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: 1523494
• 负责人: Janet Barnett
• 金额: $ 9.84万
• 依托单位: Colorado State University-Pueblo
• 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=1523494&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学生学习支持的价值。该合作项目涉及七个不同的机构，将通过利用第一手资料-数学家关于数学主题的原始历史著作，帮助学生学习和培养对基本数学概念和思想的更深兴趣，欣赏和理解。面向学生的教育材料将在所有层次的本科数学课程中开发，其设计将捕捉发现的火花并激发后续的探究线。特别是，要开发的学生项目将围绕主要原始材料建立，以指导学生，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，从而确保在使用这些教材方面拥有专业知识的大型全国性教师网络。我们将从教学、学生学习、部门和机构变革等方面调查教材和实施方法的影响。wins项目将采用综合培训和开发流程来创建和测试大约五十（50）个学生项目，其中包括(1)二十（20）个主要来源项目（psp），旨在在大约相同的课程天数内涵盖其主题，以及(2)三十（30）个为期一天的迷你psp。除了充分研究让学生参与主动学习的好处外，这种历史方法的特殊优势还包括为主题提供背景和方向。“胜利”项目的重要目标是：(a)通过研究历史上一些最伟大的思想家的作品来磨练学生的语言和演绎技能；(b)通过发现已经被纳入标准课程主题的问题和开创性的解决方案来激发本科数学课程的活力。通过密集的、以研究为基础的专业发展讲习班，wins项目还将向大约70名教师和博士生提供关于制定和实施psp各方面的培训。通过合作开发psp，同时培训全国各地的教师使用psp，研究人员将确保这些教育材料具有强大的适应性，并积极地传播到各种各样的机构设置中，同时发展一个对初级资源教学感兴趣的数学教师的持续专业社区。一项结合研究的评估研究将提供对项目的形成性和总结性评估，并有助于(i)学生对数学本质的看法如何演变，（ii）学生撰写数学论证的能力如何随时间变化，以及（iii）如何支持教师开发和实施这种基于研究的主动学习方法的一般知识库。