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...