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Now is a time of great interest in mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies on the mathematical knowledge of prospective and practicing U. S. teachers suggest ways to improve their mathematical educations. It is often assumed that because the topics covered in K-12 mathematics are so basic, they should be easy to teach. However, research in mathematics education has shown that to teach well, substantial mathematical understanding is necessary--even to teach whole-number arithmetic. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power. This volume gathers and reports current thinking on curriculum and policy issues affecting the mathematical education of teachers. It considers two general themes: (1) the intellectual substance in school mathematics; and (2) the special nature of the mathematical knowledge needed for teaching. The underlying study was funded by a grant from the U.S. Department of Education. The mathematical knowledge needed for teaching is quite different from that required by students pursuing other mathematics-related professions. Material here is geared toward stimulating efforts on individual campuses to improve programs for prospective teachers. This report contains general recommendations for all grades and extensive discussions of the specific mathematical knowledge required for teaching elementary, middle, and high-school grades, respectively. It is also designed to marshal efforts in the mathematical sciences community to back important national initiatives to improve mathematics education and to expand professional development opportunities. The book will be an important resource for mathematics faculty and other parties involved in the mathematical education of teachers.