People who learn to solve problems 'on the job' often have to do it differently from people who learn in theory. Practical knowledge and theoretical knowledge is different in some ways but similar in other ways - or else one would end up with wrong solutions to the problems. Mathematics is also like this. People who learn to calculate, for example, because they are involved in commerce frequently have a more practical way of doing mathematics than the way we are taught at school. This book is about the differences between what we call practical knowledge of mathematics - that is street...

This study addresses the process of developmental change as it occurs in the course of classroom lessons. The book aims to answer such questions as what forms of teacher-student interaction are most effective for producing developmental transformations in children's understanding. It also addresses why knowledge derived from psychological experiments on children's learning and development so often seems irrelevant to classroom teachers and how it is possible to reconcile Piaget's emphasis on the central role of independent intervention and constructive activity with learning theorists'...