Engage Students in Deep Mathematical Thinking Across Diverse Settings
Peter Liljedahl’s Building Thinking Classrooms in Mathematics series provides practical, research-based strategies to foster deep thinking and enhance learning in K-12 mathematics classrooms. Drawing from over 15 years of research, Liljedahl and co-author Maegan Giroux offer educators a comprehensive framework for implementing 14 optimal teaching practices that drive student engagement and meaningful mathematical learning.
The series starts with Building Thinking Classrooms in Mathematics, Grades K-12, a guide that explains the what, why, and how of each practice, including firsthand accounts, macro and micro moves, and rich tasks to promote thinking. Teachers will find an array of strategies to transform their classrooms into dynamic spaces for deep learning.
The follow-up supplement, Modifying Your Thinking Classroom for Different Settings, adapts these practices for a wide range of teaching environments, including socially distanced classrooms, virtual, hybrid, and homeschooling settings. It provides guidance on how to implement and adapt thinking practices to fit 12 distinct settings, offering updated tools, suggestions for unfinished learning, and recommended sequences for each context.
In Mathematics Tasks for the Thinking Classroom, Grades K-5, Liljedahl and Giroux provide practical tasks aligned with the 14 thinking practices. With 20 non-curricular and 30 curricular tasks, this resource offers step-by-step guidance on launching, facilitating, and consolidating math tasks, along with examples of student solutions, teacher prompts, and assessment strategies. The book also includes access to a companion website with downloadable resources and templates to help teachers craft their own thinking tasks.
Together, these resources empower teachers to create engaging, thinking-focused math classrooms that can adapt to any setting, providing students with meaningful learning experiences that enhance their mathematical understanding.
BigSur –
Peter Liljedhahl has written maybe the most important and practical book that just can’t be ignored by teachers of math. As a sixth grade teacher, I have searched for a book that could help me “put it all together” to complete a move away from the repetitive “I do, we do, you do” method of math instruction that is STILL so prevalent in our schools. Even teachers who may have in the past resisted changing their practices because they just weren’t sure how will be able to do it with the help of the practices outlined in his book.
I’m pretty skeptical about a lot of teaching books, because they often leave me disappointed. They are often full of theory and never get practical or explain how the ideas actually worked with real students. Many are “here are some important big ideas now go figure out how that translates into the real practical world of your classroom–good luck!”
What I most appreciate about Building Thinking Classrooms in Mathematics is that Peter’s research comes from having been in the classrooms of many teachers over many years. It’s easy to doubt ideas that come from folks who are “coaches” and don’t live the day-to-day reality of an actual classroom. Peter supports his teaching practices and elaborates on what aspects were shown to be most effective in real classrooms. If you’re a classroom teacher, you’ll know what I mean. He even relates what he thought would happen and is honest about results that either confirmed or changed what he originally thought.
Each chapter is so well-organized (and organized similarly) so that everything is easy to follow. I found myself highlighting key points and then the end of each chapter would have a super helpful summary of the macro-move for the practice and a series of micro-moves. So effective. I have heard of and incorporated several of these practices in the past but nowhere else have I seen a book that pulls so many effective practices together in one place and even organizes them such that the early practices can be incorporated first and then the rest added when ready. I am so grateful I have read this over the summer, as it will greatly influence my practices from day 1 of my upcoming school year.
Peter asks this question at the end of each chapter: “What are some of the things in this chapter that immediately feel correct?” I love that because in almost every instance I thought, “All of it!”
Another tremendous contribution of this book includes a discussion of rubrics and grading, two areas that are often not discussed as much amongst my colleagues and I because we can rarely find consensus and typically revert back to what we’ve always done. Peter’s ideas on rubrics have changed the way I will use them (most rubrics have WAY too much ambiguity to be used effectively by teachers or students or are so cumbersome they are overwhelming). His explanation of an alternative way to construct rubrics make SO much sense and will be helpful. And the grading chapter is an excellent beginning to rethinking how we can give grades (since most of us have to) in a way that will value what is important. I think that will still be the most challenging thing for me–Peter offers one good method of getting data, but it still seems like it could be time-intensive to me. I am more than willing to give it a try, however, because it is much better than the alternative.
As a classroom teacher for almost 30 years, I can truly say without a doubt this book is the BEST in making a complete case for improving math instruction and moving toward a THINKING classroom, and SHOWS YOU HOW. How many times have you thought in your heart, “this practice is probably not the best but I’m so overwhelmed with the day-to-day demands on me as a teacher I can’t figure it out so I’ll just stick with what I’m doing.” I know this has happened to me. This book will help move you into action to change some of those practices!
