How to Teach and Assess Whole Number Arithmetic: A Commentary on Chapter 11

Abstract

Chapter 11 and the different contributions in the proceedings of working group 4 have explored different aspects of the teaching and assessing of whole number arithmetic. We often underestimate teacher’s required knowledge, not only for selecting challenging and dense tasks but also, within a determined task, for assessing the diverse needs of individuals and respect to these needs. It is certainly not a little challenge for mathematics education research to describe the knowledge at stake: even within the field of WNA and even if we take a single lesson. In this chapter, I will focus on the difficulty to make coherent choices in teaching and assessing whole number arithmetic and the various pieces of knowledge that are necessary to do so. Whole number arithmetic is not a homogeneous domain in this chapter, so I will discuss some aspects: memorizing numerical facts, writing numbers and numerical sentences and additive structure’s field. These considerations will lead to a commentary about Macao’s lesson.