The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics and Science--established in 1996 as a research center and funded by the U.S. Department of Education--was instrumental in developing instructional practices supportive of high student achievement in and understanding of mathematics and science concepts. NCISLA researchers worked with teachers, students, and administrators to construct learning environments that exemplify current research and theory about effective learning of mathematics and science. The careful programs of research conducted examined how instructional content and design, assessment, professional development, and organizational support can be designed, implemented, and orchestrated to support the learning of all students. This book presents a summary of the concepts, findings, and conclusions of the Center's research from 1996-2001. In the Introduction, the chapters in this book are situated in terms of the reform movement in school mathematics and school science. Three thematically structured sections focus on, respectively, research directed toward what is involved when students learn mathematics and science with understanding; research on the role of teachers and the problems they face when attempting to teach their students mathematics and science with understanding; and a collaboration among some of the contributors to this volume to gather information about classroom assessment practices and organizational support for reform. Following a preface, this book is divided into four parts. Part I, Introduction, presents the initial chapter of the book: (1) Standards-Based Reform and Teaching for Understanding (T. A. Romberg, T.P. Carpenter, and J. Kwako). Part II, Learning with Understanding, includes: (2) Developing Modeling and Argument in the Elementary Grades (R. Lehrer and L. Schauble); (3) The Generative Potential of Students' Everyday Knowledge in Learning Science (A. S. Rosebery, B. Warren, C. Ballenger, and A. Ogonowski); (4) Developing Algebraic Reasoning in the Elementary School (T. P. Carpenter, L. Levi, P. W. Berman, and M. Pligge); (5) A Teacher-Centered Approach to Algebrafying Elementary Mathematics (J. J. Kaput and M. L. Blanton); (6) Statistical Data Analysis: A Tool for Learning (K. McCain, P. Cobb, and K. Gravemeijer); (7) Modeling for Understanding in Science Education (J. Stewart, C. Passmore, J. Cartier, J. Rudolph, and S. Donovan); (8) Learning Mathematics in High School: Symbolic Places and Family Resemblances (R. Nemirovsky, A. Barros, T. Noble, M. Schnepp, and J. Solomon). Part III, Teaching for Understanding (M. Franke and E. Kazemi) includes: (9) Changing Teachers' Professional Work in Mathematics: One School's Journey (J. Shih, S. Biagetti, and D. Battey); (10) Teacher Collaboration: Focusing on Problems of Practice (D. C. Webb, T. A. Romberg, M. J. Ford, and J. Burrill); and (11) Managing Uncertainty and Creating Technical Knowledge (W. G. Secada and T. Williams). Part IV, Cross-Cutting Studies, includes the final chapters: (12) Research in Assessment Practices (J. de Lange and T. A. Romberg); and (13) Capacity for Change: Organizational Support for Teaching for Understanding (A. Gamoran).