I am so excited to implement what I have learned this upcoming school year. I want all of my students to view themselves as “thinkers” and enjoy math as much as I do.
If you teach math in any capacity, you owe it to yourself to grab a copy of this book. You’ll be so glad you did.
Rebecca Tees –
I really enjoyed this book and the possibilities it could have for my students. This is the most usable guide for changing the environment of my classroom.The only reason I didn’t give it 5 stars is that when I got to chapter 15 (after marking it up like crazy), I had weird blank squares rather than letters/digits. I want to share this book with coworkers, but this copy isn’t good enough for what I paid. Hopefully I’ll receive an updated and edited version.
Dawn Burgess –
I am a high school math teacher, and I think this book is amazing. I waffled about buying it, since I have read all of Liljedahl’s research papers and followed the thinking classroom movement for years, and had implemented many of his suggestions. Would it really be worth it? Would I learn anything new? The answer is definitely YES. Each chapter is focused on a particular classroom practice, and Liljedahl briefly shares his reasearch process (many, many classroom implementations, and lots of student interviews) and results. Then he shares the specific moves that worked best according to his research. Each chapter has a FAQ section, which usually includes exactly the skeptical questions I would have asked, along with reasonable, specific answers. There is a TON of very clear advice in this book, actionable advice that doesn’t require a lot of money or equipment to implement. It DOES require a willingness to try some new approaches for long enough to see results. I’ve been doing this for four years, and am only growing more convinced that what Liljedahl discovered in his research works in my classrooms as well. I’m reading this book during the summer, and it’s getting me excited for next year, and I see solutions to a few of my teaching difficulties.
Concerned Consumer –
A fantastic addition to Liljedahl’s “Creating Thinking Classrooms!” It provides smart adaptations especially in these times when physical distance is necessary as much as possible.
Kw –
Great and useful ideas for teaching math questions in different formats
Kyle M –
The book came quickly, but not in great condition. The spine has a dent in it, the edges of the pages are curled, and the bottom corner of the cover and first few pages is folded.
Theresa O –
I enjoyed reading this book during the summer. There are good ideas inside backed by research that makes you question the way you been doing things. I’ll take some ideas with me next school year for sure. You should have an open mind and if you read it then that’s the first step.
Laura L. Dalton –
If you want students to think outside of the box you have to remove the box. What we’ve been doing isn’t working. I’m game to try anything. I am looking forward to trying this model in my classroom. I’ll keep what works and modify others. There are some great ideas in this book!
Amy Crum –
Every math teacher should read this book, which describes the biggest and best change I’ve ever made in my teaching! I was stuck in the rut of direct instruction for 30 years, which I now realize did not require my students to think very much as they copied notes and mimicked my methods. Now I have the tools I need to get them thinking for themselves about math, and I feel like my classes, which were half-asleep before, have come alive! Thank you, Peter, for teaching me a better way!
Stacy –
I liked how realistic and relatable the ideas in the book are . Can’t wait to implement some of the concepts .
Katherine Brooks –
This has transformed my classroom, my teaching, and my students! They are thinking more, and they love working at the boards!
Cassandra Hohne –
Many teachers in my district are making BTC moves! Listening to their success stories and challenges have been enlightening.
Leroy Yue –
It is often obvious that traditional teaching method is wrong, but people just don’t know what’s the right thing to do. Everyone is so busy chasing KPIs, no one has the time and energy to reflect on the original purpose of education, then spend energy to figure out a better way. This author’s work is thorough in thinking, creative in the approach, and scientific in establishing better ways with evidence.
Highly recommended not only for math teachers, but also teachers of other subjects, as well as inquisitive parents like me.
School has to be about thinking and creativity, and inspiring kids to want to learn, not rote memorising of procedures and facts which are bound to destroy kids natural ability and desire to learn.
Stephanie Moore –
I had to stop reading after chapter 4 because I didn’t want to consume the entire book in a few short hours. Ye, it is that special.
Stephanie Levy –
This book provides a plethora of suggestions to get your students thinking. My favorite part is the FAQ section of each chapter. It provides real scenarios and real answers to those hard questions about implementing a new teaching philosophy.
Sadie –
There are several fantastic ideas that help teachers to get their students thinking rather than mimicking aka copying what we write on the board. I highly recommend it.
