Orchestrating Discussions Around Proof

数学课堂上，结合学生的讨论已被证明是从事学生在真实的数学活动，并支持学生的概念理解的发展。虽然主要组织（例如，美国数学协会）已经呼吁在所有数学课程中从纯粹的讲课转变，大学数学教师几乎没有什么支持来帮助他们在课堂上包括学生讨论。该项目旨在解决这一需求，帮助教师建立讨论到他们的抽象代数课程，并研究这些讨论。摘要代数是美国许多数学专业和中学数学教师都开设的一门基于证明的课程。项目团队将设计可用于促进富有成效的讨论的讲师支持（任务、工具和协议）。 我们的目标是帮助教师指导课堂讨论，推进一堂课的数学议程，同时真正融入学生的想法和声音。通过设计过程，本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。该项目的国家影响在于教师支持纳入讨论和直接研究的本科生参与讨论在高等数学course.This项目包括一个两阶段的设计为基础的研究研究，重点是适应研究为基础的K-12的做法，编排讨论的背景下，本科证明为基础的数学课程。项目团队将通过一系列基于任务的访谈（第一阶段）和课堂实施（第二阶段），假设、试点和完善一个促进生产性讨论的模型。分析将集中在教学动作和任务组件，促进学生参与三个关键活动连接到证明：理解，验证和构建。这些研究的结果有可能通过测试K-12支持本科证明为基础的设置的可转移性，为该领域做出贡献。项目成果可以扩大有关支持富有成效的讨论的知识，并有助于改进和具体的本科证明为基础的设置原则。该项目还将提供一个真实的证明为基础的课程设置的学生与教师的互动分析，补充目前的文献基础，主要使用临床设置。 该项目旨在通过以下方式影响研究界、教师和基于证明的课程的学生：（1）满足对资源的真正需求，以支持数学教师摆脱仅讲授的教学法;（2）为学生提供参与重要数学活动的机会，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）为数学本科生提供参与学生话语驱动的数学课堂的机会;和（4）通过扩展和测试结果，为使用基于证据的K-12教学策略在本科证明设置，以促进富有成效的讨论。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估支持使用基金会的知识价值和更广泛的影响审查标准。

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.