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The more you listen to students' mathematical thinking, the more you will be amazed by what students can do… —Thomas Carpenter, Elizabeth Fennema, Megan Franke, Linda Levi, & Susan Empson

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The Impact of Cognitively Guided Instruction

The highly anticipated second edition of Children's Mathematics builds on the legacy of this best-selling classic, further exploring the power of Cognitively Guided Instruction (CGI) for developing children's mathematical thinking. The second edition includes new and revised content based on the authors' research, experiences, and new understandings about CGI over the last 15 years. It has been updated to include:

  • New and revised chapters reflecting over 30 years of research on how children think about and learn mathematics
  • A new, expanded collection of over 90 online video episodes illustrating children's mathematical thinking
  • Examples and teacher reflections that help you implement the philosophy of CGI and Children's Mathematics in your classroom

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Praise for Childrens Mathematics

“The continuing popularity of this book is testimony to the importance of its central message: Young children can think mathematically and instruction that builds on their thinking takes them further and deeper into the core concepts of arithmetic than teachers might imagine. As a teacher, one of the surest ways to appreciate the thinking of children, and then feel compelled to redesign instruction to take advantage of their thinking, is to listen to them solve mathematics problems. This book provides one of the best resources available for learning how to do this.”

— James Hiebert, Robert J. Barkley Professor of Education, University of Delaware

Children's Mathematics gives readers a fascinating glimpse into children's mathematical ideas and their foundational role in instruction. Building on the core research from the best-selling original book, the authors provide new and extended sections on the structure of children's base-ten thinking, how to interpret children's strategies in written work, and ways to use children's ideas as the centerpiece for rich discussions of mathematics. The complexity and mathematical power in young children's thinking are showcased throughout the book and also come to life through an extensive collection of videos. This exemplary resource is essential for teachers, professional developers, and researchers who are interested in understanding, supporting, and extending children's ways of reasoning.”

— Vicki Jacobs, Yopp Distinguished Professor of Mathematics Education, UNC Greensboro

Educator Testimonials

  • “Cognitively Guided Instruction not only changed the way I teach and restored my passion for teaching; it has had a positive impact on thousands of children.”
  • —Debbie Gates, elementary mathematics specialist


  • “I am far more engaged and excited about teaching math myself because Children's Mathematics helped me understand what questions to ask and what student comments to listen for that will lead to student discovery.”
  • — Lesley Wagner, teacher


  • “The training we have had in Cognitively Guided Instruction and through Children's Mathematics has shown us that understanding "how" children think mathematically is so much more valuable to their ongoing development than trying to "give" them the way to think. Our students have flourished.”
  • — Kathy Goecke, principal


  • Children's Mathematics is by far the most powerful and practical book that I have used in my work with teachers. The potential it has to not only deepen students' conceptual understanding of mathematics but their teachers as well is unparalleled…it is essential reading for every teacher who teaches mathematics.“
  • —Andrew Jenkins, principal


  • “This book is about helping students make sense of math. But don't be surprised if you start to make more sense of math yourself, which in turn will help you in teaching”
  • —Susan Gehn, mathematics specialist


  • Children's Mathematics should be at the top of the resource list of any teacher/leader who believes in the power of children's mathematical capability. The authors thoughtfully and thoroughly allow us to peek inside children's minds as they construct flexible mathematical understanding.
  • — Turtle Toms, mathematics specialist, Tweets @TurtleToms


  • Children's Mathematics and CGI give teachers a window into understanding children's mathematical thinking, how their thinking grows over time, and comprehending the deep conceptual mathematical ideas embedded in their reasoning.”
  • —Linda Jaslow, mathematics specialist


  • “CGI changes mathematics instruction from a focus on teaching to a focus on learning.”
  • —Jeanie Behrend, Professor, Curriculum and Instruction (Mathematics Education), California State University, Fresno


  • This new edition continues to cognitively guide teachers and researchers to look at children as earnest thinkers and doers of mathematics.
  • —James Brickwedde, Assistant Professor, Hamline University


  • “Teachers will gain essential knowledge of how children grow in their understanding of math concepts and develop increasingly more advanced strategies for addition, subtraction, multiplication, and division.”
  • —Tanya Vik Blais, elementary mathematics PD consultant


  • “Cognitively Guided Instruction, as laid out in Children's Mathematics, changed the way I teach mathematics”
  • —Christina Tondevold, teacher educator, www.TheRecoveringTraditionalist.com


  • “Each time I work with teachers on ideas related to CGI, whether in university courses or teacher study groups, I am impressed by the accessibility and the power of the Children's Mathematics text, and its usefulness for teachers from a diverse range of grade levels and teaching contexts”
  • —Erin Turner, Associate Professor, University of Arizona


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