Unpacking Students' Use of Mathematics in Upper-division Physics

TL;DR

This paper reviews diverse research on how upper-division physics students use mathematics, highlighting the need to connect different approaches for better understanding and improving student learning.

Contribution

It synthesizes two main research approaches on students' mathematical reasoning in upper-division physics and advocates for integrating these perspectives to enhance educational strategies.

Findings

Different research approaches focus on challenges or reasoning

Recent efforts aim to connect these approaches

Recommendations for future research directions

Abstract

In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop an understanding of the underlying physics through solving such problems. Some of the research at the upper-division focuses on how students use mathematics in these problems, and what challenges students encounter along the way. There are a number of different and diverse research studies on students' use of mathematics in the upper-division. These typically utilize one of two broad approaches, with some researchers primarily seeking out and addressing challenges students face, and others working chiefly to unpack students' in-the-moment reasoning. In this paper, we present and discuss both approaches, and then review research efforts that strive to connect these two approaches in order to make sense of students' use of mathematics as well as to uncover particular challenges that students encounter. These recent efforts represent a small step towards synthesizing the two approaches, which we argue is necessary to more meaningfully impact student learning at the upper-division. We close our review and discussion with suggested refinements for future research questions for the physics education research community to consider while it works to understand how students use math in upper-division courses.