This volume synthesizes the implications of research done by the National Center for Research in Mathematical Sciences on integrating two somewhat diverse bodies of scholarly inquiry: the study of teaching and the study of learning mathematics. This research was organized around content domains and/or continuing issues of education, such as equity and assessment of learning, and was guided by two common goals - defining the mathematics content of the K-12 curriculum in light of the changing mathematical needs of citizens for the 21st century, and identifying common components of classrooms that enable students to learn the redefined mathematics with understanding. To accomplish these goals, classrooms in which instruction facilitated the growth of understanding were established and/or studied. This volume reports and discusses the findings which grew out of this research, and subsequent papers and discussions among the scholars engaged in the endeavour. Part 1 focuses on two major questions that have connected mathematics education and its various reform movements for the last 50 years: what mathematics should be taught? and how should students' understanding of that mathematics be defined and increased? Part 2 includes vignettes from diverse classrooms which illustrate classroom discourse, student work and student engagement in the mathematics and the mental activities described earlier in the book. Part 3 takes a closer look at "Critical Issues in Developing Classrooms That Promote Undestanding". In the final section, the editors look at the diverse classrooms, describe common points in instruction and curriculum, and provide a synthesis of findings in light of the previous chapters, with a re-emphasis on the opening discussion. Researchers, mathematics supervisors, teachers, policymakers, graduate students and the general lay public interested in mathematics education should find this book timely and relevant. Unlike many volumes reporting research, this one is written at a level appropriate for master's-degree students. Very few references are included in the chapters themselves, instead, each chapter includes a short annotated list of articles for expanded reading which provides the scholarly basis and research substantiation for this volume.