Mathematics-for-teaching: Insights from the case of annuities

Craig Pournara

doi:10.4102/pythagoras.v35i1.250

Abstract

Shulman’s notations of subject matter knowledge (SMK) and pedagogical content knowledge (PCK) have been very influential in education research on teachers’ knowledge for teaching. However, there is little empirical evidence in support of these as separate analytical constructs. Furthermore, attempts to distinguish SMK and PCK highlight the complex and multidimensional nature of teachers’ knowledge and hence the difficulty of separating SMK and PCK. The author adopts the notion of mathematics-for-teaching (MfT) and argues that teachers’ knowledge for teaching annuities comprises knowledge of mathematical aspects, knowledge of pedagogical aspects and contextual knowledge of finance. Drawing from a larger study in which the author taught a financial mathematics course to pre-service secondary mathematics teachers, four examples of teachers’ knowledge for teaching annuities are identified, each of which illustrates how knowledge of mathematics, knowledge of pedagogy and contextual knowledge of finance are intertwined.

Highlights

The first time I taught annuities, it was to a group of pre-service secondary mathematics teachers
When dealing with annuities, the compound interest formula needs to be viewed as an adjustment mechanism because the individual payments are being moved forwards or backwards in time to determine their contribution to a loan, outstanding http://www.pythagoras.org.za balance or projected savings
Based on discussions with actuaries working in the financial sector and in academia, the adjustment view is the one that they use most often and that is captured in typical statements such as ‘discounting a payment back to T0’

Summary

Introduction

The first time I taught annuities, it was to a group of pre-service secondary mathematics teachers. When dealing with annuities, the compound interest formula needs to be viewed as an adjustment mechanism because the individual payments are being moved forwards or backwards in time to determine their contribution to a loan, outstanding http://www.pythagoras.org.za balance or projected savings. Based on discussions with actuaries working in the financial sector and in academia, the adjustment view is the one that they use most often and that is captured in typical statements such as ‘discounting a payment back to T0’ (i.e. the point at which a loan is taken or an annuity is purchased) This suggests that the prevalent view of the compound interest formula in school mathematics does not reflect its dominant use in the banking sector and in actuarial science. BOX 1: Elimination method to derive formula for future value of an ordinary annuity

Which leads to FVn

Findings

Conclusion