Extending Children's Mathematics: Fractions & Decimals by Susan B.
Extending Children's Mathematics: Fractions & Decimals
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Extending Children's Mathematics: Fractions & Decimals

Innovations In Cognitively Guided Instruction

By Susan B. Empson, Linda Levi
Foreword by Thomas P Carpenter

This book lays a foundation for the conceptual understanding fractions and decimals. It shows how the same kinds of intuitive knowledge and sense making that provides the basis for children’s learning of whole number arithmetic can be extended to fractions and decimals.

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“With the collaboration of a number of dedicated teachers and their students, Susan Empson and Linda Levi have produced a volume that is faithful to the basic principles of CGI while at the same time covering new ground with insight and innovation.”

—Thomas P. Carpenter

This highly anticipated follow-up volume to the landmark Children’s Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts.   Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning.  They show how the same kinds of intuitive knowledge and sense making that provides the basis for children’s learning of whole number arithmetic can be extended to fractions and decimals.  Just as they did in Children’s Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children’s thinking and alternative approaches to solving problems. Three themes appear throughout the book:

  • building meaning for fractions and decimals through discussing and solving word problems
  • the progression of children’s strategies for solving fraction word problems and equations from direct modeling through relational thinking
  • designing instruction that capitalizes on students’ relational thinking strategies to integrate algebra into teaching and learning fractions.

With illuminating examples of student work, classroom vignettes, “Teacher Commentaries” from the field, sample problems and instructional guides provided in each chapter, you’ll have all the tools you need to teach fractions and decimals with understanding and confidence.

Contents

Introduction: Issues in Learning Fractions and Decimals: Rethinking Our Approach
1. Equal Sharing Problems and Children's Strategies for Solving Them
2. From the Classroom: Getting Started with Fractions
3. Multiple Groups problems and Children's Strategies for Solving Them
4. Relational Thinking: Connecting Fractions and Algebra
5. From the Classroom: Making Relational Thinking Explicit
6. Understanding Fraction Equivalence and Order
7. Understanding Decimals
8. Understanding Operations on Fractions and Decimals
9. The Long View: Learning to Use Children's Thinking to Guide Instruction

Samples

Reviews

This book is enthusiastically recommended to my colleagues and curriculum coordinator, and it is recommended with equal enthusiasm to the readers of Mathematics Teaching in the Middle School.
--reviewer, Mathematics Teaching in the Middle School