Collaborative Research: Scaffolding the Calculus in Calculus Based Physics

This project aims to serve the national interest by advancing the understanding of the mathematical ideas and practices that students encounter in introductory calculus-based physics, with a particular emphasis on concepts and procedures covered in introductory calculus. The project will investigate how students perceive and reason with the mathematics that they experience in introductory calculus-based physics. The results will be used to develop and assess research-based instructional exercises that can be incorporated into a standard physics course. This project focuses on the first semester introductory calculus-based physics course, which generally covers classical mechanics, and in which students begin to encounter calculus in physics, applied to both scalar and vector quantities. This project will generate valuable new knowledge on the role of calculus and the interplay between calculus and physics in a crucial introductory course for many science and engineering majors. The work will take place at three institutions with high percentages of first-generation college students, one that is a Hispanic-Serving Institution. This project will perform research on the mathematical ideas and practices that students encounter in introductory calculus-based physics, with three goals: (1) Conduct research on practices in introductory mathematics and physics courses relevant to physics instruction; (2) Study how students perceive and reason with the mathematics that they experience in introductory calculus-based physics; and (3) Develop and assess a series of research-based instructional exercises that can be incorporated into a standard calculus-based introductory course. Findings from research in undergraduate mathematics education and physics education will inform studies of disciplinary understanding and perception of calculus as well as the development of instructional strategies and materials. This will generate relevant and necessary pedagogical content knowledge for effective development of mathematical modeling, quantitative and covariational reasoning, and knowledge transfer between mathematics and physics among students in the introductory sequence, applied to both scalar and vector quantities. Research methods will be mixed, including qualitative studies of individual students and classroom observations as well as quantitative data collected on surveys of content understanding and disciplinary practices. The NSF IUSE: EDU 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.