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

by Peter Liljedahl

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

Genres: Education, Teaching, Mathematics, Nonfiction, School, Teachers, Parenting

344 pages, Paperback

Published October 30, 2020

Reviews

[Laura Wheeler · Rating 5 out of 5]

The Thinking Classroom framework transformed by 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 (don't wait for September to try this!) and next steps to continue incorporating as my practice evolved with the 14 elements Liljedahl proposes. Students began to talk to each other, think through complex problems, rely less on me & more on each other and best of all had better success in the course. This book taught me so much even though I'd already been using the Thinking Classroom framework for years; especially around assessment and evaluation. And I've used the Thinking Classroom framework in subjects like Leadership and Teacher Education; it's not just for Math teachers. This is a must-read for all teachers!
(Full disclosure - I am the illustrator of this book)

[Maxwell · Rating 5 out of 5]

The future of mathematics education.

[Patrick · Rating 4 out of 5]

A worthwhile read for any math teacher!

The organization of the chapters -- defining the issue and the problem, discussing potential solutions, and then summarizing with tangible next steps -- will appeal to many readers. And many of the suggestions will challenge teachers' conventional assumptions of effective teaching.

I found the first couple of chapters to be the strongest! I'll definitely be explicit about the distinction between "mimicking" and "thinking" with my students. I also really liked the suggested use of visuals in the chapters about note-taking and formative assessment. Some other chapters, however, left me wanting more explicit discussion of the research, and the chapter on homework was bizarrely thin and superficial 🤷🏾‍♂️

Anyways, always glad to get the teaching brain going again before the school year :)

[Marissa · Rating 1 out of 5]

This/ constructivism/ inquiry based/ whatever you want to call it will ruin math education much like Lucy Calkins and F&P did for literacy.

[Natalia · Rating 4 out of 5]

To be honest, I thought it would be boring and wanted to force myself through, instead, it was very insightful.

[Alexis · Rating 5 out of 5]

Mathematics education researcher Peter Liljedahl recognized that how we teach math doesn’t work, so he set out to do the opposite of our current flawed practices. Over the course of 15 years, he collected what he found and refined in hundreds of classrooms. This book offers the 14 macro-practices, the accompanying micro-practices, their results, and their explanations, along with a fifteenth chapter about the most effective order of implementation of those practices.

This might be the best PD book I’ve ever read. It’s incredibly practical, but it is also challenging. Even though it’s written for math teachers, the framework can definitely be adapted to any content area. I partially think this was such a good read because it came at just the right time in my career. I already tried implementing some aspects of the framework last year and saw massive results, but I also feel like a lot of the more “progressive” aspects of the Building Thinking Classroom Framework are ones that I’ve already wrestled with and adapted as I’ve been teaching. For example, one of the later practices is about evaluating what we value, like the transferable skills of perseverance, risk-taking, and collaboration. I’ve already started making that shift in my classroom, but I can see how if you are completely new to the idea of standards-based grading, evaluating non-content specific skills might be such a huge leap that you feel immediately intimidated or turned off to the framework at all. But I also think this book is still for you. Liljedahl breaks down where to start and why and makes it clear how you can work your way into this framework if it is a complete overhaul of your current practices. No matter where you are in your pedagogical journey, I think the BTC framework genuinely has something to offer you that will challenge you and help you move the needle in your class. I know I sound like an evangelist but I really think the system in this book is that impactful.

[Kyle Berry · Rating 3 out of 5]

The author observed 40 classrooms - really, he wants you to know it was 40 - and identified barriers, caused by the designs of the room and the curriculum, to “thinking”. He offers strategies that help take down these barriers.

Pros: The author creates some useful verbiage that teachers can use, such as “Studenting”, “Mimicking”, and “Stop thinking questions”. Some of the strategies, such as using vertical whiteboards, are useful, as are some of the thinking tasks.

