This volume emerges from a partnership between the American Federation of Teachers and the Learning Research and Development Center at the University of Pittsburgh. The partnership brought together researchers and expert teachers for intensive dialogue sessions focusing on what each community knows about effective mathematical learning and instruction. The chapters deal with the research on, and conceptual analysis of, specific arithmetic topics (addition, subtraction, multiplication, division, decimals, and fractions) or with overarching themes that pervade the early curriculum and constitute the links with the more advanced topics of mathematics (intuition, number sense, and estimation). Serving as a link between the communities of cognitive researchers and mathematics educators, the book capitalizes on the recent research successes of cognitive science and reviews the literature of the math education community as well.
"…teacher trainers and curriculum developers could certainly benefit from its rich analysis of the nature of arithmetic, its review of research on how children learn it, and the implications it draws for curriculum and teaching practice….The book, in fact, is an exercise in what it preaches: by grounding their discussions of research in discussions of what mathematics really is, the authors model a pedagogy that would likely increase children's 'number sense' and mathematical understanding, were it implemented in the classroom."
—Harvard Educational Review
"…offers a wealth of useful information and is thorough in its presentation….What is refreshing about this book is that it helps us appreciate the complexity of the conceptual underpinnings of arithmetic and the enormous task teachers face in providing experiences to help students make sense of these ideas."
"…the chapters…portray arithmetic as a thoughtful building of a flexible knowledge of our complex number system, rich in concepts, connections, and patterns that are crucial for understanding most of the rest of mathematics….One of the welcome additions to this book is the review in each chapter of textbook treatments of the domains of arithmetic….a valuable step in linking research and practice."
—Journal for Research in Mathematics Education
"…a comprehensive synthesis of research on the teaching and learning of several basic topics in arithmetic. The detailed comparison of textbook treatments of these topics with relevant research findings is informative."
—Journal of Curriculum Studies
Contents: Preface. J.T. Sowder, Making Sense of Numbers in School Mathematics. K.C. Fuson, Research on Learning and Teaching Addition and Subtraction of Whole Numbers. P. Nesher, Solving Multiplication Word Problems. M. Lampert, Teaching and Learning Long Division for Understanding in School. J. Hiebert, Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions. T.E. Kieren, Rational and Fractional Numbers as Mathematical and Personal Knowledge: Implications for Curriculum and Instruction. L.B. Resnick, From Protoquantities to Operators: Building Mathematical Competence on a Foundation of Everyday Knowledge. M. Rauth, L. Billups, Epilogue.