Collaborative Research: Beyond Procedures: A Research-Based Approach to Teaching Mathematical Methods in Physics

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This interdisciplinary project brings together physics education research (PER) and research in undergraduate math education (RUME). It combines efforts at identifying and addressing student conceptual difficulties in physics with efforts toward understanding the ways students use and reason about mathematics in physics contexts. The work targets the mathematical methods course, a key course for physics majors as it begins the transition to using advanced calculus, linear algebra, etc. in physics problems and serves as a gateway to the upper-division in physics. The project will strengthen the research base in a portion of the curriculum that has, to this point, largely gone unexamined, and will touch upon, and build upon, work in related areas, such as research on other upper division physics courses, as well as the extensive research base in undergraduate mathematics education. Prior mathematical success is a strong indicator of success in physics, and the gap of knowledge available between what is taught in mathematics courses and physics course may be a significant source of attrition for physics majors that can be addressed through this work. The project will investigate the development of students' mathematical understanding in the context of learning and understanding middle- and upper-division physics. The team will conduct an integrated program of research, curriculum development, and assessment of topics found in middle- and upper-division physics courses, with particular focus on the sophomore- or junior-level mathematical methods course. The primary objectives of the project are: (a) to conduct research on student understanding of mathematics in upper-division physics contexts, with an emphasis on the core mathematical methods and reasoning covered in an intermediate-level mathematical methods course; and (b) to develop a library of modular curricular materials (such as, student-centered tutorials and Peer Instruction tasks) emphasizing mathematical methods and reasoning suitable for use in a wide variety of upper-division physics courses.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.