ABSTRACT
This chapter reviews evidence that common difficulties in learning and becoming confident with mathematics are a consequence of a dominant style of teaching in schools which has exposed the weaknesses of human beings as learners, rather than exploited our strengths. School maths has typically been bereft of any real, meaningful or supporting context, has been reliant upon abstract symbolism, involved the learning of new ‘pencil and paper’ strategies unrelated to naturally developed mental strategies, and has been taught as a set of unexplained and prescribed procedures. The chapter sets out an analysis of how we learn by processes of induction, by developing more efficient ways of using our limited ‘working memory’ capacity, and through increasing metacognitive awareness and control of our own learning. This analysis supports the development of a new ‘emergent’ approach to teaching mathematics which involves placing tasks in meaningful contexts, requiring children to make their own representations, encouraging and developing children’s strategies, and employing a style of teaching which focuses on processes rather than products.
