Algebra in the Early Grades

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.