Extending Children's Mathematics : Fractions and Decimals: Innovations in Cognitively Guided Instruction

“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.

Thomas Carpenter was Professor Emeritus of Curriculum and Instruction at the University of Wisconsin-Madison, where he 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 (2004) among other awards. Tom passed away in August 2018, leaving behind a vast legacy to mathematics education thanks to his research into Cognitively Guided Instruction (CGI). That work, created by him and his team of researchers and authors, is available to all teachers in his influential and popular books Children's Mathematics, Thinking Mathematically, and Young Children's Mathematics. In addition, members of Tom's team have already begun the process of extending out from his work in CGI with Extending Children's Mathematics.

​Read more about Tom and his legacy, including warm remembrances from other influential members of the field of mathematics education.

Susan Empson is a professor and the Richard Miller endowed chair of mathematics education at the University of Missouri. Her research has consistently been supported by the National Science Foundation and the Spencer Foundation, including a recent NSF grant to study elementary teachers’ learning and development centered on teaching in ways that are responsive to children’s mathematical thinking in the domain of rational numbers.

Susan is a coauthor of bestselling books focused on Cognitively Guided Instruction (CGI), including Children's Mathematics and Extending Children's Mathematics.

Read a blog post adapted from Extending Children's Mathematics: How to Build Meaning for Fractions with Word Problems

Linda Levi is the Director of the CGI Math Teacher Learning Center, an agency devoted to supporting teachers’ understanding of children’s mathematical thinking through Cognitively Guided Instruction. She works directly with schools, districts, education cooperatives, and State Departments of Education to provide CGI professional development.

Linda is coauthor of three influential CGI books, all published by Heinemann: Children’s Mathematics, second edition (2014), Extending Children's Mathematics (2011), and Thinking Mathematically (2003). These books have helped hundreds of thousands of teachers understand children’s intuitive problem-solving strategies and computational skills.

Learn more about Cognitively Guided Instruction here: Heinemann.com/CGImath

Click here for updates about the CGI Math Teacher Learning Center.

Follow Linda on Twitter: @LLeviCGIMath