Extending Children’s Mathematics

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 穢2011 Book News, Inc., Portland, OR (booknews.com)