Candidate: M. Lynn Breyfogle

Degree of: Doctor of Philosophy

Department: Mathematics

Title: Changing Mathematical Discourse: A Case of a Secondary School Mathematics Teacher

Committee:
Dr. Laura Van Zoest, Chair
Dr. Kate Kline
Dr. Christian Hirsch
Dr. Steven Ziebarth
Dr. Jianping Shen

Date: Monday, July 23, 2001, 4:00 p.m. - 6:00 p.m.
Alavai Commons, 6^th Floor, Everett Tower

Abstract:
Teachers often face challenges when establishing a classroom environment conductive to meaningful mathematical discussion. In this study, a teacher-researcher collaboration established with a secondary school mathematics teacher using an intervention based upon focused reflection on videotapes of his instruction. The purpose was to investigate the nature of change that occurred in both the teaching and reflection practices associated with the classroom mathematics as he used a reform curriculum

Data included audiotaped pre-, mid-, and post-interviews, and collaboration sessions that used a Discourse Reflection Tool (DRT) in conjunction with the viewing of videotaped episodes, and videotaped classroom observations.

Analysis of transcripts from interviews, collaboration sessions, and selected episodes from the videotaped observations led to a series of findings. In terms of the change in the teacher's reflection, the analysis gave rise to the observations. First, The teacher exhibited a shift from explaining away or defending his practices to openly reflecting and considering alternative ways of thinking. Second, the teacher shifted from using general terms while talking about the "natural" development of the discourse to more clearly identifying and articulating the role the teacher plays in developing meaningful mathematical discussions. Third, the teacher held as a consistent focus students' comfort as opposed to learning the mathematics.

In terms of the classroom mathematics discourse, three more observations resulted from the study. First, an analysis of the data showed a shift in talking from teacher to student. Second, there was a shift in the teacher's talk from eliciting merely answers to probing students' student thinking. Finally, a tendency not to talk about meaningful mathematical content persisted.

The implications of this study for professional development can be summarized as six necessary components for encouraging teachers' change: (a) an awareness of a series of affective phases related to teacher change; (b) an awareness of teachers' sense of efficacy; (c) a willingness to listen to teachers and to provide guidance without evaluation; (d) providing reflection on videotaped episodes of teachers' classrooms; (e) a focus on the importance of students' mathematical thinking; and (f) a focus identifying and reconciling inconsistencies in teachers' practice.

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