Deepening pre-service secondary teachers’ mathematical content knowledge through engaging with peers’ mathematical contributions

Abstract

Depth and rigour in mathematical knowledge for pre-service secondary school mathematics teachers may be found in particular experiences of learning and doing school-level mathematics. Drawing on two cases from a course on financial mathematics for secondary school teachers, I illustrate opportunities for exploring compound and exponential growth. I show that when some students unexpectedly produced a quadratic model for an exponential relationship, opportunities are opened up to study the usefulness of the quadratic function as a model of the given situation. Further opportunities are also opened up to explore the relationship between the quadratic and exponential functions, which in turn require students to draw on advanced mathematics. I also argue that the use of the compound growth formula in a situation where it is not typically used provides opportunity to deepen knowledge of the essential features of the formula. Finally, I reflect on how suitable opportunities for engaging with peers’ mathematical contributions might be included in a pre-service programme for secondary school mathematics teachers.