What Is Learned About the Roles of Mathematics in Physics While Learning Physics Concepts? A Mathematics Sensitive Look at Physics Teaching and Learning

Abstract

The starting point for this chapter is the assumption that knowing and reflecting about different roles of mathematics in (learning) physics is part of the desirable body of knowledge about the nature of science (NOS). On the one hand, a NOS approach that does not address roles of mathematics is simply not adequate, as mathematics is as important as are experiments for generating and communicating physics knowledge. On the other hand, the understanding of the roles of mathematics may strongly influence other, more general NOS aspects, e.g. to recognize physics as a creative human endeavour. This chapter aims at examplifying potential learning opportunities based on two case studies. The case studies have been chosen to represent an inductive and a deductive approach to teaching the physics around two equations included in most, if not all, secondary physics curricula. To illustrate the inductive approach ``uniform motion'' has been chosen, ``image formation by a thin (converging) lens'' is chosen as an example for a deductive approach. Both case studies shed some light on what is taught implicitly and what could be taught explicitly and reflectively about the roles of mathematics in physics, suggesting exemplary fields of reflection for a first encounter.