Examining student thinking about series approximations using potential energy in a series of charge configurations

Series approximations are a critical concept in mathematical physics, and its applications across a wide range of topics make it a vital tool for physicists. Despite this, little has been documented on student thinking when learning to apply approximations. Introduction to Mathematical Physics is a junior level undergraduate course offered at Texas State University where students engage with series approximations in familiar physical conditions. We are developing an artifact to explore student reasoning related to series approximations. Our instruction sequence begins with students analyzing simple cases of double point charge configurations and then leads into a guided written activity of approximating electric potential energy of a test charge between two coaxial rings of like charge. We have learned that some students are hesitant to take certain physical limits and struggle to relate these to mathematical formalism. We have also observed students using productive cognitive resources involving rolling marbles when thinking about stability.