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.

part |4 pages

I: The Nature of Early Algebra

chapter |14 pages

1 What Is Algebra? What Is Algebraic Reasoning?

ByJames J. Kaput

chapter |38 pages

2 Algebra From a Symbolization Point of View

ByJames J. Kaput, Maria L. Blanton, Luis Moreno

chapter |38 pages

4 Quantitative Reasoning and the Development of Algebraic Reasoning

ByJohn P. Jack, Patrick W. Thompson

part II|4 pages

Students’ Capacity for Algebraic Thinking

chapter 6|20 pages

Classroom Stories: Examples of Elementary Students Engaged in Early Algebra

ByVirginia Bastable, Deborah Schifter

chapter 7|16 pages

Children’s Reasoning About Change Over Time

ByCornelia Tierney, Stephen Monk

chapter 9|24 pages

Visualizing Algebraic Reasoning

ByTimothy Boester, Richard Lehrer

chapter |38 pages

Early Algebra Is Not the Same as Algebra Early

ByDavid W. Carraher, Analúcia D. Schliemann, Judah L. Schwartz

chapter |30 pages

Multiple Notational Systems and Algebraic Understandings: The Case of the “Best Deal” Problem

ByBárbara M.. Brizuela, Darrell Earnest

chapter |26 pages

Signed Numbers and Algebraic Thinking

ByIrit Peled, David W. Carraher

part |4 pages

Issues of Implementation: Taking Early Algebra Into the Classroom

chapter 13|28 pages

Content Matters: Algebraic Reasoning in Teacher Professional Development

ByMegan Loef Franke, Thomas P. Carpenter, Dan Battey

chapter 14|28 pages

Building District Capacity for Teacher Development in Algebraic Reasoning

ByMaria L. Blanton, James J. Kaput

chapter 15|24 pages

Measure Up: A Quantitative View of Early Algebra

ByBarbara Dougherty

chapter 16|36 pages

Early Algebra: What Does Understanding the Laws of Arithmetic Mean in the Elementary Grades?

ByDeborah Schifter, Stephen Monk, Susan Jo Russell, Virginia Bastable

chapter 17|30 pages

Early Algebra: The Math Workshop 1 Perspective

ByE. Paul Goldenberg, Nina Shteingold

chapter 18|32 pages

Early Algebra as Mathematical Sense Making

ByAlan H. Schoenfeld