This state-of-the-art analysis of the psychology of mathematics concentrates on early competence in various areas of mathematical skill and on the representation of mathematical information. The contributors discuss a wide range of topics, including the development of mathematical skills ininfancy, the relation between imaginal and propositional cognitions in children's approaches to arithmetic word problems, and the roles of associative and rule-based knowledge. The book indicates areas where further research is required and emphasizes the need for more sophisticated theories ofmathematical understanding by educators in mathematics.