**Jeremy Kilpatrick,** *Chair,* is Regents Professor of Mathematics Education at the University of Georgia. He is currently studying the process of changing the school mathematics curriculum, which includes documenting the history of reform efforts in the United States. He is a former vice president of the International Commission on Mathematical Instruction, was a charter member of the Mathematical Sciences Education Board (MSEB) of the National Research Council (NRC), was a member of the National Council of Teachers of Mathematics’ Commission on the Future of the Standards, and currently serves on the NRC’s Board on International Comparative Studies in Education. He also chaired the MSEB study that produced *Measuring What Counts* (NRC, 1993). Kilpatrick has published extensively on mathematics education issues, including “Confronting Reform,” in the *American Mathematical Monthly,* and “Reflections on Verifying Change in School Mathematics,” in the *Journal of Classroom Interaction*. He has engaged in numerous editorial activities, most recently with Anna Sierpinska editing *Mathematics Education as a Research Domain: A Search for Identity* (1998); and with George Stanic editing *A History of School Mathematics* (in preparation). He is the recipient of multiple awards and honors, including the John W.Wilson Memorial Award and several Fulbright lecturer and scholar awards. He holds an honorary doctorate from the University of Gothenburg. Kilpatrick received an A.A. in mathematics and science from Chaffey College; an A.B. in mathematics and an M.A. in education from the University of California, Berkeley; and an M.S. in mathematics and a Ph.D. in mathematics education from Stanford University.

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BIOGRAPHICAL SKETCHES
Jeremy Kilpatrick, Chair, is Regents Professor of Mathematics Education at the University of Georgia. He is currently studying the process of changing the school mathematics curriculum, which includes documenting the history of reform efforts in the United States. He is a former vice president of the International Commission on Mathematical Instruction, was a charter member of the Mathematical Sciences Education Board (MSEB) of the National Research Council (NRC), was a member of the National Council of Teachers of Mathematics’ Commission on the Future of the Standards, and currently serves on the NRC’s Board on International Comparative Studies in Education. He also chaired the MSEB study that produced Measuring What Counts (NRC, 1993). Kilpatrick has published extensively on mathematics education issues, including “Confronting Reform,” in the American Mathematical Monthly, and “Reflections on Verifying Change in School Mathematics,” in the Journal of Classroom Interaction. He has engaged in numerous editorial activities, most recently with Anna Sierpinska editing Mathematics Education as a Research Domain: A Search for Identity (1998); and with George Stanic editing A History of School Mathematics (in preparation). He is the recipient of multiple awards and honors, including the John W.Wilson Memorial Award and several Fulbright lecturer and scholar awards. He holds an honorary doctorate from the University of Gothenburg. Kilpatrick received an A.A. in mathematics and science from Chaffey College; an A.B. in mathematics and an M.A. in education from the University of California, Berkeley; and an M.S. in mathematics and a Ph.D. in mathematics education from Stanford University.

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Deborah Loewenberg Ball is Arthur F.Thurnau Professor of Mathematics Education and Teacher Education at the University of Michigan. An experienced elementary teacher, Ball conducts research on instruction and on the processes of learning to teach. She also investigates efforts to improve teaching through policy, curriculum, reform initiatives, and teacher education. Ball’s publications include articles on teacher learning and teacher education; the role of subject matter knowledge in teaching and learning to teach; endemic challenges of teaching; and the relations of policy and practice in instructional improvement.
Hyman Bass is the Roger Lyndon Collegiate Professor of Mathematics and Professor of Mathematics Education at the University of Michigan. From 1959 to 1998, he was a member of the Mathematics Department at Columbia University. His mathematical research publications cover broad areas of algebra, with connections to geometry, topology, and number theory. He has received the Cole Prize in Algebra from the American Mathematical Society and the Van Amringe Book Award from Columbia University for a book that helped found the subject of algebraic K-theory. He has held visiting research and faculty positions at mathematical centers around the world, including Princeton, Paris, Bombay, Rio, Cambridge, Stockholm, Mexico, Rome, Trieste, Hong Kong, Berkeley, and Jerusalem. He has lectured widely, in particular as a Phi Beta Kappa National Visiting Scholar. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. Bass currently serves as President of the American Mathematical Society. He formerly chaired the Mathematical Sciences Education Board of the National Research Council and the Committee on Education of the American Mathematical Society and is President of the International Commission on Mathematics Instruction.
Jere Brophy is University Distinguished Professor of Teacher Education and Educational Psychology and formerly Co-Director of the Institute for Research on Teaching at Michigan State University. He has done extensive research on teacher effectiveness, the interpersonal dynamics of teacher-student relationships, teacher expectation effects, classroom management, and student motivation. He received a Ph.D. in human development and clinical psychology from the University of Chicago.
Felix Browder is University Professor of Mathematics at Rutgers, The State University of New Jersey, and Max Mason Distinguished Service Professor

