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theses

In 1989, the National Research Council recommended “a shift from teaching routine procedures to developing mathematical reasoning”. Since that time, professional development programs (Santagata 2009; Jacobs, Lamb, & Phillip 2010, Bell, Wilson, Higgins & McCoach, 2010) have attempted to increase teachers’ knowledge for recognizing student reasoning and supporting students in their developing mathematical reasoning. As evidenced by international comparisons (PISA 2008) the shift to developing mathematical reasoning has yet to occur in the USA on a large scale. The purpose of this study is to trace teachers’ developing knowledge in a graduate mathematics-education course that has a goal that the participating teachers grow in their recognition of student reasoning. The research questions guiding the study are: 1. What forms of reasoning do middle-school mathematics teachers identify from the following: a. Their own solutions to a series of mathematical tasks during a PD intervention; b. Their students’ solutions to the same mathematical tasks implemented in their own classrooms; c. Students’ solutions working on the same or similar mathematical tasks from assigned VMC videos, and d. Teachers’ pre and post-test responses concerning the forms of reasoning used by fourth grade students to solve mathematical tasks in the Gang of Four VMC video? 2. What changes, if any, can be identified in teachers’ beliefs about learning or teaching mathematics? 3. What pedagogical moves or strategies are used by the instructor to facilitate the teachers’ construction of knowledge about mathematical reasoning as the teachers: a. Work on tasks in a combinatorics strand b. Study student reasoning from video, and c. Analyze samples of their own students’ written work the tasks? Data for the study include video data of teachers working on mathematics tasks and sharing samples of student work, text of teachers’ discussions in an online forum, and final projects consisting of samples of students’ collected written work, with teachers’ reflections about the student work, the tasks in general, and the teacher’s own assessment of their implementation of the tasks in each of three cycles. Video data of course meetings were transcribed and verified. All data were coded using Dedoose, and coded data were analyzed to identify patterns and trends relative to the research questions. Findings suggest that videos provided formative experiences for teachers. Solution arguments based on inductive reasoning and reasoning by cases were frequently referred to by teachers using the names of the students in videos who made the arguments. Findings also suggest that the course instructor effectively modeled the type of teacher interactions necessary to engage teachers in justifying solutions to mathematical tasks and developing convincing arguments. This study adds to a body of research involving professional development initiatives that attempt to help teachers attend to student reasoning. Its findings may be of value to designers of professional development initiatives, particularly those that seek to improve teachers’ recognition of the variety of forms of reasoning their students employ.

ETD_7162

Ed.D.

Includes bibliographical references

by William Gabriel McGowan

doi:10.7282/T3F47R99

ETD doctoral

The author owns the copyright to this work.