Connecting Arithmetic to Algebra: Strategies for Building Algebraic Thinking in the Elementary Grades

“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.

Susan Jo Russell is a principal scientist at the Education Research Collaborative at TERC. Following ten years of classroom teaching and coaching in elementary schools, Dr. Russell directed projects focused on mathematics professional development, research on students' and teachers' understanding of mathematics, and mathematics curriculum. She co-directed the development of the NSF-funded elementary curriculum, Investigations in Number, Data, and Space and the professional development materials, Developing Mathematical Ideas. Her recent work is on supporting teachers to integrate a focus on generalizing about the operations into their core arithmetic instruction.

Deborah Schifter is Principal Research Scientist at the Education Development Center (EDC) where she leads a range of projects concerning professional development in mathematics and research into student learning. Working with a variety of colleagues, she is coauthor of Reconstructing Mathematics Education, Developing Mathematical Ideas, The Mathematical Education of Teachers, and the Second Edition of Investigations in Number, Data, and Space. She also edited What's Happening in Math Class? (an anthology of teacher writing) and is co-editor of A Research Companion to the NCTM Standards. Deborah loves learning from the teachers with whom she works.

Virginia Bastable has been the Director of the SummerMath for Teachers Program at Mount Holyoke College since 1993. She taught middle school and high school mathematics for more than twenty years. She is coauthor of the Developing Mathematical Ideas professional development curriculum and the Second Edition of Investigations in Number, Data, and Space. Dr. Bastable particularly enjoys helping others to discover their interest and abilities in mathematics, even if those interests and abilities have been blunted by past negative experiences with the subject.