Examining student understanding of matrix algebra and eigentheory

Abstract

Matrix algebra and eigentheory are important to students’ learning of physics in upper division physics courses. In this study, we investigated how students apply matrix algebra and eigentheory in various physics contexts, excluding quantum mechanics. The data collected consist of student written responses taken from a math methods course. We used the Physical-Mathematical Model (Uhden et al., 2011) to categorize each question by the three skills the model presents: mathematization, interpretation, and technical operation. The results from our data show that students have difficulty with mathematizing and interpreting the mathematical and physical system of a matrix equation, but are fluent in technical operations. We will present examples of student responses illustrating student reasoning, and discuss implications for classroom instruction.