ABSTRACT
This chapter discusses the roles that perceiving and using patterns play in the pupils' cognitive development. It analyses how shaping their thinking can enable them to meet the demands that school makes of them. The chapter explores how teachers can make schemas an explicit focus of their pupils' attention and study and thereby help them think for themselves. Teachers' teaching cannot give pupils their learning as though it were a drink or a present. People act and learn, learn and act, by constructing and reconstructing neural patterns, making and remaking mental and muscular maps. It is an ongoing part of people's mental activity that they continually find similarities and differences, rules and exceptions in the world and in ourselves. Elizabeth Carruthers and Maulfry Worthington have described how valuable it is to engage with children's cognitive instincts and inventions, in particular when they use objects, pictures and diagrams to help them count and make sense of numbers.
