Upper-division physics simulations with equation manipulation

Digital simulations are powerful instructional tools for physics education. They are often designed to visualize canonical physical phenomena, with adjustable parameters for influencing the system. While this is sufficient for developing conceptual and qualitative intuitions, it does little to help physics students build connections between physical systems and the mathematical models and equations that represent them. We present PhysMath, a suite of interactive physics simulations for use in upper-division courses. These simulations allow students to explore connections between mathematical equations and the phenomena they represent by inputting, modifying, and observing changes in system behavior. In this paper, we describe our first simulation—the Bead-On-Hoop for Classical Mechanics—and report findings from pilot interviews with intermediate physics students interacting with the simulation. Our findings validate the simulations’ design and highlight its potential for scaffolding students’ mathematical sensemaking.