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

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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.