Algebra in the Early Grades

This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be “the initial topical choice for focused and coordinated research and development [in K-12 mathematics].”

This book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes:

• The Nature of Early Algebra
• Students’ Capacity for Algebraic Thinking
• Issues of Implementation: Taking Early Algebra to the Classrooms.

The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings.
 
Algebra in the Early Grades aims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.

Contents: Preface. Skeptic's Guide to Algebra in the Early Grades. Part I: The Nature of Early Algebra. J.J. Kaput, What Is Algebra? What Is Algebraic Reasoning? J.J. Kaput, M.L. Blanton, L.M. Armella, Algebra From a Symbolization Point of View. J. Mason, Making Use of Children’s Powers to Produce Algebraic Thinking. J.P. Smith III, P.W. Thompson, Quantitative Reasoning and the Development of Algebraic Reasoning. E. Smith, Representational Thinking as a Framework for Introducing Functions in the Elementary Curriculum. Part II: Students’ Capacity for Algebraic Thinking. V. Bastable, D, Schifter, Classroom Stories: Examples of Elementary Students Engaged in Early Algebra. C. Tierney, S. Monk, Children’s Reasoning About Change Over Time. N. Mark-Zigdon, D. Tirosh, What Is a Legitimate Arithmetic Number Sentence? The Case of Kindergarten and First Grade Children. T. Boester, R. Lehrer, Visualizing Algebraic Reasoning. D.W. Carraher, A.D. Schliemann, J.L. Schwartz, Early Algebra Is Not the Same as Algebra Early. B.M. Brizuela, D. Earnest, Multiple Notational Systems and Algebraic Understandings: The Case of the “Best Deal” Problem. I. Peled, D.W. Carraher, Signed Numbers and Algebraic Thinking. Part III: Issues of Implementation: Taking Early Algebra to the Classrooms. M.L. Franke, T.P. Carpenter, D. Battey, Content Matters: The Case of Algebra Reasoning in Teacher Professional Development. M.L. Blanton, J.J. Kaput, Building District Capacity for Teacher Development in Algebraic Reasoning. B. Dougherty, Measure Up: A Quantitative View of Early Algebra. D. Schifter, S. Monk, S.J. Russell, V. Bastable, Early Algebra: What Does Understanding the Laws of Arithmetic Mean in the Elementary Grades? P. Goldenberg, N. Shteingold, Early Algebra: The MW Perspective. Afterword: A. Schoenfeld, Early Algebra as Mathematical Sense-Making.