CAREER: Investigation of Beginning Teachers' Expertise to Teach Mathematics via Reasoning and Proof

支持教师将推理和证明作为一种数学实践融入中学数学课是一项持久的挑战。这些学科实践对学习和教学都具有挑战性，并且经常以一种仅限于高中几何课程背景下的程序性方式教授。虽然人们对数学推理和证明的强大本质以及教授数学所需的内容知识了解很多，但对初级教师如何发展这些知识以及如何将这些知识转化为课堂实践知之甚少。该项目旨在培养中学教师候选人教授推理和证明的知识，并跟随他们进入第一年的独立实践，以更好地了解他们如何使用这些知识。该项目的目标是更好地了解初任教师的知识、性格和与证明相关的实践如何随着时间的推移而演变，以及学校教师的社会文化背景和支持结构如何影响他们的推理和证明教学。本项目分为职前教师准备、教学实习、新手教学（前两年独立实习）三个阶段。在教师准备阶段，职前教师将参加以推理和证明为重点的顶点课程，包括在当地中学开设与推理和证明相关的课程。使用数学知识教学证明框架，教师的知识和倾向推理和证明将通过课前和课后的评估和调查进行评估。他们的范例课程将被录像，并根据证明内容进行分析，他们将参加课后访谈。在下一阶段，在为期一年的学生教学实习期间，他们将被要求将推理和证明整合到课堂实践中。将记录和分析一组目标课程，收集和分析完整的单元文物，并对教师进行课前和课后访谈。第三阶段跟随教师进入他们头两年的教学实践，并要求他们确定与推理和证明相关的两个单元作为数据源。研究小组将与教师进行年初和年底的访谈，收集单元和相关文物的录像，管理对证据调查的安排，并进行单元前后的访谈。教师还将参加一个专业的学习社区，旨在支持他们的教学与推理和证明。数据将跨三个阶段进行分析，使用案例研究方法来描述与推理和证明相关的知识、性格和实践模式。该项目还将提供与顶点课程和专业学习社区相关的教育材料，这将进一步支持教师的知识和推理和证明教学能力的发展。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Supporting teachers in integrating reasoning and proving as a mathematical practice into secondary math classes is a persistent challenge. These disciplinary practices are challenging to learn and to teach, and are frequently taught in a procedural way that is limited to the context of high school geometry courses. While much is known about the robust nature of reasoning and proving in mathematics and the content knowledge needed to teach it, less is known about how beginning teachers develop that knowledge and how that knowledge is translated into classroom practice. This project aims to develop the knowledge to teach reasoning and proving with secondary teacher candidates, and to follow them into they first years of independent practice to better understand how they are using that knowledge. The goals of the project are to better understand how beginning teachers' knowledge, dispositions, and proof-related practices evolve over time, and how the sociocultural context and support structures of the schools teachers are in influences their teaching of reasoning and proving.This project consists of three stages: preservice teacher preparation, the teaching internship, and novice teaching (the first two years of independent practice). During the teacher preparation phase, preservice teachers will take part in a capstone course focused on reasoning and proving, including enacting lessons in related to reasoning and proving in local middle schools. Using the Mathematical Knowledge for Teaching Proof framework, teachers' knowledge and dispositions towards reasoning and proving will be assessed through pre- and post-course assessment and surveys. Their example lessons will be video recorded and analyzed with respect to proof content, and they will engage in post-course interviews. In the next phase, during year-long student teaching internships, they will be asked to integrate reasoning and proving into their classroom practice. A set of target lessons will be recorded and analyzed, with full unit artifacts being collected and analyzed and pre- and post-unit interviews with the teacher conducted. The third phase follows teachers into their first two years of teaching practice and asks them to identify two units related to reasoning and proving to serve as data sources. The research team will conduct start and end of year interviews with the teachers, collect video recordings of the units and associated artifacts, administer a dispositions towards proof survey, and conduct pre- and post-unit interviews. Teachers will also participate in a professional learning community designed to support their teaching related to reasoning and proving. Data will be analyzed across the three phases using case study methodology to characterize patterns of knowledge, dispositions, and practice related o reasoning and proving. The project will also make available educational materials related to the capstone course and the professional learning community that will further support the development of teachers' knowledge and capacity for teaching reasoning and proving.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.