Synopses & Reviews
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.
Review
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
Synopsis
In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic
Synopsis
System requirements: Window/PC. Pentium Processor (233 MHz or higher); Windows 98 or higher; 64 MB RAM (minimum); 4X CD-ROM drive (faster recommended); QuickTime 5.0 or greater. Macintosh. PowerPC Processor; System 8 or greater; 64 MB RAM (or higher); 4X CD-ROM drive (faster recommended); QuickTime 5.0 or greater.
Includes bibliographical references and index.
Synopsis
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. Speci
Synopsis
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.
About 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.
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