This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: what is the nature of arithmetic expertise? and how can instruction best promote it? Contributors from a variety of specialities, including cognitive, developmental, educational and neurological psychology; mathematics education; and special education, offer theoretical perspectives amd empirical evidence about these issues. As reported in this volume, both theory and research indicate that the nature of arithmetic expertise and how best to promote it are are far more complex than conventional wisdom and many scholars, past and present, have suggested.