As in previous volumes, Kamii uses Piaget's groundbreaking work in constructivism as well as her own years of research in classrooms to closely observe what third grade children actually do when solving problems of addition, subtraction, multiplication and division. Her work translates Piaget's theory into a concrete programme that encourages children to use maths in real ways that stimulate them to reinvent arithmetic. She also challenges quick-fix theories of educational reform, replacing these with one that revolutionises our understanding of how human beings acquire knowledge, and thus drastically changing what we think schools should try to do. Educators have long been trying to transmit knowledge to children from the outside. What reform needs is a focus inside the child to maximise the process of construction from within. The volume is divided into four parts. The first gives a theoretical foundation, the second, goals and objectives, the third consists of chapters on problem solving, group games and other activities. The final part presents principles of teaching and answers frequently asked questions. The last chapter is about the evaluation of constructivist teaching and documents how children with three years of constructivist maths were able to reason far better than traditionally instructed children.