Orchestrating Discussions Around Proof

围绕证明组织讨论

• 批准号: 1836559
• 负责人: Kathleen Melhuish
• 金额: $ 29.96万
• 依托单位: Texas State University - San Marcos
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-11-01 至 2022-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1836559&HistoricalAwards=false
• 关键词: Orchestrating; Discussions; Around; Proof

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.

结合学生讨论的数学课已被证明能让学生参与真正的数学活动，并支持学生发展概念理解。尽管主要组织（例如，美国数学协会）已经呼吁在所有数学课程中放弃纯粹的讲座，但大学数学教师几乎没有可用的支持来帮助他们在课堂上加入学生讨论。本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《抽象代数》是美国许多数学专业学生和职前中学数学教师都选修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指导者支持（任务、工具和协议）。目标是帮助教师引导课堂讨论，推进课程的数学议程，同时真正融入学生的想法和声音。通过设计过程，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一活动。该项目的全国影响在于，在高等数学课程中，教师对讨论的支持和对本科生参与讨论的直接研究的发展。该项目包括两个阶段的基于设计的研究，重点是将基于研究的K-12实践用于协调讨论，以适应本科基于证明的数学课程的背景。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、试验和完善一个模型，以促进在这种背景下的富有成效的讨论。分析将集中在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支持到本科证明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，并为本科校样环境提供具体的改进和原则。该项目还将在真实的基于证据的课程设置中提供学生与教师互动的分析，以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研究界、教师和基于证据的课程的学生：(1)满足对资源的真正需求，以支持数学教师从讲座式教学法的转变；(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)为数学本科学生提供参与学生话语驱动的数学课堂的机会；(4)通过扩展和测试在本科背景下使用基于证据的K-12教学策略的结果，促进富有成效的讨论，为该领域的知识做出贡献。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。

项目成果

Comparing Authenticity in Proof Activity in an In-Person and Online Setting

比较现场和在线环境中证明活动的真实性

• 发表时间: 2022
• 期刊: Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education
• 作者: Tucci, A.;Melhuish, K.
• 通讯作者: Melhuish, K.

Lessons Learned About Incorporating High-Leverage Teaching Practices in the Undergraduate Proof Classroom to Promote Authentic and Equitable Participation

将高杠杆教学实践纳入本科证明课堂以促进真实和公平参与的经验教训

• DOI: 10.1007/s40753-022-00200-0
• 发表时间: 2022
• 期刊: International Journal of Research in Undergraduate Mathematics Education
• 影响因子: 1.5
• 作者: Melhuish, Kathleen;Dawkins, Paul C.;Lew, Kristen;Strickland, Sharon K.
• 通讯作者: Strickland, Sharon K.

Comparing Student Proofs to Explore a Structural Property in Abstract Algebra

比较学生证明以探索抽象代数中的结构性质

• DOI: 10.1080/10511970.2020.1827325
• 发表时间: 2020
• 期刊: PRIMUS
• 作者: Melhuish, K.;Lew, K.;Hicks, M.
• 通讯作者: Hicks, M.

Relationships Between Dimensions of Authenticity During an Inquiry- Oriented Abstract Algebra Activity

面向探究的抽象代数活动中真实性维度之间的关系

• 发表时间: 2022
• 期刊: Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
• 作者: Zolt, Z.;Tucci, A.;Melhuish, K
• 通讯作者: Melhuish, K

Semiotic Conflicts in Students' Collective Proof Comprehension Activity

学生集体证明理解活动中的符号冲突

• 发表时间: 2021
• 期刊: RUME 2021
• 作者: Guajardo, L.;Melhuish, K.;& Zolt, H.
• 通讯作者: & Zolt, H.