Questions about the origins of mathematical knowledge and how that knowledge changes over childhood are central to both the field of cognitive development and that of mathematics education. Developmental psychologists have long been interested in questions about the origins of mathematical knowledge and its relation to other aspects of cognitive development. Nevertheless, they have seldom investigated children’s knowledge about the mathematical topics taught in school, other than simple addition and subtraction. Mathematics education researchers, conversely, have given a great deal of attention to school topics and to alternative methods of instruction in those topics, but have seldom considered their relation to the kinds of mathematical thinking children engage in prior to receiving any formal schooling. A basic premise of this book is that theoretical and empirical progress in both fields will benefit greatly from integration and synthesis of their respective findings and analytic perspectives.