The impact of context on introductory student performance on vector product tasks

As part of a larger project exploring student understanding of mathematics in physics, we present findings of student understanding of vector products. We discuss student responses to multiple-choice tasks that ask separately about the magnitude and direction of vector products, dot and cross, in a mathematics context and in multiple physics contexts including work, torque, electric flux, and magnetic force, in two semesters of introductory physics. On tasks asking about the magnitude of products, the features of diagrams, in particular which angles were given, impacted the response distributions. On the tasks asking about the direction of the dot and cross product there is an improvement in performance as the course level increases, and the most common incorrect answer is consistent between both classes. Within each class, the proportion of correct responses does not differ between the mathematics and physics contexts, (although the students responding correctly to each task are not all the same) but the distribution of distractors selected does. There is also a difference in the response profiles between the physics contexts asked in each class. These findings suggest that the mathematical properties of vector products are not broad outcomes of (physics) instruction. Additionally, for a given physics task, students seem to be cued to context-specific responses that is consistent with language used in texts and in instruction.