This book synthesizes the implications of research done by the National Center for Research in Mathematical Sciences (NCRMS) by integrating two bodies of research: the study of teaching and the study of learning mathematics. This research was organized around content domains and/or continuing issues in education such as equity and assessment of learning, and was guided by two common goals: (1) defining the mathematics content of K-12 curriculum in light of the changing mathematical needs of citizens for the 21st century; and (2) 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 or studied. This volume reports and discusses findings that grew out of this research and is organized in three parts: (1) Setting the Stage; (2) Classrooms That Promote Learning; and (3) Developing Classrooms That Promote Understanding. Chapters include: (1) "Mathematics Worth Teaching, Mathematics Worth Understanding" (Thomas A. Romberg and James J. Kaput); (2) "Teaching and Learning Mathematics with Understanding" (Thomas P. Carpenter and Richard Lehrer); (3) "Equity as a Value-Added Dimension in Teaching for Understanding in School Mathematics" (Walter G. Secada and Patricia Williams Berman); (4) "Learning Basic Number Concepts and Skills as Problem Solving" (Thomas P. Carpenter, Elizabeth Fennema, Karen Fuson, James Hiebert, Piet Human, Hanlie Murray, Alwyn Olivier, and Diana Wearne); (5) "Building on Children's Intuitions to Develop Mathematical Understanding of Space" (Richard Lehrer, Cathy Jacobson, Vera Kemeny, and Dolores Strom); (6) "Promoting Learning in Middle-Grades Mathematics" (Judith Sowder and Randolph Philipp); (7) "Understanding of Statistics" (Susanne P. Lajoie); (8) "Teaching and Learning a New Algebra" (James J. Kaput); (9) "Assessment in Classrooms That Promote Understanding" (Mary C. Shafer and Thomas A. Romberg); and (10) "Creating Classrooms That Promote Understanding" (Elizabeth Fennema, Judith Sowder, and Thomas P. Carpenter). (SOE)