Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School

In Children's Mathematics: Cognitively Guided Instruction, Thomas Carpenter, Megan Franke, and Linda Levi helped hundreds of thousands of teachers understand children's intuitive problem-solving and computational processes and how to use that knowledge to enhance students' understanding of arithmetic.

In Thinking Mathematically, the same author team shows how Operations and Algebraic Thinking can be viewed as a unified field by understanding how children's intuitive strategies naturally draw upon the properties of operations and other algebraic concepts.  This book shows how teachers can recognize and support children’s use of the properties of operations and other algebraic concepts in a manner that deepens students’ understanding of arithmetic and provides a solid foundation for learning algebra. This book also shows how teachers can increase their own knowledge of mathematics in the process of interacting with their children and reflecting about their practice.

Thinking Mathematically provides numerous examples of classroom dialogues that indicate how properties of operations and other algebraic ideas emerge in children's thinking and what problems and questions help to elicit them. Special features of the book help teachers develop their own understanding of mathematics along with their students':

Teacher Commentaries capture the voices of a number of teachers, providing realistic portrayals of what happens in class.

End-of-chapter Challenges offer a variety of problems and activities for teachers to increase their own knowledge of mathematics and to help their students develop algebraic thinking.

Additional Online Resources provide rich illustrations of ideas in the book, including extended interactions with individual children or classroom episodes―all clearly linked to the text.

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.

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.

Read a recent blog by Megan: What is Cognitively Guided Instruction?

Follow her on Twitter @meganlfranke

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