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Building Thinking Classrooms in Mathematics, Grades K-12

Building Thinking Classrooms in Mathematics, Grades K-12
14 Teaching Practices for Enhancing Learning

First Edition

Foreword by Tracy Johnston Zager, Illustrations by Laura Wheeler

Additional resources:

October 2020 | 344 pages | Corwin

A thinking student is an engaged student

Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling “non-thinking” student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide

  • Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions
  • Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples
  • Offers a plethora of macro moves, micro moves, and rich tasks to get started
  • Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year
When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

Foreword by Tracy Johnston Zager
Chapter 1: What Are the Types of Tasks We Use in a Thinking Classroom?
Chapter 2: How We Form Collaborative Groups in a Thinking Classroom
Chapter 3: Where Students Work in a Thinking Classroom
Chapter 4: How We Arrange the Furniture in a Thinking Classroom
Chapter 5: How We Answer Questions in a Thinking Classroom
Chapter 6: When, Where, and How Tasks are Given in a Thinking Classroom
Chapter 7: What Homework Looks Like in a Thinking Classroom
Chapter 8: How We Foster Student Autonomy in a Thinking Classroom
Chapter 9: How We Use Hints and Extensions in a Thinking Classroom
Chapter 10: How we Consolidate a Lesson in a Thinking Classroom
Chapter 11: How Students Take Notes in a Thinking Classroom
Chapter 12: What We Choose to Evaluate in a Thinking Classroom
Chapter 13: How We Use Formative Assessment in a Thinking Classroom
Chapter 14: How We Grade in a Thinking Classroom
Chapter 15: Pulling the 14 Practices Together to Build a Thinking Classroom


Building Thinking Classrooms prompts us to reflect on the potential of mathematics classrooms, teachers, and learners. Supported by numerous stories from classrooms, Peter methodically exposes the familiar structures of school mathematics that suppress the potential of learners, then carefully outlines a set of opportunities around which teachers of mathematics can organize a dynamic and responsive classroom.”   

Nat Banting
Mathematics Teacher

“Though there are many innovations in the area of teaching mathematics, few speak with a particular lens in terms of setting up an environment where thinking is made visible and public, where positive interdependence is connected to individual and group accountability, and where students rely on their own agency as well as the wisdom of their peers. One where the teacher is freed up to have eyes on all student work, and watch the thinking process in action.  In other words, thinking becomes a clearly visible driver in this environment.  All of this supports the release of responsibility to the students.  It honors their voices, allows for the bumps in learning, and makes the thinking more public, thus supporting and encouraging risk-taking in a safe and supportive environment.” 

Yana Ioffe
School Principal

“This book is timely and provides an accurate portrayal of what is occurring in mathematics classroom across the country. The book is a valuable reflexive tool that teachers can use as they analyze their own teaching practices.”

Kenneth Davis
High School Mathematics Teacher and Department Chair

Peter’s work in Building Thinking Classrooms has been the single most impactful (driver for) change in secondary mathematics education that I have witnessed. I have never seen another idea/approach/model capture so many teachers immediately, and make it past the point from learning to actual implementation in almost every classroom or instance that I have witnessed.”

Mishaal Surti
Educational Consultant

“For teachers hoping to transform their teaching practice, Peter has written a definitive source. Peter’s conversational style makes this work both interesting to read and easy to follow. He describes a rich set of practices that will help mathematics teachers transform, in a positive way, everything about their classroom. Peter turns the daunting challenge into something manageable with advice that is both believable and practical.”

David Wees
DreamBox Learning

The lucid explanations of how children think. The practical and accessible examples.

Mr Andre ChenFeng
Teacher Education, Claremont Graduate University
December 15, 2022

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