On becoming a geometry teacher: a longitudinal case study of one teacher learning to teach proof

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Cirillo, Michelle
Major Professor
Beth Herbel-Eisenmann
Corey Drake
Heather Thompson
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Curriculum and Instruction

My experiences as a teacher and as a researcher led me to pursue the topic of this dissertation - how a new teacher learns to teach proof to high school geometry students. Through my work on a research project, I became interested in this 10th grade teacher after watching him teach proof for the first time. I anticipated that, not unlike my own experience as a teacher of geometry, this teacher's proof-related teaching and discourse practices would look different in subsequent years. This classroom provided a context for me to study how a beginning teacher, using a conventional textbook, develops his practice related to teaching proof.;In order to pursue this dissertation topic, I designed a longitudinal case study in which I collected data across three years, including classroom observation data, interviews, reflective writings on the daily lessons, and instructional materials that were used in the classroom (e.g., the textbook). In addition, interviews conducted for a larger research project provided background information that was relevant to this study.;Drawing from the literatures on new teacher induction, curriculum enactment, proof in school mathematics, and classroom discourse, I discuss how and why this beginning teacher's practice changed across time. More specifically, in this dissertation, I describe how and why the teacher: supplemented the written curriculum with additional proofs and tasks; explicitly increased his focus on the process of proving; and created more space for student participation. I argue that the teacher purposefully made these changes in order to enact a practice that was more like what he called "real math" than like school mathematics.;Three significant findings of this study are related to issues of curriculum use, authentic mathematical practices, and professional development in the area of classroom discourse. For example, the teacher explored the use various proof forms, and his participation in a professional development experience motivated him to experiment with various discourse moves. This study has implications for teacher educators, curriculum developers, mathematics supervisors, and researchers interested in understanding issues related to the teaching and learning of proof in school mathematics.

Tue Jan 01 00:00:00 UTC 2008