Artefacts and Tasks in the Mathematical Preparation of Teachers of Elementary Arithmetic from a Mathematician’s Perspective: A Commentary on Chapter 9

Abstract

The main focus of this chapter is the mathematical preparation of primary school teachers in relation to the teaching of elementary arithmetic. Comments are offered, from the perspective of a mathematician involved in the education of pre-service teachers, on the importance and variety of artefacts (often of a cultural and historical nature) that can be used to support the learning of whole number arithmetic, as well as on the role played by mathematical tasks in fostering the ‘mathematical message’ that may be conveyed through the artefacts. I will discuss concrete examples taken from an arithmetic course created by my department specifically for prospective primary school teachers, intending so doing to illustrate a crucial observation about artefacts and tasks, namely, that they form an inseparable pair in the teaching and learning of mathematics. This chapter addresses the mathematical preparation of primary school teachers. The learning of arithmetic by actual primary school pupils is not an immediate aim of the work we do with our student teachers, but we claim that many of the artefacts and tasks discussed in our arithmetic course (and in this chapter) can be transferred to pupils – but of course with a necessary adaptation to young children new at such notions.