In recent years, increasing stress has been placed on the importance of giving young children a good start in mathematics. This book shows how children as young as five and of all abilities can be encouraged to carry out their own mathematical explorations whilst covering the content of a prescribed curriculum. A substantial part of the book is taken up with actual case studies of children working with Marion Bird in a reception classroom, fully illustrated with examples of the children's work. These case studies are then analyzed to show how a prescribed syllabus can be effectively covered through an investigational approach: a point which is of paramount importance to teachers concerned with the introduction of the National Curriculum. The role of the teacher is also examined carefully in order to identify those parts of a teacher's repertoire which seem to be particularly fruitful in encouraging young children's active mathematical thinking. Throughout, readers are encouraged to apply and amend ideas to suit their own particular circumstances.