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Emeritus of Mathematics at the University of Chicago, where he was a faculty member from 1963 to 1986. He also served as Vice President for Research at Rutgers University from 1986 to 1991. Browder is the immediate Past President of the American Mathematical Society and was awarded the Presidential National Medal of Science in 1999. He is a member of the National Academy of Sciences (NAS) and the American Academy of Arts and Sciences. He has served as a member of the Council of the NAS and its Committee on Science, Engineering, and Public Policy. His research interests include topological methods in analytical problems; history and philosophy of mathematics and science; problems of scientific organizations and institutions; and mathematics and science education.
Thomas Carpenter is Professor of Curriculum and Instruction at the University of Wisconsin-Madison. He is currently Director of the National Center for Improving Student Learning and Achievement in Mathematics and Sciences, and he is a former editor of the Journal for Research in Mathematics Education. Along with Elizabeth Fennema, Megan Franke, and others, he developed the Cognitively Guided Instruction research and professional development project. His research investigates the development of children’s mathematical thinking, how teachers use specific knowledge about children’s mathematical thinking in instruction, and how children’s thinking can be used as a basis for professional development. He is currently focusing on the development of algebraic thinking in elementary school. Carpenter received a B.S. from Stanford University and a Ph.D. from the University of Wisconsin.
Carolyn Day is Associate Director for Elementary Mathematics and Science for the Dayton Public Schools in Ohio. She has been with the district for 28 years, first as an elementary teachers, then as a teacher of mathematics in grades 6 through 8, and for the past 10 years as a mathematics supervisor. Day has a B.S. in elementary education from Central State University in Wilberforce, Ohio, and an M.Ed, in curriculum, instruction, and administration from Wright State University. She currently serves on the board of the Ohio Mathematics Leadership Council, the Aullwood Audubon Center in Ohio, and the National Council of Supervisors of Mathematics as secretary.
Karen Fuson is Professor of Education and Psychology in the School of Education and Social Policy at Northwestern University. She received her B.A. in mathematics from Oberlin College and her M.A.T. and Ph.D. from the University of Chicago. Her research interests concern young children’s

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mathematical understanding and the classroom and school conditions that can facilitate such understanding. She seeks to identify and describe developmental or experiential sequences in children’s understanding of various mathematical domains, particularly for ages 2 through 11, and to use this understanding of children’s thinking to build classroom teaching and learning experiences that will support children’s thinking. She is the author of numerous research articles and review articles, including a chapter on addition and subtraction in the Handbook of Research on Mathematics Teaching and Learning. Her book Children’s Counting and Concepts of Number focuses on understanding children’s counting and their conceptual advances in using counting in various situations. She has done extensive work on children’s multidigit addition and subtraction and on word problem solving and has more recently focused on various aspects of multiplication, division, and fractions at grades 3 through 6 as well as on aspects of geometry and measure. She is directing the Children’s Math Worlds project, which focuses on research to design effective methods of teaching and learning in grade K-5 English-speaking and Spanish-speaking urban and suburban classrooms.
James Hiebert is H.Rodney Sharp Professor of Education at the University of Delaware, where he works with preservice and inservice teachers. His professional interests focus on mathematics teaching and learning in classrooms. He has edited books, including Conceptual and Procedural Knowledge: The Case of Mathematics and Number Concepts and Operations in the Middle Grades, and he co-authored the books Making Sense: Teaching and Learning Mathematics with Understanding and The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom. He currently serves as the mathematics content specialist on the Video Study of the Third International Mathematics and Science Study-Repeat. He received a B.A. in mathematics from Fresno Pacific College, an M.A. in mathematics from the University of Illinois, and a Ph.D. in mathematics education from University of Wisconsin.
Roger Howe is a Professor of Mathematics at Yale University where he has been since 1974. He received his Ph.D. from the University of California at Berkeley, and prior to joining the Yale faculty, spent five years at the State University of New York at Stony Brook. He has been a visiting professor at many universities, both in the United States and abroad. Howe’s mathematical research focuses on symmetry and its consequences. He is a member of the Connecticut Academy of Science and Engineering, the American Academy of Arts and Sciences, and the National Academy of Sciences. He has

