Orchestrating Discussions Around Proof

包含学生讨论的数学课程已被证明能让学生参与真实的数学活动，并支持学生概念理解的发展。尽管主要组织(如美国数学协会)呼吁在所有数学课程中不再单纯讲授，但大学数学教师几乎没有什么支持来帮助他们在课堂上进行学生讨论。这个项目旨在解决这一需求，帮助教师在他们的抽象代数课程中建立讨论，并研究这些讨论。摘要代数是美国许多数学专业学生和中学数学预科教师开设的一门以证明为基础的课程。项目团队将设计可用于促进富有成效的讨论的教师支持(任务、工具和协议)。其目标是帮助教师指导课堂讨论，推动一节课的数学议程，同时真正纳入学生的想法和声音。通过设计过程，这项研究还将记录学生的讨论，以帮助教师和未来的研究人员更深入地了解这项活动。该项目在全国范围内的影响在于开发教师支持以纳入讨论，以及在高等数学课程中为参与讨论的本科生提供直接学习。该项目包括两个阶段的基于设计的研究性研究，重点是将基于研究的K-12实践用于编排讨论，以适应基于本科生验证的数学课程的背景。项目团队将通过一系列基于任务的访谈(阶段1)和课堂实施(阶段2)来假设、试验和改进在此背景下促进富有成效的讨论的模式。分析将集中于促进学生参与与证明相关的三个关键活动的教学动作和任务组成部分：理解、验证和构建。这些研究的结果有可能通过测试K-12支持到基于本科生验证的设置的可转移性来为该领域做出贡献。项目成果可以扩展关于支持富有成效的讨论的知识，并有助于针对本科生以证据为基础的环境的改进和原则。该项目还将在真实的以证据为基础的课程设置中提供对学生和教师互动的分析，补充目前主要使用临床设置的文献基础。该项目旨在通过以下方式影响以证据为基础的课程的研究社区、教师和学生：(1)满足对资源的真正需求，以支持数学教师从单纯讲授的教学转变；(2)为学生提供参与重要的数学活动的机会，这些活动有可能支持更深入的数学理解和更公平的课堂；(3)为本科生提供参与学生话语驱动的数学课堂的机会；以及(4)通过在本科生证明环境中使用基于证据的K-12教学策略来促进富有成效的讨论的扩展和测试结果，为该领域的知识做出贡献。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Mathematics classes that incorporate student discussion have been shown to engage students in authentic mathematical activity and support students' development of conceptual understanding. Although major organizations (e.g., the Mathematical Association of America) have called for a shift away from pure lecture in all mathematics courses, college mathematics instructors have few supports available to help them include student discussion in their classes. This project aims to address this need helping faculty build discussion into their Abstract Algebra courses, and to study those discussions. Abstract Algebra is a proof-based course taken by many mathematics majors and preservice secondary mathematics teachers in the United States. The project team will design instructor supports (tasks, tools, and protocols) that can be used to promote productive discussion. The goal is to help faculty guide classroom discussion that advances a lesson's mathematical agenda, while genuinely incorporating student ideas and voices. Through the design process, the study will also document student discussion to aid in deeper knowledge of this activity for both instructors and future researchers. The national impact of the project lies in both the development of instructor supports for incorporating discussion and the direct study of undergraduate students engaged in discussions in an advanced mathematics course.This project consists of a two-phase design-based research study focused on adapting research-based K-12 practices for orchestrating discussion to the context of an undergraduate proof-based mathematics course. The project team will hypothesize, pilot, and refine a model for promoting productive discussion in this context through a series of task-based interviews (Phase 1) and classroom implementations (Phase 2). The analysis will focus on the teaching moves and task components that promote students' engagement in three key activities connected to proof: comprehending, validating, and constructing. Results of these studies have the potential to contribute to the field by testing the transferability of K-12 supports to the undergraduate proof-based setting. Project outcomes could expand knowledge about supporting productive discussions, and contribute refinements and principles specific to the undergraduate proof-based setting. The project will also offer analyses of student-instructor interactions in an authentic proof-based course setting, complementing the current literature base that primarily uses clinical settings. The project aims to affect the research community, instructors, and students of proof-based courses by: (1) meeting the genuine need for resources to support mathematics instructors' shift away from lecture-only pedagogy; (2) providing opportunities for students to engage in important mathematical activities that have the potential to support deeper mathematical understanding and more equitable classrooms; (3) providing undergraduate mathematics students with an opportunity to participate in a student-discourse driven mathematics classroom; and (4) contributing to the field's knowledge via expanding and testing results for using evidence-based K-12 instructional strategies in undergraduate proof settings to promote productive discussion.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.