldian genealogy of the deployment of mathematics teaching. ill dedicated to mr. jack, ms. lynch, ms. prahst, and mr. taft and especially to mom and dad for wonderful moments of life iv ACKNOWLEDGMENTS Douglas Owens has supported me all the way and has provided enough space for my self-transformation. Patti Brosnan saved me from too many difficult moments of indecision about my own work and just about anj^hing that had to deal with life. I have drawn much inspiration from cultural feminist Suzanne Damarin, a truly, terrific adviser par excellence. This work is as much hers as it is mine. Dr. Damarin painstakingly read through and critiqued each page and saved me from “being buried beneath my own prose,” her words. Beyond the technical aid and especially in moments of struggle (there were many), I learned from Dr. Damarin what it meant to be a true scholar in the field. I learned much from the conversations I have had with Betsy McNeal, who was never afraid to say whether or not I made sense. Truly a (wo)man for others, Fr. Ben Nebres, S.J., has been very supportive of my work. The last person on my list knew just what it meant to be the best, whose absent presence made this work “absolutely” meaningful. This work is a result of the generosity of these people. I know words fail... Amor fati. V VITA September 26, 1968 ................................................ Bom - Manila, Philippines 1989 .......................................................................... B.S., University of Santo Tomas 1995 ........................................................................ M.A. (Mathematics), University of the Philippines 1995 - 1998 ............................................................... Graduate Research Associate, Department of Educational Theory and Practice, The Ohio State University Graduate Teaching Associate, Department of Mathematics, The Ohio State University 1998 .......................................................................... M.A. (Mathematics Education), The Ohio State University FIELDS OF STUDY Major Field: Education (with Douglas Owens, Sigrid Wagner, and Patti Brosnan) Cultural Studies of Education (with Suzanne Damarin, Beverly Gordon, and William Pinar) Postpositivist Research: Theory and Method (with Patti Lather and Laurel Richardson) VI TABLE OF CONTENTS ACKNOWLEDGMENT ......................................................................................... v VITA ....................................................................................................................... W LIST OF TABLES ................................................................................................ xii LIST OF FIGURES .............................................................................................. xiii CHAPTER PAGE 1 WITHIN THE POST(sTRUCTURAL): THEORIZING THE ETHNOGRAPHY OF MATHEMATICS CLASSROOMS ......................................................................................... 1 1.0 Introduction ...................................................................................... 1 1.1 What is School Mathematics About? Some Preliminary (Foucauldian) M usings ................................................................... 4 1.2 "Mathematics Classrooms:" Bodies Without Organs ................... 9 1.2.1 Research Question 1 : Specificity of Urban Mathematics Teachers' W ork ................................................................... 12 1.2.2 Research Question 2: Mathematics Pedagogy as a Discursive Practice ........................................................... 14 1.3 Summary............................................................................. 16 2 URBAN MATH TEACHERS' WORK, CULTURE, AND PEDAGOGICAL PRACTICES AS LINES AND FOLDS; A RHIZOMATIC (CONCEPTUAL) FRAMEWORK................................ 21 2.0 Introduction ...................................................................................... 21 2.1 Framing a Discourse on Pedagogy: Immolating Ideology and Problematizing Truth ........................................ 24 2.2 Foucauldian Genealogy .................................................................. 28 2.3 Techniques of Subject(ificat)ion: Gore's Model of Power Relations ......................................................................................