By the time they begin school, most children have already developed a sophisticated, informal understanding of basic mathematical concepts and problem-solving strategies. Too often, however, the mathematics instruction that we impose upon them in the classroom fails to connect with this informal knowledge. Children's Mathematics was written to help you understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding.
Based on more than twenty years of research, this book portrays the development of children's understanding of basic number concepts. The authors offer a detailed explanation and numerous examples of the problem-solving and computational processes that virtually all children use as their numerical thinking develops. They also describe how classrooms can be organized to foster that development. Two accompanying CDs provide a remarkable inside look at students and teachers in real classrooms implementing the teaching and learning strategies described in the text. Together, the book and CDs provide you with the foundation necessary to engage children in discussions of how they think through problems—providing suggestions for what problems to give and insight into what responses to expect, and how children's thinking will evolve.
Contents:
1. Children's Mathematical Thinking
2. Addition/Subtraction: Problem Types
3. Addition/Subtraction: Children's Solution Strategies
4. Multiplication/Division: Problem Types and Children's Solution Strategies
5. Problem Solving as Modeling
6. Multidigit Number Concepts
7. Beginning to Teach Using Cognitively Guided Instruction
8. CGI Classrooms
Appendix: The Research Base for Cognitively Guided Instruction
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"I highly recommend this book for in-service and preservice teachers and their instructors. It is a valuable resource to help understand children's intuitive mathematical thinking and to use that knowledge to help children learn mathematics with understanding."
--Teaching Children Mathematics
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