Cons: There is very little in this book that would be new to a teacher with a decade or so in teaching. De-centered workspaces with vertical writing surfaces were obviously cribbed from Silicon Valley conference rooms. An endless amount of thinking problems have been available online for years. Most all of the barriers to thinking are well known to teachers; giving them a new term doesn’t help much. The book is rather light on references to the literature, especially if you subtract his self-references. I have books that are half as think that use two or three times as much evidence to support their claims. It feels a bit like “Mindset” all over again.

Your students will enjoy the novelty of the activities, and you’ll rush on to social media to share pictures of your “thinking classroom” as so many have already. Once the novelty wears off, time will tell how much this will actually improve your classroom.

It’s worth a read, especially if you are a new or student teacher, but don’t expect a revolution except that of imagination about how students might be doing.

[North Landesman · Rating 2 out of 5]

Building Thinking Classrooms is a popular book right now in mathematics education. Liljedahl has some excellent points. Students do not think enough in school. His chapters on answering questions, note taking, and homework make intelligent points.
His overall premise that engagement and thinking are more important than learning that can be shown in a test does not make sense to me. He derides much of learning as "mimicking," but much of human learning is mimicking.
Pershan makes the point that all of his "research" is about engagement, not actual learning. He measures how students feel, but I don't see them judged by any objective standards.

[Cassie Benedict · Rating 4 out of 5]

There has never been a book that I both simultaneously, wholeheartedly agree with yet want to argue and debate the ideas within.

I look forward to figuring out how these concepts will work for me and my classroom.

This is an important book for math educators. Read it.

[Nicole · Rating 4 out of 5]

Like most educational theory books, I think this should’ve been a very long article instead of a book. Always a lot of filler to get the page count. Anyway, I can honestly say this book changed my teaching practice and made me reconsider some long held beliefs. So big win on that.
I also really like the author on a personality level. Listened to him speak and LOVED his demeanour, while others I work with found him abrupt. He’s definitely an enneagram 8. lol. DIRECT!

[John Kusmec · Rating 5 out of 5]

I’ve been trying to keep work out of my home, but I routinely found myself sitting in my favorite chair to read this because it didn’t feel like work. I’m very excited to try some of these principles in my classroom this year and plan on circling back to this review with results from class.

[Julianne · Rating 5 out of 5]

WOW. 🤯

Peter Liljedahl needs to meet Donalyn Miller.

[Allison Dietze · Rating 5 out of 5]

A must read for any math teacher!

[Zosia Kuflikowska · Rating 5 out of 5]

5 / 5
To jest jedna z takich książek, które zmieniają życie. Czytana w wersji polskiej, wydana przez Szkołę Edukacji, ale jako że tłumaczenia na Goodreads ani na rynku nie ma, zaznaczyłam oryginał.
Nie umiem opisać tego, jak ta książka zmieniła moje podejście do nauczania. Jak wywróciła dotychczasową wiedzę na temat edukacji matematycznej do góry nogami. Oparta na wieloletnich badaniach, konfrontująca wszystkie niewygodne wnioski: dla kogo ma się uczyć uczeń? Co tak naprawdę powinien umieć? Jak stworzyć klasę, która zachęca do myślenia, a nie wkuwania schematów? Coś wspaniałego.
Dla osób zainteresowanych tematem: mogę książkę pożyczyć. Koniecznie musi do mnie wrócić, bo jest dla mnie ważna, ale na względnie krótki czas mogę się z nią rozstać ;))

[Shelby Bernadette · Rating 5 out of 5]

Such a great PD read, I especially liked the candidness of the FAQ questions at the end of each chapter and the summary Macro and Micro moves. Best chapters were 1, 2, 5, 6, & 8.

