Probing student reasoning with multivariable expressions

We have been exploring student reasoning with multi-variable expressions across a range of contexts. One example is the potential difference defined by the equation V_AB = -W_AB/q_test. Many students erroneously believe that an increase in the value of a test charge moving in an external electric field between points A and B results in a decrease in the potential difference between these points. In order to investigate the sources of reasoning errors associated with multi-variable expressions within this context, we have developed instructional assessments grounded in the Dual Process Theory of Reasoning (DPToR). Recognizing that relevant knowledge is essential for effective reasoning, our study particularly focused on exploring what relevant math knowledge the students possess, how they apply this knowledge in physics, and how it impacts their reasoning in this specific context. We will present the findings from the calculus-based introductory course on electricity and magnetism and discuss their implications for instructional practices.