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served on Mathematical Sciences Education Board and on the board of directors of the Connecticut Academy for Education in Mathematics, Science, and Technology. He served as chair of the American Mathematical Society (AMS) Association Review Group for revision of the National Council of Teachers of Mathematics Standards and is currently chair of the AMS Committee on Education.
Carolyn Kieran is Professor of Mathematics Education at the University of Quebec, Montreal. Her research interests include the learning and teaching of school algebra, the use of technology in school mathematics, the role of collaboration in mathematical discourse, and the application of historical and psychological models to mathematics education research. Her publications include Research Agenda for Mathematics Education: Research Issues in the Learning and Teaching of Algebra with S.Wagner, Approaches to Algebra: Perspectives for Research and Teaching with N.Bednarz and L.Lee, and a chapter on “The Learning and Teaching of School Algebra” in the 1992 Handbook of Research on Mathematics Teaching and Learning. She has served as president of the International Group for the Psychology of Mathematics Education, vice president of the Canadian Mathematics Education Study Group, and chair of the editorial panel of the Journal for Research in Mathematics Education. Her degrees include a Ph.D. from the Department of Educational Psychology at McGill University and a Master’s in the Teaching of Mathematics from Concordia University in Montreal. In addition to teaching mathematics and mathematics education courses to preservice and inservice teachers at both the graduate and undergraduate levels, Kieran has also taught mathematics at public school.
Richard E.Mayer is Professor of Psychology at the University of California, Santa Barbara (UCSB), where he has served since 1975. His major research interests are in educational psychology, with a focus on instructional methods that promote problem-solving transfer. He is a former president of the Division of Educational Psychology of the American Psychological Association and a former chair of the Department of Psychology at UCSB. In 2000 he received the American Psychological Association’s E.L.Thorndike Award for lifetime achievement in educational psychology. He was editor of Educational Psychologist and Instructional Science and currently serves on the editorial boards of 12 journals. He has authored 13 books including Thinking, Problem Solving, Cognition (2nd edition) and The Promise of Educational Psychology: Learning in the Content Areas. He has authored more than 200 articles and chapters, mainly in the area of educational psychology.

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Kevin Miller is Associate Professor in the departments of Psychology, Educational Psychology, and the Beckman Institute of the University of Illinois at Urbana-Champaign. His research focuses on how cognitive tools such as number-naming systems, writing systems, and other representational systems affect children’s learning. Recent research involves cross-cultural comparisons of the learning of reading and mathematics by children in China and the United States and research on how videotaped representations of classroom teaching can be used to improve mathematics education in the United States. He received a Ph.D. in child psychology from the Institute of Child Development of the University of Minnesota and taught at Michigan State University and the University of Texas prior to coming to the University of Illinois.
Casilda Pardo has been a teacher for 18 years. She became a full-time mathematics resource teacher in 1998 at Valle Vista Elementary School in Albuquerque, New Mexico. From 1994 to 1998, she was a half-time classroom teacher and half-time mathematics resource teacher at Armijo Elementary School in Albuquerque. She is also a national trainer for the Investigations in Number, Data, and Space curriculum. From 1992 to 1994, she served as a clinical supervisor of student teachers, which included teaching mathematics and science methods courses. Among her professional activities, she has taught mathematical methods at the University of New Mexico (UNM), has been a teacher in the State Initiative in Math and Science Education summer institutes, and has taught Thinking Mathematics I and II at the Continuing Education division of UNM. Pardo received a B.A. from Marymount College and an M.A. from the University of Wisconsin.
Edgar Robinson was Vice President and Treasurer of the Exxon Corporation upon retirement in 1998. In that role he oversaw various financial activities of the Corporation. During his almost 40 years with Exxon he held many senior management positions in Texas, New York, and London. Robinson holds an A.B. in economics from Brown University and an M.B.A. from Harvard Business School. He served as member of President Reagan’s Private Sector Survey on Cost Control (the Grace Commission). He has also been a member of the Conference Board’s Council of Financial Executives (1990–1998). He is a trustee emeritus of Brown University and a past chairman and life member of the Dean’s Advisory Council at Chicago Business School. Robinson is current Past President of the Dallas Zoological Society and the Vogel Alcove Childcare Center for the Homeless, a project of the Dallas Jewish Coalition. He is a member of the boards of the Dallas Symphony, the Dallas Theater

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Center, the Greenwall Foundation, and the American Trust for the British Library.
Hung-Hsi Wu is Professor of Mathematics at the University of California, Berkeley. His area of expertise is real and complex geometry. He received his A.B. from Columbia University and his Ph.D. from the Massachusetts Institute of Technology. He has authored several articles on mathematics education and is also a technical reviewer of the 1999 California Mathematics Framework. Almost all his writings in education can be found on his homepage: <http://www.math.berkeley.edu/~wu/>.

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