Examining consistency of student errors in vector operations using module analysis

Abstract

It has been well documented that introductory physics students struggle with vector addition and subtraction. We use the results of a multiple-choice assessment on one-dimensional vector addition and subtraction, administered to students in a large-enrollment algebra-based physics sequence, to explore the consistency in the types of errors students make. The assessment was analyzed using Module Analysis for Multiple Choice Responses, a type of network analysis that highlights groups of responses commonly given together. We find evidence for five distinct modules that are consistent across multiple semesters. Of these groups, two support the method of "closing-the-loop", two are consistent with students performing the wrong operation, and one suggests that students provide an answer independently of whether they were prompted to add or subtract two vectors, though only for vectors that are anti-aligned.