For students in calculus-based physics courses, reasoning with calculus is more than a prerequisite--it's a gateway to understanding the structure and logic of the discipline. Throughout the curriculum, core physics ideas depend on the dynamic interplay between mathematical representations and physics meaning. Yet many students struggle to develop this kind of reasoning, especially in the transition from introductory to advanced coursework.
My research group has operationalized Physics Quantitative Literacy (PQL)—the skills and habits of mind that support the effective use of mathematics in physics, with a focus on calculus-based reasoning. As part of this work, we investigate how students make sense of rates of change, accumulation, and covarying quantities—both scalar and vector—in physical contexts; how expert reasoning differs from novice thinking; and how instruction can support the development of these reasoning skills. Our work spans introductory and sophomore-level courses, including labs and mathematical methods, and informs the design of research-based instructional materials.
In this talk I will present a research perspective on characterizing, assessing, and strengthening PQL. I will share an empirical model of PQL across the physics major, highlight common conceptual difficulties, and provide examples of instructional strategies that support learning, belonging, and persistence in physics.