Students' reasoning with multi-variable expressions in the context of potential difference*

Research suggests that some reasoning difficulties persist even after targeted instruction. One such instance is the student’s incorrect reasoning with multi-variable expressions in the context of Electromagnetism in the calculus-based introductory physics course. This talk will focus on student reasoning with Potential Difference, DELTA V=-W_EF/q_test. Specifically, after relevant instruction, students struggle to recognize that if the value of a test charge moving between two points is changed, the potential difference between the two points remains the same.  We designed instructional intervention (a blend of web-based assignments and classroom instruction) to prob students' reasoning with multivariable expressions in the context of (1) math problems and (2) analogous problems in the context of physics. We interpret the results through the lens of the dual-process theory of reasoning.