# Hands-on, Practical Guidance for Educators

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# Building Thinking Classrooms in Mathematics, Grades K-12

** 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.

**Grade Level:**PreK-12**ISBN:**9781544374833**Published By:**Corwin**Series:**Corwin Mathematics Series**Year:**2020**Page Count:**344**Publication date:**October 16, 2020

**Price: $38.95**

## Description

**A thinking student is an engaged student**

*helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide*

**Building Thinking Classrooms in Mathematics, Grades K–12**- 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

## Author(s)

### Peter Liljedahl

**Dr. Peter Liljedahl** is a Professor of Mathematics Education at Simon Fraser University in Vancouver, Canada. He is the current president of the Canadian Mathematics Education Study Group (CMESG), past-president of the International Group for the Psychology of Mathematics Education (IGPME), editor of the International Journal of Science and Mathematics Education (IJSME), on the editorial board of five major international journals, and a member of the NCTM Research Committee. Peter has authored or co-authored numerous books, book chapters, and journal articles on topics central to the teaching and learning of mathematics. He is a former high school mathematics teacher who has kept his research close to the classroom and consults regularly with teachers, schools, school districts, ministries of education, and universities on issues of teaching and learning, assessment, and numeracy. Peter is a sought after presenter who has given talks all over the world on the topic of Building Thinking Classrooms, for which he has won the Cmolik Prize for the Enhancement of Public Education and the Fields Institute's Margaret Sinclair Memorial Award for Innovation and Excellence in Mathematics Education.

## Table of Contents

**Foreword by Tracy Johnston Zager**

**Introduction**

**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**

**References**

## Reviews

*“*Building Thinking Classrooms in Mathematics* exudes enthusiasm for students, how they think, and how those thoughts coalesce into powerful thinking classrooms. It's also deeply practical, describing how everything from the teacher's questions to the arrangement of the furniture can add to your students' learning.”*

Dan Meyer

“Building Thinking Classrooms in Mathematicsexudes enthusiasm for students, how they think, and how those thoughts coalesce into powerful thinking classrooms. It's also deeply practical, describing how everything from the teacher's questions to the arrangement of the furniture can add to your students' learning.”

Chief Academic Officer, Desmos

“I*f your students are not the ones doing the thinking in your classroom, then this book is for you! Peter Liljedahl provides concrete advice on each of 14 research-based practices, along with answers to frequently asked questions and suggestions for getting started, which will help you build a classroom where student thinking is the norm*.”

Peg Smith“I

f your students are not the ones doing the thinking in your classroom, then this book is for you! Peter Liljedahl provides concrete advice on each of 14 research-based practices, along with answers to frequently asked questions and suggestions for getting started, which will help you build a classroom where student thinking is the norm.”

University of Pittsburgh

*“Peter Liljedahl’s Thinking Classroom framework transformed my mathematics classroom overnight. I was frustrated that despite my best teaching efforts, some of my students still couldn’t solve simple problems by their final exam. This framework gave me a starting point that I started implementing the very next day and next steps to continue incorporating as my practice evolved. Students began to talk to each other, think through complex problems, rely less on me and more on each other and best of all had better success in the courses I taught. The Thinking Classroom framework was exactly what my students and I needed!*”

Laura Wheeler

“Peter Liljedahl’s Thinking Classroom framework transformed my mathematics classroom overnight. I was frustrated that despite my best teaching efforts, some of my students still couldn’t solve simple problems by their final exam. This framework gave me a starting point that I started implementing the very next day and next steps to continue incorporating as my practice evolved. Students began to talk to each other, think through complex problems, rely less on me and more on each other and best of all had better success in the courses I taught. The Thinking Classroom framework was exactly what my students and I needed!”

Ottawa Carleton District School Board

*“Peter refers to his research as 'mucking about,' and that is the key thing for me, that he goes into actual classrooms, and does math with students. We learn the most from being in actual classrooms, talking to students, and figuring out how they think about mathematics tasks. We need our students to be better thinkers, and to see mathematics for what it is: a beautiful way of thinking. We need them to see that they, too, can have powerful insights into interesting mathematics problems.”*

Matthew Oldridge

“Peter refers to his research as 'mucking about,' and that is the key thing for me, that he goes into actual classrooms, and does math with students. We learn the most from being in actual classrooms, talking to students, and figuring out how they think about mathematics tasks. We need our students to be better thinkers, and to see mathematics for what it is: a beautiful way of thinking. We need them to see that they, too, can have powerful insights into interesting mathematics problems.”

Author of Teaching Mathematics Through Problem-Solving in K-12 Classrooms

*“An in-depth action plan backed with significant research and data, Liljedahl’s plan is one that can improve every classroom for the better, and he foresees and addresses any questions or concerns you may have regarding implementation. It is clear Liljedahl understands the students I teach in his list of student behaviors and this book outlines methods to increase the thinking and engagement of all my students. I was able to implement many of the methods the very next day.”*

Leslie Mohlman

“An in-depth action plan backed with significant research and data, Liljedahl’s plan is one that can improve every classroom for the better, and he foresees and addresses any questions or concerns you may have regarding implementation. It is clear Liljedahl understands the students I teach in his list of student behaviors and this book outlines methods to increase the thinking and engagement of all my students. I was able to implement many of the methods the very next day.”

