Title: Coordinatization Activated: How Students Understand and Apply Coordinate-Independent Integral Equations to Physics Situations

Introductory calculus-based physics requires students to apply their knowledge of differentiation and integration to investigate physical phenomena. This dissertation will look at how physics majors at the beginning of their junior year and again at the beginning of the senior year address coordinate independent variables and infinitesimals in their problem-solving through a process I call coordinatization. My observations find student acts of coordinatization to be discrete, locally coherent, and context-dependent pieces of a problem solution. Analysis of student work through their acts of coordinatization allow for discovery of the conceptual understandings a student holds and how that connects to the math they use.