CAREER:Reasoning in High School Geometry Classrooms: Understanding the Practical Logic Underlying the Teacher's Work

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This project seeks to understand how students build mathematical reasoning skills through working with teachers on geometric proofs. Although the NCTM Standards put an emphasis on students' development of these skills, teachers often do not know how to effectively use proofs to assist students. This project will focus on understanding the dynamics of working with proofs that occur between teachers, students, and the subject matter. The proposer will conduct classroom observations, interviews, and focus groups with teachers. Replacement units will be used by the teachers during some observations that will allow for both descriptive observation as well as flexibility in the treatment conditions. The researcher will use this research in his teaching in several ways. Preservice teachers will be invited to spend part of their practicum in the observation classes. Several courses will be created including a master's-level course on teaching and learning of geometry. The research will also infuse an existing course on conceptualization in mathematics.