�Rules without a Reason�: ODEs in a concept image framework

Elementary ODEs are seen as prerequisite knowledge gained from the introductory calculus sequence for any physics student entering the upper division. In this paper, we provide evidence that while students might be well-versed in the rules and notations of ODEs, this does not necessarily translate to the application of these “rules without a reason” to novel physics tasks. Using the mathematics education researchers Tall and Vinner’s concept image framework, we propose that the body of knowledge or concept image a student brings to an upper division physics environment regarding ODEs is restricted. We present, via four student interviews, three potential signals of this “restricted concept image”: mathematical processes that are formally taught in introductory calculus and physics courses but are not reliably evoked when faced with a novel physics task. Our goal for this paper, as part of a larger project exploring student difficulties regarding ODEs, is to create a “proof of concept” that can be used in future work to more definitively identify the presence of a restricted ODE concept image.