Connecting Arithmetic to Algebra (Professional Book) Strategies for Building Algebraic Thinking in the Elementary Grades

ISBN-10: 0325041911

ISBN-13: 9780325041919

Edition: 2011

Authors: Susan Jo Russell, Deborah Schifter, Virginia Bastable

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"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 BastableAlgebra 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 allchildren, 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. Both the NCTM Principles & Standards and the new Common Core State Standards (CCSS) for Mathematics call for providing elementary students with a strong mathematics foundation through algebraic thinking.Connecting Arithmetic to Algebrainvites 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 Bastableand 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.
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Book details

List price: $28.13
Copyright year: 2011
Publisher: Heinemann
Publication date: 10/11/2011
Binding: Paperback
Pages: 176
Size: 7.25" wide x 9.25" long x 0.25" tall
Weight: 0.924
Language: English

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.

Generalizing in Arithmetic Getting Started, Part I-Noticing
Generalizing in Arithmetic Getting Started, Part II-Helping Students Share What They Notice
Generalizing in Arithmetic with a Range of Learners
Articulating General Claims
Developing Mathematical Arguments Representation-Based Proof
Focus on the Range of Learners When Students Struggle and When They Excel
Learning Algebraic Notation Looking at Two Things at Once
Developing Mathematical Arguments What Is the Domain?
Looking Ahead to the Middle Grades
Building Across the School Year Teachers and Students Learning Together
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