"Advancing Students' Proof Practices in Mathematics through Inquiry, Reinvention, and Engagement"

“通过探究、重塑和参与推进学生的数学证明实践”

• 批准号: 1916490
• 负责人: Sean Larsen
• 金额: $ 111.6万
• 依托单位: Portland State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-10-01 至 2023-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1916490&HistoricalAwards=false
• 关键词: Advancing; Students; Proof; Practices; Mathematics

With support from the NSF Improving Undergraduate STEM Education Program: Education and Human Resources (IUSE: EHR), this project aims to serve the national interest by improving undergraduate mathematics education. It will do so by creating curriculum modules for a transition-to-proof course for both two-year and four-year institutions. The modules, grounded in inquiry-based instruction, will be developed through a collaboration between California State University Chico, Clackamas Community College, Michigan State University, Butte College, and Mount Hood Community College. The Teachers Development Group will provide expertise in developing pedagogical strategies for implementing the modules. The project will use established methods to create knowledge, as well as innovative tools that have potential to improve the quality of education experienced by mathematics students. Actively engaging students in learning through inquiry-based instruction may enhance the student learning experience in the transition to proofs. This improvement may increase student entry into and persistence in proof-based mathematics courses, thus contributing to a mathematically sophisticated STEM workforce. The products created by the project will be freely available as web-based resources, such as an online Wiki-style textbook and web-based multimedia instructor supports.The project seeks to draw on established design research methodology to develop inquiry-based curricular materials and a suite of resources designed to support instructors in taking on the challenges associated with ambitious student-centered pedagogy. Project deliverables will include a modular curriculum (for use in courses designed to help students transition to advanced proof-based mathematics), web-based instructor support materials, a Wiki-textbook template, and a professional development workshop. The project will be designed to create an ideal starting point for mathematics faculty to begin teaching with student-centered inquiry methods that are known to be more supportive of student success. The project will investigate how students can be supported in reinventing foundational topics in real analysis as well as how inquiry-based instruction can provide equitable outcomes. The project will also investigate the supports instructors need in implementing inquiry-based instruction. The project outcomes will be disseminated through a professional development workshop, an open-access repository, conference presentations, and publications. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.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.

在NSF改善本科STEM教育计划：教育和人力资源(IUSE：EHR)的支持下，该项目旨在通过改善本科数学教育来服务于国家利益。它将通过为两年制和四年制院校创建过渡到证明课程的课程模块来做到这一点。这些模块以探究式教学为基础，将由加州州立大学奇科、克拉卡马斯社区学院、密歇根州立大学、巴特学院和芒特胡德社区学院合作开发。教师发展小组将提供专门知识，制定实施这些单元的教学战略。该项目将使用现有的方法来创造知识，以及有可能改善数学学生所经历的教育质量的创新工具。通过探究式教学让学生积极参与学习，可以提高学生在向校对过渡的过程中的学习体验。这一改进可能会增加学生进入以证明为基础的数学课程并坚持下去，从而有助于培养一支数学熟练的STEM劳动力队伍。该项目创建的产品将以网络资源的形式免费提供，例如在线维基风格的教科书和基于网络的多媒体教师支持。该项目寻求利用既定的设计研究方法来开发基于探究的课程材料和一套资源，旨在支持教师应对与雄心勃勃的以学生为中心的教学法相关的挑战。项目成果将包括模块课程(用于帮助学生过渡到基于高级证明的数学的课程)、基于网络的教师支持材料、Wiki教科书模板和专业发展研讨会。该项目旨在为数学教师创造一个理想的起点，以学生为中心的探究方法开始教学，这种方法被认为更有助于学生的成功。该项目将调查如何支持学生在实际分析中重新创造基础主题，以及以探究为基础的教学如何提供公平的结果。该项目还将调查教师在实施探究式教学时所需的支持。项目成果将通过专业发展讲习班、开放式资料库、会议报告和出版物进行传播。NSF IUSE：EHR计划支持研究和开发项目，以提高所有学生的STEM教育的有效性。通过参与的学生学习路径，该计划支持有前景的实践和工具的创建、探索和实施。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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

A functional perspective on student thinking about the grammar of multiply quantified statements

学生思考多重量化陈述语法的功能视角

• DOI: 10.1016/j.jmathb.2022.100992
• 发表时间: 2022
• 期刊: The Journal of Mathematical Behavior
• 作者: Vroom, Kristen

Students’ Thinking about the Structure of Constructive Existence Proofs

学生 — 思考构造性存在证明的结构

• DOI: 10.1007/s40753-022-00170-3
• 发表时间: 2022
• 期刊: International Journal of Research in Undergraduate Mathematics Education
• 影响因子: 1.5
• 作者: Vroom, Kristen;Alzaga Elizondo, Tenchita
• 通讯作者: Alzaga Elizondo, Tenchita