Analytic Framework for Students' Use of Mathematics in Upper-Division Physics

TL;DR

This paper introduces an analytical framework designed to help identify and understand students' difficulties with mathematical tools in upper-division physics courses, aiding instructors and researchers.

Contribution

The paper presents a new framework for analyzing students' mathematical difficulties in advanced physics, with practical applications demonstrated in electricity, magnetism, and classical mechanics.

Findings

Identified common student difficulties with direct integration and Taylor series.

Demonstrated the framework's utility in characterizing mathematical challenges.

Provided insights to improve instructional strategies in advanced physics courses.

Abstract

Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and researchers in characterizing students' difficulties with specific mathematical tools when solving the long and complex problems that are characteristic of upper-division. In this paper, we present this framework, including its motivation and development. We also describe an application of the framework to investigations of student difficulties with direct integration in electricity and magnetism (i.e., Coulomb's Law) and approximation methods in classical mechanics (i.e., Taylor series). These investigations provide examples of the types of difficulties encountered by advanced physics students, as well as the utility of the framework for both researchers and instructors.