ABSTRACT
Chapter 1 introduced you to the significance of mental models. This chapter explains how a richer understanding of how the mental model functions support reasoning helps you to create challenging activities that promote mathematical reasoning for the pupils in your class. Establishing and implementing stimulating activities for pupils makes for very exciting pedagogical practice because of the uncertainty of some outcomes and the abundant opportunities to develop new knowledge that are possible. One of the aims of the national curriculum of England and Wales (DfE, 2013), which is also evident in Primary mathematic curricula around the world, is to provide opportunities for children to reason mathematically. Reasoning means to follow some type of logical pathway of thinking or, as Johnson-Laird (2008, p. 3) says, contains “a set of processes that construct and evaluate implications among sets of propositions”. Reasoning is procedural, and while suggesting that the thinking involved follows a ‘pathway’, it is clear that it can get a bit messy at times. If we consider Johnson-Laird’s (2008) definition that includes the creation and evaluation of the effect of a range of possible solutions of an investigation, then we begin to appreciate the ‘messiness’ that is probable for mathematical reasoning activity because of the individual ways of constructing and evaluating understanding.
