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Thinking Mathematically

Integrating Arithmetic & Algebra in Elementary School

By Thomas P. Carpenter, University of Wisconsin and the Wisconsin Center for Education Research, Megan L. Franke, University of California, Los Angeles, Linda Levi, Teachers Development Group
Foreword by Hyman Bass, Deborah Loewenberg Ball

In Children's Mathematics: Cognitively Guided Instruction, Thomas Carpenter, Megan Franke, and Linda Levi helped hundreds of thousands of teachers understand children's intuitive problem-solving and computational processes and how to use that knowledge to enhance students' understanding of arithmetic. In this book, the same author team shows how Operations and Algebraic Thinking can be viewed as a unified field by understanding how children's intuitive strategies naturally draw upon the properties of operations and other algebraic concepts.  This book shows how teachers can recognize and support Read More


In Children's Mathematics: Cognitively Guided Instruction, Thomas Carpenter, Megan Franke, and Linda Levi helped hundreds of thousands of teachers understand children's intuitive problem-solving and computational processes and how to use that knowledge to enhance students' understanding of arithmetic. In this book, the same author team shows how Operations and Algebraic Thinking can be viewed as a unified field by understanding how children's intuitive strategies naturally draw upon the properties of operations and other algebraic concepts.  This book shows how teachers can recognize and support children’s use of the properties of operations and other algebraic concepts in a manner that deepens students’ understanding of arithmetic and provides a solid foundation for learning algebra. This book also shows how teachers can increase their own knowledge of mathematics in the process of interacting with their children and reflecting about their practice.

Thinking Mathematically provides numerous examples of classroom dialogues that indicate how properties of operations and other algebraic ideas emerge in children's thinking and what problems and questions help to elicit them. Special features of the book help teachers develop their own understanding of mathematics along with their students':

Teacher Commentaries capture the voices of a number of teachers, providing realistic portrayals of what happens in class.

End-of-chapter Challenges offer a variety of problems and activities for teachers to increase their own knowledge of mathematics and to help their students develop algebraic thinking.

An accompanying CD provides rich illustrations of ideas in the book—extended interactions with individual children or classroom episodes—all clearly linked to the text.

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ISBN 978-0-325-00565-2 / 0-325-00565-6 / 2003 / 160pp / BOOK WITH CD
Grade Level: K - 6th
*Price and availability subject to change without notice.

Contents

1. Developing Mathematical Thinking
2. Equality
3. Developing and Using Relational Thinking
4. Making Conjectures About Mathematics
5. Equations with Multiple Variables and Repeated Variables
6. Representing Conjectures Symbolically
7. Justification and Proof
8. Ordering Multiple Operations
9. "If… Then…" Statements: Relations Involving Addition, Subtraction, Multiplication, Division, and Equality
Answers for Selected Challenges

Samples