Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School / Edition 1

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Overview

In Children's Mathematics: Cognitively Guided Instruction, Thomas Carpenter, Megan Franke, and Linda Levi helped tens of thousands of teachers understand children's intuitive problem-solving and computational processes. More important, the authors helped teachers figure out how to use that knowledge to enhance students' understanding of arithmetic. In this book the same author team takes teaching and learning mathematics to the next level, revealing how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic and provide 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 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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Editorial Reviews

From the Publisher
“Thinking Mathematically provides a rich portrait of arithmetic set in a broader perspective on mathematics, and on what it means to do and learn it. . . . The book overflows with supports for the mathematical work of the teacher in pressing students, provoking, supporting, pointing, and attending with care.”–Hyman Bass and Deborah Loewenberg Ball
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Product Details

  • ISBN-13: 9780325005652
  • Publisher: Heinemann
  • Publication date: 1/16/2003
  • Edition description: BK&CD-ROM
  • Edition number: 1
  • Pages: 160
  • Sales rank: 206,686
  • Product dimensions: 7.60 (w) x 9.30 (h) x 0.39 (d)

Meet the Author

Thomas Carpenter is Professor of Curriculum and Instruction at the University of Wisconsin-Madison, where he has taught for twenty-five years. He is the former editor of the National Council of Teachers of Mathematics (NCTM) Journal for Research in Mathematics Education, and has received the NCTM Lifetime Achievement award for Distinguished Service to Mathematics Education among other awards.

Megan Loef Franke is an Associate Professor in the Department of Education at the University of California-Los Angeles and Director of Center X: Where Research and Practice Intersect for Urban School Professionals. Her work focuses on understanding and supporting teacher learning through professional development.

Linda Levi is the Director of Cognitively Guided Instruction (CGI) Initiatives at Teachers Development Group, a nonprofit organization dedicated to increasing all students' understanding and achievement through teacher professional development. She currently works with schools, districts, education cooperatives and State Departments of Education to provide CGI professional development. Linda was coauthor of Thinking Mathematically (Heinemann 2003), and coauthor of Heinemann's top selling math title Children's Mathematics: Cognitively Guided Instruction, which has helped tens of thousands of teachers understand children's intuitive problem-solving and computational skills. Children's Mathematics remains a hallmark contribution to mathematics education since its publication in 1999.

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Table of Contents

Developing Mathematical Thinking

Equality

Developing and Using Relational Thinking

Making Conjectures About Mathematics

Equations with Multiple Variables and Repeated Variables

Representing Conjectures Symbolically

Justification and Proof

Ordering Multiple Operations

"If... Then..." Statements: Relations Involving Addition, Subtraction, Multiplication, Division, and Equality Answers for Selected Challenges

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