Collaborative Research: Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS)

合作研究：通过主要历史资料转变本科数学教学（TRIUMPHS）

• 批准号: 1523747
• 负责人: Jerry Lodder
• 金额: $ 11.5万
• 依托单位: New Mexico State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2021-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1523747&HistoricalAwards=false
• 关键词: Collaborative; Research; Transforming; Instruction; Undergraduate

Mathematics faculty members and educational researchers are increasingly recognizing the value of the history of mathematics as a support to student learning. This collaborative project, involving seven diverse institutions, will help students learn and develop a deeper interest in, and appreciation and understanding of, fundamental mathematical concepts and ideas by utilizing primary sources - original historical writings by mathematicians on topics in mathematics. Educational materials for students will be developed at all levels of undergraduate mathematics courses, and will be designed to capture the spark of discovery and to motivate subsequent lines of inquiry. In particular, the student projects to be developed will be built around primary source material to guide students, including pre-service teachers, mathematics majors, and other STEM discipline majors, to explore the mathematics of the original discovery in order to develop their own understanding of that discovery. Mathematics faculty and graduate students from over forty (40) institutions will participate in the development and testing process, thereby ensuring a large national network of faculty with expertise on the use of these educational materials. The impacts of the materials and approaches to implementing them will be investigated in terms of teaching, student learning, and departmental and institutional change. The TRIUMPHS project will employ an integrated training and development process to create and test approximately fifty (50) student projects, which will include (1) twenty (20) primary source projects (PSPs) designed to cover its topic in about the same number of course days as classes would otherwise and (2) thirty (30) one-day mini-PSPs. In addition to the well-researched benefits of engaging students in active learning, particular advantages of this historical approach will involve providing context and direction for the subject matter. Important goals of the TRIUMPHS project are to (a) hone students' verbal and deductive skills through studying the work of some of the greatest minds in history and (b) invigorate undergraduate mathematics courses by identifying the problems and pioneering solutions that have since been subsumed into standard curricular topics. Through intensive, research-based professional development workshops, the TRIUMPHS project will also provide training in various aspects of developing and implementing PSPs to approximately seventy (70) faculty and doctoral students. By working collaboratively to develop PSPs while training faculty across the country in their use, the investigators will ensure that these educational materials are robustly adaptable and proactively disseminated to a wide variety of institutional settings, while simultaneously developing an ongoing professional community of mathematics faculty interested in teaching with primary sources. An evaluation-with-research study will provide formative and summative evaluation of the project, as well as contribute to the general knowledge base of (i) how student perceptions of the nature of mathematics evolve, (ii) how students' ability to write mathematical arguments changes over time, and (iii) how to support faculty in developing and implementing this research-based, active learning approach.

数学教师和教育研究人员越来越认识到数学史作为对学生学习的支持的价值。这个合作项目涉及七个不同的机构，将帮助学生通过利用原始资料--数学家关于数学主题的原始历史著作--来学习和培养对基本数学概念和思想的更深层次的兴趣，以及欣赏和理解。将为学生开发各级本科数学课程的教材，旨在捕捉发现的火花，并激发后续的探究路线。特别是，要开发的学生项目将围绕主要的原始材料来构建，以引导学生，包括职前教师、数学专业和其他STEM学科专业的学生，探索原始发现的数学，以便发展他们自己对该发现的理解。来自40多个机构的数学教师和研究生将参与开发和测试过程，从而确保拥有使用这些教育材料的专业知识的大型全国教师网络。这些材料和实施方法的影响将从教学、学生学习以及部门和机构变化的角度进行调查。Triumphs项目将采用综合培训和发展过程来创建和测试大约五十(50)个学生项目，其中将包括(1)二十(20)个主要来源项目(PSP)，旨在在与课程相同的课程天数内涵盖该主题，以及(2)三十(30)个一天的迷你PSP。除了让学生参与主动学习的经过充分研究的好处外，这种历史方法的特殊优势还包括为主题提供背景和方向。凯旋项目的重要目标是(A)通过学习历史上一些最伟大的思想家的工作来磨练学生的口头和演绎技能，以及(B)通过确定后来被纳入标准课程主题的问题和开创性的解决方案来振兴本科数学课程。通过密集的、以研究为基础的专业发展讲习班，Triumphs项目还将为大约70(70)名教职员工和博士生提供制定和实施PSP的各个方面的培训。通过合作开发PSP，同时培训全国各地的教师使用PSP，调查人员将确保这些教育材料具有很强的适应性，并主动传播到各种机构设置，同时发展一个持续的数学教师专业社区，他们对使用初级资源进行教学感兴趣。评价与研究相结合的研究将为项目提供形成性和终结性的评价，并有助于建立(I)学生对数学本质的认知如何演变，(Ii)学生撰写数学论点的能力如何随时间变化，以及(Iii)如何支持教师发展和实施这种基于研究的主动学习方法的一般知识基础。