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
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.
1. Developing Mathematical Thinking
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
" Statements: Relations Involving Addition, Subtraction, Multiplication, Division, and Equality
Answers for Selected Challenges
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