From knowledge acquired at academic mathematics courses to significant changes in instructional practices

Abstract

This non-interventional study investigates the contribution of university mathematics to teaching high-school mathematics. Data sources included interviews with five teachers who taught high-school mathematics before, during, and after their academic mathematics studies. All teachers provided tangible examples of fundamental changes in instructional practices that they explicitly linked to new knowledge acquired in the academic mathematics courses. The domain of analysis in general, and the topics of integrals and derivatives in particular, were central in the teachers’ illustrations of changes they made in their teaching, although other mathematical topics and domains were also mentioned. The reported changes were mostly associated with emphasis on mathematical explanations, exposition of two key elements of the deductive structure of mathematics: definition and proof, an increased focus on formal mathematics, and portrayal of mathematics as a wide and varied discipline. The study results are discussed in light of the relevant literature.