The bestselling first edition of Children’s Mathematics helped hundreds of thousands of teachers understand children’s intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding. The highly anticipated Second Edition provides new insights about Cognitively Guided Instruction based on the authors’ research and experience in CGI classrooms over the last 15 years. Highlights include:

how children solve problems using their intuitive understanding of addition, subtraction, multiplication, and division
the development of children’s mathematical thinking throughout the primary grades
instructional practices that promote children’s active engagement in mathematics
connections between children’s strategies and powerful mathematical concepts

A new expanded collection of over 90 online video episodes illustrating children’s mathematical thinking, interactions between students and teachers, and classroom instruction that builds on children’s mathematical thinking.

Together, the Second Edition and videos provide a detailed research-based account of the development of children’s mathematical thinking and problem solving, and how teachers can promote this development in ways that honor children’s thinking.

About the Author

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.

Elizabeth Fennema is Emerita Professor of Curriculum and Instruction and Senior Scientist at the Wisconsin Center for Education Research at the University of Wisconsin-Madison. She has studied the teaching and learning of mathematics throughout her professional career, and is well known for her work on gender and mathematics.

Megan Loef Franke is a Professor in the Graduate Department of Education at UCLA where her research focuses on supporting teacher learning for both pre- and in-service teachers, diversity in mathematics education, and leadership in urban low performing schools. She was recently elected to the National Academy of Education.

Megan is known for her work on Cognitively Guided Instruction (CGI), her leadership in UCLA's Center X, and her ongoing professional development work to support teachers, schools, and communities.

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.

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.

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