[Heidi Green · Rating 2 out of 5]

This is actually the 2nd time I’ve read this book… I tried a second time to see if I was being unfair the first time I read it. I may be the only person that does not like this book, but I think the tips could’ve been shared in a pamphlet and the author(and his fans) act like this is the end all be all to increase thinking in the classroom. Whereas, in reality, it’s just a few tips to increase engagement and that can be done in a variety of different ways. I don’t think the ideas are bad, they’re just no magic bullet and it really bothers me when people in education say things are evidence based when the “evidence” is anecdotal.

[Kara Leenas · Rating 4 out of 5]

Yes I had to read this for work and yes it is counting toward my reading challenge

[Tracy Renee · Rating 5 out of 5]

This book is revolutionizing the mathematics classroom. Turns out the traditional way we have been teaching math for a century isn’t the most conducive to thinking. This book lays out 15 years of research showing how implementing 14 practices that shift the norms of the math classroom will build thinking individuals. What this book describes is very similar to what companies do in their creative rooms when brainstorming the next device or program. I love this book, and am excited to implement the practices of the Thinking Classroom when I return to work.

[Kyle Webb · Rating 5 out of 5]

Who knew how little actual thinking was happening classrooms?

This book is an absolute game changer for teaching math (and can certainly be applied to other subject areas). If you know a teacher, are a teacher, or have children taught by a teacher this book is worth your time.

This book is easy to read and the 14 practices are realistic for teachers to implement and are backed by extensive research.

[Amber · Rating 5 out of 5]

This book is life changing if you are any kind of math teacher. I have implemented the first 3 practices and already see huge changes in my students. I read it right before returning to in-person learning for the first time in over a year and it really helped set the tone for class and get me excited to try something new.

[Eco · Rating 3 out of 5]

PD book.
Definitely could have done this in a pre-COVID classroom. A bit harder now that students refuse to learn. I see it plausible again when the new crop reaches 7th grade in 2029.
Sad to say we have a lost segment of the current generation going through school right now.

[Anna · Rating 4 out of 5]

I like this book. Some of his ideas challenge my experience as an educator, but I want to try out his ideas for myself and see if I can create greater growth in my students
Chapter summary:
1. Start a lesson with an engaging non-curricular task. (examples on p. 21, 80,96,99,116,143,168, 185, 206, 227)
a. transition to scripted curriculum thinking tasks. Begin by asking a question about prior knowledge and encourages an extension of that knowledge. Ask students to do something without telling them how.
2. Establish random collaborative groups. In K-2 form groups of 2, grades 3-12 form groups of 3.
3. Use vertical non-permanent surfaces. (Have one marker per group and the person with the marker is taking notes of what others said. Rotate so everyone has a chance to write. Don't erase wrong work. Value wrong ideas.)
4. Defront the classroom. Cluster desks and tables away from vertical surfaces. Move around the room when you are talking to students. Position desks and tables so chairs point in different directions.
5. Answer only keep-thinking questions. When asked a proximity or stop thinking question that you do not want to answer, answer with a question like, Show me how you did that? Why don't you try another one? Explain the three types of questions to students p85-87.
6. Give the first thinking task in the first five minutes after you begin the lesson. Have students stand to work on vertical surfaces. Give instructions verbally. Create locations in the room for students to stand comfortably in groups.
7. Homework gives students an opportunity to check their understanding on their own.Use phrases like this is your opportunity. Provide worked solutions a day or so after giving check your understanding questions.
8. Mobilize knowledge and have groups see what others are doing. Model active interactions by suggesting groups talk to each other
9. Build and maintain flow by offering challenges, extensions and hints. Make groups responsible for the learning of every member of the group. Start with low challenge tasks, and create sequences of tasks that are incrementally more challenging.
10. Consolidate the tasks. Use a red marker to draw a box around student thinking.Use hints to get missing ideas on vertical surfaces. Keep the students standing and walking around to other student work. Do not let students present their own work.
11. Have students make meaningfu notes with a graphic organizer with ideas undefined. Emphasize notes are meaningful by them for them. Prompt students to write notes to their future forgetful selves. Emphasize the importance of worked examples and annotate incorrect examples. Give students tasks where they can use their notes a few weeks later.
12. Evaluating work. Example rubric p 212. Evaluate what you value and create T charts with students showing continuum of growth. Assess one competency at a time.
13. Help students see where they are and where they are going. Use a navigation instrument p 235
14. Grading in a thinking classroom. Grade based on data. Create instruments that delineate complexity levels. Gather observational and conversational data. Organize tests so basic questions are on the first page.

