Calculus (ideas)-Based Physics: Reasoning without the formalism

Calculus, procedurally and conceptually, is often considered essential to an introductory physics course. Instructors and education researchers alike cite quantitative reasoning (including reasoning about rate of change and accumulation) as a key skill across all STEM disciplines. However, discipline-based education researchers across STEM are increasingly asking what kinds of quantitative reasoning are authentically valuable for subsets of the broad population that enroll in introductory courses. In this talk, I will share some of my work at the interface of mathematics and physics education research examining how students and experts reason about the rate of change and accumulation of scientific quantities. I will also share the implications of that work on the development of a calculus ideas-based introductory physics course that emphasizes conceptual calculus reasoning without requiring, or assuming facility with, calculus formalism.