Alpine School District

*“Peter Liljedahl’s work is accessible, inspired by research, and embedded in classroom practice. He digs deeply and concisely into what it means to teach, learn, and assess in a thinking mathematics classroom. Elementary teachers, especially, will recognize themselves in this resource. Peter makes visible the often intuitive moves of elementary classroom teachers, describing what it is we are doing when it all just works, and how to meaningfully shift our practice when it doesn’t. From the way the furniture is arranged to how mathematical questions are posed, from who holds the pen to how to foster productive struggle and resilience, Peter sets the stage for genuine mathematical engagement in learners of all ages.”*

Carole Fullerton“Peter Liljedahl’s work is accessible, inspired by research, and embedded in classroom practice. He digs deeply and concisely into what it means to teach, learn, and assess in a thinking mathematics classroom. Elementary teachers, especially, will recognize themselves in this resource. Peter makes visible the often intuitive moves of elementary classroom teachers, describing what it is we are doing when it all just works, and how to meaningfully shift our practice when it doesn’t. From the way the furniture is arranged to how mathematical questions are posed, from who holds the pen to how to foster productive struggle and resilience, Peter sets the stage for genuine mathematical engagement in learners of all ages.”

Mind-Full Educational Consulting

*“Research in education that turns right around and informs our practice is invaluable in today’s schools and classrooms. Peter uses evidence gathered in mathematics classrooms to directly inform how we make changes to our teaching and learning that enhances learning. This is the essence of evidence-based practice, practice based on evidence from the very classrooms we seek to influence."*

John Almarode

“Research in education that turns right around and informs our practice is invaluable in today’s schools and classrooms. Peter uses evidence gathered in mathematics classrooms to directly inform how we make changes to our teaching and learning that enhances learning. This is the essence of evidence-based practice, practice based on evidence from the very classrooms we seek to influence."

James Madison University

*“After years of leading lessons in an ‘*I do, we do, you do

*’ format, I found that my students lacked a productive disposition towards mathematics and would give up on problems easily. I knew something had to change, but what was I going to change in my teaching practice and how was I going to get there? After 10 years of experimenting with different pedagogical approaches, classroom environment setups, and developing my own content knowledge, I realize that this book is the resource that could have helped me expedite the transformation I was after - moving from a classroom of “mimickers” to building a classroom of “thinkers”. Save yourself years of experimentation by investing a few hours reading this excellent book. Your students will thank you.”*

Kyle Pearce“After years of leading lessons in an ‘I do, we do, you do’ format, I found that my students lacked a productive disposition towards mathematics and would give up on problems easily. I knew something had to change, but what was I going to change in my teaching practice and how was I going to get there? After 10 years of experimenting with different pedagogical approaches, classroom environment setups, and developing my own content knowledge, I realize that this book is the resource that could have helped me expedite the transformation I was after - moving from a classroom of “mimickers” to building a classroom of “thinkers”. Save yourself years of experimentation by investing a few hours reading this excellent book. Your students will thank you.”

MakeMathMoments.com & Greater Essex County District School Board

*is an instructional tour de force for any math teacher. From his extensive research, Peter offers remarkably actionable classroom structures and teacher facilitation moves that get students to think and move forward in their thinking. I'm thrilled it's finally here!"*

"Building Thinking ClassroomsFawn Nguyenis an instructional tour de force for any math teacher. From his extensive research, Peter offers remarkably actionable classroom structures and teacher facilitation moves that get students to think and move forward in their thinking. I'm thrilled it's finally here!"

Rio School District

*"For years I have heard about Thinking Classrooms in workshops, articles, and online. This engaging book has taken all the pieces that I have heard and seen and presents them in an easy to read, and more importantly, actionable package. Things that seemed a little too “I could never do that” for me now seem doable and I am inspired to begin to make changes. I am left with plenty to reflect upon in my current practice even as I begin to think about moving to a Thinking Classroom."*

Casey McCormick"For years I have heard about Thinking Classrooms in workshops, articles, and online. This engaging book has taken all the pieces that I have heard and seen and presents them in an easy to read, and more importantly, actionable package. Things that seemed a little too “I could never do that” for me now seem doable and I am inspired to begin to make changes. I am left with plenty to reflect upon in my current practice even as I begin to think about moving to a Thinking Classroom."

Math Teacher, Grades 5-8

*“*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

“Building Thinking Classroomsprompts 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.”

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“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.”

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

“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.”

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“

Peter’s work inBuilding Thinking Classroomshas 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.”

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

“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.”

DreamBox Learning

### For Instructors

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### Related Resources

- Access to companion resources is available with the purchase of this book.
- Book Study Guide [Lessons and strategies]
- Building Thinking Classrooms in Mathematics: Part 1 [Video]
- Building Thinking Classrooms in Mathematics: Part 2 [Video]
- What is Building Thinking Classrooms? [Lessons and strategies]