[Kelly · Rating 5 out of 5]

A must-read for all educators who teach math! This book was created after years of research in several different classrooms with the end goal of getting students to think, which results in getting students to learn. The book is well-organized and addresses several questions from teachers at the end of each chapter. I’m looking forward to implementing these strategies in my classroom. I found myself thinking about so many of my students while reading this book. There were several ideas and passages that I highlighted throughout the book and here is one of my favorite:

“We accepted the idea of differentiated instruction a long time ago because we recognized that all students are different. If this is true, then we must also accept the idea of differentiated assessment.” (p. 275)

[Meghan Bruns · Rating 4 out of 5]

“We have to also create a culture where thinking is not only valued but also necessitated—we have to build a thinking classroom.” -Peter Liljedahl

This book, along with the math course I took with it, has changed my math teaching practices in the best way possible. Through 14 teaching practices, I was able to implement a number of strategies to engage my students in my favorite subject ever: MATH. Students in my past two years of classes (while implementing) have gone from moaning and groaning about math to asking if we can “use the boards” or “get our cards” to find partners and work together. Makes my mathematics-loving heart so warm. ☺️

[Ellen Deckinga · Rating 5 out of 5]

As an ELA teacher, this book is phenomenal in building systems for learning no matter the content area. Implementing any of these practices will have an impact on student learning and productivity. I started the year with thinking tasks and vertical surfaces. Kids say they enjoy my class and I can see the high levels of thinking in their conversations and work. It’s a win / win. In addition to this, these strategies work well with other instructional practices such as workshop and Patterns of Power.

[Lindy · Rating 5 out of 5]

This book was exciting and affirming. It takes so many of the math teaching practices I know to be effective and helped me organize and grow them, for myself and for my students. Unlike lots of professional development (often taught by people with very little classroom experience, disconnected from reality, and added to the already full plates of teachers), Peter Liljedahl has spent time in classrooms. He respects the work of students and teachers. Last year, I implemented the first 5 practices and saw immediate results. I'm so excited to take on more this year!

[Elissa Granger · Rating 5 out of 5]

I'm not one for reading a lot of educational strategies books, but I read this for a math networking workshop I attended. The practices laid out in this book are phenomenal, and I honestly wish I had been introduced to this at the beginning of my teaching career. Throughout this year, I've been trying to culminate a Thinking Classroom, but this book has me very excited for next year to start off with these practices and really hone in on my students' thinking capabilities.

[Alexa · Rating 5 out of 5]

Absolutely incredible book for math teachers that provides buildable and very easy to implement techniques into the math lesson! I love the creativity and science behind building thinking classrooms. If you're reading this as a math teacher, you'll find yourself shaking your head yes to so many struggles of this book. Do yourself and your students a favor. Don't just read it, implement it.

"Problem solving is what we do when we don't know what to do."

[Sydney Roberts · Rating 5 out of 5]

BTC is a game changer. I’m excited (and a bit nervous) to start using these practices in my math class this fall. The ideas are practical, research-based, and supported by an amazing online community of educators.

The only part that didn’t quite work for me was the grading chapter. It’s tough to apply with my school’s grade book requirements. Still, I’m planning to explore how others are adapting it.

Highly recommend for any math teacher ready to rethink their classroom!

[Ella Ibañez · Rating 5 out of 5]

Well organized and very concrete book about how to create a thinking classroom in a math class. Super excited to implement all these ideas in the next school year. Highly recommend to all math teachers!