Comparing Student Performance on Isomorphic Math and Physics Vector Representations

We designed isomorphic mathematics and physics free-response vector quizzes to evaluate student understanding of vectors in both contexts. Questions are identical, with only the context of the question changing in each case. To validate our test, we carried out task-based interviews with introductory physics students completing a semester\u27s instruction. We used our results from the interviews to develop a multiple-choice version of the vector quizzes which was then administered to introductory physics students before and after instruction. Overall, student performance on these isomorphic vector tasks is similar before instruction, different after an initial lecture on vectors in a math context, and different after a semester of instruction in our introductory mechanics course. In general student performance on the math vector tasks, after an initial lecture on vectors in an abstract context, seems to be indicative of performance on the physics vector tasks after a semester of instruction. No general trends were found relating to either the context dependence of the student performance or the responses distributions between individual math and physics isomorphic tasks. We find many students inconsistently apply vector manipulation tools and incompletely apply procedures across different vector tasks and contexts