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

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 c2011 Book News, Inc., Portland, OR (booknews.com)

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 ProblemsLinda 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.