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Connecting Arithmetic to Algebra (Professional Book)

Strategies for Building Algebraic Thinking in the Elementary Grades

See how investigating the behavior of the operations can help move students on to more complex mathematical ideas. Each chapter includes real classroom examples that illustrate how elementary teachers can shape their instruction to prepare all students for higher level math.

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Full Description

“To truly engage in mathematics is to become curious and intrigued about regularities and patterns, then describe and explain them. A focus on the behavior of the operations allows students starting in the familiar territory of number and computation to progress to true engagement in the discipline of mathematics.”

—Susan Jo Russell, Deborah Schifter, and Virginia Bastable

Algebra readiness:  it’s a topic of concern that seems to pervade every school district.  How can we better prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction?  The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra.

Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking:  investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to:
*notice and describe consistencies across problems
*articulate generalizations about the behavior of the operations
*develop mathematical arguments based on representations to explain why such generalizations are or are not true.

Through such work, students become familiar with properties and general rules that underlie computational strategies—including those that form the basis of strategies used in algebra—strengthening their understanding of grade-level content and at the same time preparing them for future studies.

Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles.

Staff Developers:  Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course.
For information on the PD course offered through Mount Holyoke College, download the flyer.

Additional Resource Information

(click any section below to continue reading)



Chapter 1 Generalizing in Arithmetic: Noticing

Chapter 2 Generalizing in Arithmetic: Helping Students Share What They Notice

Chapter 3 Generalizing in Arithmetic with a Range of Learners

Chapter 4 Articulating General Claims

Chapter 5 Developing Mathematical Arguments

Chapter 6 Focus on the Range of Learners: When Students Struggle and When They Excel

Chapter 7 Learning Algebraic Notation: Looking at Two Things at Once

Chapter 8 Developing Mathematical Arguments: What is the Domain?

Chapter 9 Looking Ahead to the Middle Grades

Chapter 10 Building Across the School Year: Teachers and Students Learning Together



Supporting Materials

Also available, a digital Course Facilitator's Guide for Connecting Arithmetic to Algebra provides leaders with tools and resources for implementing a workshop or pre-service course. Click here to learn more.


“One often hears that algebra is generalized arithmetic. But little guidance is provided to teachers of mathematics on how to make these critical connections beginning as early as first grade and continuing throughout the elementary grades. This wonderfully accessible book, written in ways that place the reader in the center of a thinking, questioning, and reasoning classroom, provides this guidance with practical strategies and explicit techniques.”

Steven Leinwand, American Institutes for Research, author of Accessible Mathematics

“The ideas from this book are extremely important for teachers and teacher educators who want to provide effective teaching and learning in mathematics.”

Marshall Lassak, Mathematics Teaching in the Middle School