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

这个项目旨在了解学生如何通过与教师合作进行几何证明来建立数学推理技能。 虽然NCTM标准强调学生的这些技能的发展，教师往往不知道如何有效地使用证明，以帮助学生。 这个项目将侧重于了解与教师，学生和主题之间发生的证明工作的动态。 提议者将进行课堂观察，访谈，并与教师进行焦点小组讨论。 教师将在某些观察期间使用替代单位，这将允许描述性观察以及治疗条件的灵活性。 研究者将以几种方式在他的教学中使用这项研究。 职前教师将被邀请在观察班进行部分实习。 将开设几门课程，包括一门关于几何教学的硕士课程。 这项研究还将注入现有的数学概念化课程。

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.