Reasoning with calculations
F. C. Lewis, Amanda Wilkinson, Marcus Witt · 2021
This chapter explores ways of developing children’s reasoning through calculation. It explores how teachers can make simple ‘rich tweaks’ to the kinds of calculations that their children will be doing as a matter of course. Given the importance of reasoning for children’s subsequent mathematical development, teachers recommend incorporating reasoning into children’s experiences of calculation once they have a secure understanding of mathematical operations. Reasoning about different calculations may also support the children to develop efficient calculation strategies, which are founded on a clear understanding of the operation, rather than a half-remembered set of tricks and processes. Robert Kaplinsky has a fantastic resource for encouraging children to engage with calculation in a way that develops reasoning. He terms his problems ‘open middle’ to reflect the fact that they have the same opening for all children and the same end-point, but the way to get to the answer, the ‘middle’ part of the problem, is much more open.