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Extending Children's Mathematics: Fractions and Decimals

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Synopses & Reviews

Publisher Comments:

"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.

Book News Annotation:

Empson (science and mathematics education, U. of Texas at Austin) and Levi, who directs Cognitively Guided Instruction in Initiatives, show how the same kinds of intuitive knowledge and sense making that are the basis for children's learning of whole-number arithmetic can be extended to fractions and decimals. They extend research presented in Children's Mathematics: Cognitively Guided Instruction (1999) and Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School (2003), especially Cognitively Guided Instruction, as they categorize the types of strategies that children in grades one through six use to solve problems in fractions and decimals, how these evolve, and teaching vignettes illustrating how to explain the math. They focus on the role of early understanding of algebraic relationships in developing their understanding of fractions and decimals, how to use fractions to develop use of algebraic relationships, and how a focus on these relationships helps students learn fractions. They draw on formative experiences of sharing and partitioning and discuss building meaning for fractions through solving and discussing word problems, the progression of children's strategies for solving problems, and designing instruction that integrates algebra and fractions. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

About the Author

Susan B. Empson is an Associate Professor of Science and Mathematics Education at The University of Texas at Austin. Her research has been supported by the National Science Foundation and the Spencer Foundation, and has been published in numerous journals including Cognition and Construction, Journal for Research in Mathematics Education, Teaching Children Mathematics, and Journal of Mathematics Teacher Education. Susan was 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.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.

Product Details

ISBN:
9780325030531
Subtitle:
Innovations In Cognitively Guided Instruction
Author:
Empson, Susan B.
Author:
Levi, Linda
Publisher:
Heinemann
Subject:
General education.
Subject:
Education-Teaching Math and Science
Publication Date:
20110329
Binding:
Paperback
Language:
English
Pages:
272
Dimensions:
9.2 x 7.4 x 0.56 in 1.06 lb
Age Level:
from 6 up to 11

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Education » General
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Education » Teaching » Math and Science

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