Comparing Student Use of Mathematical and Physical Vector Representations

Abstract

Research has shown that students have difficulties with vectors in college introductory physics courses and high school physics courses; furthermore, students have been shown to perform worse on a vector task with a physical context when compared to the same task in a mathematical context. We have used these results to design isomorphic mathematics and physics free‐response vector test questions to evaluate student understanding of vectors in both contexts. To validate our test, we carried out task‐based interviews with introductory physics students. We used our results to develop a multiple‐choice version of the vector test which was then administered to introductory physics students. We report on our test, giving examples of questions and preliminary findings.