Roles of mathematics in physics education: A systematic review

Mathematics plays many roles in physics and physics education. While these roles have previously been extensively discussed in the physics education research community, no systematic picture of the multifaceted considerations has yet been formed. To gain a comprehensive overview of the previous studies on the topic, we conducted a systematic literature review on 122 journal articles published between 2000 and 2023 that examine the role of mathematics in physics and physics learning. In the reviewed articles, we employed qualitative content analysis, coded each article for its characteristics, and used network maps for visualization. We identified eight thematic article categories, highlighting the complex integration of mathematics in, for example, physical reasoning, problem solving, modeling, and experiments. Additionally, the review examines theoretical frameworks and contexts, revealing an overemphasis on problem solving in mechanics and a limited exploration of advanced physics topics like quantum mechanics. A detailed inductive analysis further identified six overarching roles that mathematics plays in physics and physics education: (i) supporting learning and achievement, (ii) enabling mathematical manipulations, (iii) guiding reasoning and sensemaking, (iv) facilitating experiments and modeling, (v) serving as a language, and (vi) providing a structural foundation for physics as a science. Based on the analysis, we discuss how the roles assigned to mathematics have been conceptualized in the reviewed articles and provide an overall picture of the types and features of the reviewed corpus. Our findings suggest opportunities for future research, including deeper explorations of underrepresented physics contexts and targeted investigations into specific roles of mathematics in teaching and learning.