Mathematization: Enhancing learning by fostering physics creativity

Experts in physics create and communicate knowledge through mathematization, the mental practice of translating between the physical world and the symbolic world. While PER at the upper division undergraduate level has uncovered many specific challenges that students understandably face with sophisticated mathematization, there is a growing body of evidence that even well prepared introductory college physics students struggle with the idiosyncratic ways that familiar mathematics is used in physics. This talk describes measuring and categorizing mathematization difficulties in a large-scale study (N > 600) designed to investigate trends in student reasoning with ratio and proportion, quantification, and symbolizing within the calculus-based introductory physics course. Our results foreshadow some of the difficulties that students encounter making mathematical sense in subsequent physics courses reported on in the literature. I conclude that physics mathematization is not an outcome of prerequisite mathematics courses, and that a coordinated effort of physics instructors and education researchers is necessary in order to effectively foster mathematical creativity in physics. I will share one instructional method piloted at Rutgers University, Western Washington University and New Mexico State University that engages students in mathematical creativity in the introductory course, and some preliminary evidence highlighting the challenges of producing more expert-like mathematization. ​