Heidi J. Cohan –
After implementing the first three practices, my students are begging for math tasks when they walk into the classroom each morning. They want to start math early to see what challenge I have for them that day and there’s excitement about who they get to work with on these tasks. There is a new found energy and excitement for our math block now for both me and my students!
Claire E Schwarzentraub –
I am a first year math teacher and read this book in my classes at school. I decided to reread it after student teaching. I plan to implement the practices in my first classroom. There are great examples that make the concepts easier to grasp. There’s also a FAQ section after each chapter which is helpful because a lot of these ideas are new and break the mold of traditional education. I think all teachers should read this because it makes us rethink what education should look like!
Ali F. –
Awesome resource for getting students to THINK rather than mimic! The book is super well laid out. LOTS of great info without feeling overwhelming. I suggest you read his first book first, which is more about the WHY and the HOW TO of BTC with a few tasks to get you started.
Laura –
I did a math book club virtually last summer with Mix & Math 360 where we read Building Thinking Classrooms in Mathematics. I was AMAZED at the difference the BTC mindset had on my classroom of mixed ability learners. The only problem was that everyone that read the book needed to find non-curricular thinking tasks and problems to use alongside the BTC framework, but there weren’t a lot of clear resources to find them.This book is THICK. It’s broken down by grade levels/bands that would be appropriate for different grades. I really appreciate the detail of showing a range of grades for each task, and how the level of difficulty reduces for each consecutive grade using that same task. It’s essentially a breakdown of how challenging any given problem will be for the typically developing math classroom. If you wanted to focus on building your TBC routines at the beginning of the year, you could choose some problems from their previous year to build confidence in the new math strategies. If you teach a group of advanced learners, you can find problems that will be more challenging for your students.Building Thinking Classrooms is all about, you guessed it, getting students to -actually- think about what they are doing to learn math in a more holistic way, and moves away from “plug and chug” answer-centered computation. Mathematics Tasks will help educators have a streamlined resource to help us break away from individual, paper and pencil work to build the math literacy our student deserve. We are the ones that need to change and grow our thinking about math teaching to truly help all of our students bloom. Yay, math! (Never did I think I’d say that 25 years ago! 😉)P.S. hot tip for building your random daily groupings: I use a deck of SushiGo! cards that I organized in sets of three cards for each type. I keep them in a ziplock bag on my desk, I count how many groups of three I need each morning, grab that many sets of cards, lightly shuffle, and pass them out face down. The kids love finding and matching up with their other sushi partners! Second tip: Always have your groups hand back their cards in the set of three so they are always matched up and ready to rock each morning. Happy math teaching! 🤓💕
Nancy Murphy –
Waited for this one! Love using the thinking classroom in my fifth grade class. Gets the scholars collaborating and sharing their thinking while building their understanding and knowledge
Nicole Anderson –
This was an easy read with researched techniques to help students think for themselves mathematically. It also looks to combat some of the misconceptions about learning mathematics.
Amber –
I am not a teacher of grades K-5 but this book was extremely useful since part 1 about updates or clarifications to BTC practices. I had some minor issues after the original book and all of those were addressed in part 1 of this book.
Busy Lady –
It is extremely helpful to teach math in a whole new way that is fun and gets kids thinking. They learn to work with peers to find answers and learn critical thinking skills while having fun.
Dinna Spradlin –
I read Building Thinking Classrooms two years ago and it revolutionized my teaching style. This companion book is just as wonderful. I teach high school math, and even though this book is written for K-5, I’ve already found many ways I will use the tasks and information given.
ChrisInCali –
There is a A TON of useful information in this book for math teachers. Very easy to read and so many useful techniques to try! 100% worth buying!
Loraine Hallberg –
Packaging is good. Book in perfect condition.
Danelle –
Peter Liljedahl’s Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning is an essential guide for educators aiming to foster critical thinking in math. The book presents 14 research-based practices that transform traditional classrooms into engaging environments where students collaborate and tackle real problems. By prioritizing student-centered learning, Liljedahl equips teachers with practical strategies to enhance student engagement and deepen mathematical understanding. A must-read for anyone looking to invigorate their math instruction!
Kelly Leguizamon –
I teach middle school and still found the tasks useful, but above all the updates to many of the practices here were very valuable. Especially the updates to the Meaningful Notes, the process here was much more useful than in the red book and has been successful with my 7th and 8th graders.
Alison –
We need more of this kind of research to give the entire education “system” an overhaul!