How the Building Thinking Classrooms' 14 teaching practices can transform your math instruction
Dr. Peter Liljedahl is a Professor of Mathematics Education at Simon Fraser University in Vancouver, Canada. Peter has authored or coauthored numerous books, book chapters, and journal articles on topics central to the teaching and learning of mathematics, and is most known as the author of the global phenomenon Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning.
When I first began reading about Peter’s 14 practices, I knew Building Thinking Classrooms was special. In terms of transformation of the math classroom, nothing - and I do mean nothing - has jumped out to me in educational research to be as effectual in fixing the problems faced by teachers on a daily basis. And, I also quickly realized that his ideas blended seamlessly with the pedagogy behind our Core Curriculum with instructional moves that would supercharge implementation of MidSchoolMath. I had the chance to sit down with Peter to dive deeper into his work.
MSM: We’ve been working with thousands of teachers across the country, and everywhere we go, people are talking Building Thinking Classrooms. Why do you think districts are so excited?
PL: My theory is this: There are a lot of really good ideas in math education, right? Like, promoting problem-based learning, problem-solving, inquiry, and numeracy. But the challenge has always been that we've tried to implement them inside of a space that hasn't changed in 150 years. We're trying to do 21st century pedagogy inside of a 19th century classroom.
And from the student perspective, what's happening is we're asking them to behave differently in a setting that throughout their entire career has told them to behave a certain way.
I think what Building Thinking Classrooms did was tackle the environment. It actually looks at the conditions that are necessary for collaborating, thinking, problem solving, reasoning, persevering, and entering into productive struggle based on what, we as teachers, have to do differently inside of the environment. And I think teachers who have a passion for implementing the Building Thinking Classrooms practices can then implement some of the really good ideas in math education.
MSM: Is there one primary thought or piece of research that underlies the Building Thinking Classrooms practices?
PL: I would say there are two. Number one: If students are not thinking, they're not learning, period. This is not my idea. This has existed for decades. We've known this, right? Students need to be actively and cognitively present in order for learning to happen. Of course, there's something to be said for immersion and passive learning and so forth, but not the kinds of analytic, critical, and creative thinking that we need students to do. They need to be cognitively present and actively involved in order for that to happen.
Number two: What we do as a teacher has an impact on what students do as learners. We have to start to recognize that our actions have important consequences on what students do in the classroom in ways that are explicit and implicit. And one of the things that kept coming up over and over again in the data was that students don't listen to what we say.
And what is that communicating to kids? What kind of expectations and norms are being communicated through what we do? What values are being communicated through what we do? When we look at student behavior and ask ourselves, what is it that we're doing as a teacher to create that behavior? And what can we do differently? What do we have to do to create the behavior we want to see?
MSM: What’s your best, most convincing, response to the phrase “My students can’t do that”?
PL: What I say is I've been in 160 different classrooms in the last two years, and we've made it work in every one of them. I find it difficult for you to convince me that your collection of students is inherently so much more different than any of those that we've encountered. But I don't think teachers are wrong when they say that, right?
Two things are true at the same time. Number one, I think their students are very much like every other group of students we've ever encountered. And number two, I do believe that they believe that their students can't do it.
Now, why would they believe that they can't do it? Because they have no recent evidence to indicate that they can. All of our judgment of students is based on what they show us on a day-to-day basis. But we come back to what we talked about previously. What our students are showing us is really a reflection of what we're doing, right?
But nonetheless, students are showing us that they're incapable, that they've got learned helplessness, that they are apathetic, they're uninterested, they're incapable, they don't know their basic facts, they don't know how to persevere.
But the reality is that they've shown me that in environment A. And environment A has incentivized those sorts of behaviors. In many cases, it's rewarded those types of behaviors. And in many ways, it's created those behaviors.
But what if we put them into environment B? Because who students are in our classroom is a product of who we are as a teacher and the environment that we create in the classroom and the environment we create in the school.
I think this is the greatest strength of Building Thinking Classrooms is the tasks and the practices for teachers to try in their classrooms. Then they see how their students are different. And then they can say, “Oh, my students can do that!”
MSM: You also encourage teachers to “push questions back at students along with walking away" as an instructional move?
PL: So, the idea of walking away serves a whole bunch of purposes, right? At its outset, notice that, especially when you give students a hint, if you linger, you make them very uncomfortable. A hint is supposed to be cryptic. They actually need to talk with each other to process what you just said. You need to give the hint and walk away and give them processing time.
Then come back, see if the hint landed. If it doesn't, you can give another hint. If it did land, you just keep moving. One of the hardest things to do as a teacher is to not answer questions, right? We want to be helpful.
Walking away is a form of forcing function. By me walking away, it forces me not to help. And what does it communicate to kids? To drop a hint and walk away sends a clear message: “I believe you can do this.” And it's also sort of a signal. The last thing that was said was really important. You guys should talk about that a bit more.
MSM: What advice do you have for teachers when they are giving students tasks?
PL: We don't want the task to give too much away at the beginning to make sure that everyone can be successful. So, we've got to hold a lot of cards back. But then to compensate for that, we need to have the teacher be present and be ready to step in and support and extend and provide hints where necessary so that everyone can have a positive experience with the task.
Tasks are inert. No matter how good the task is, it is still inert. It takes pedagogy to bring it to life and it takes a teacher to keep it alive.
MSM: At MidSchoolMath, we use film and a rich, narrative story to deliver tasks to students. Have you done any research on the impact of story?
PL: Love it. Yeah, I really do. So, one of the books that I wrote a long time ago that nobody reads is called Teaching Math through Storytelling. The role of story and narrative are really valuable. What story does is it hooks a student, because it gives students context. It personalizes, contextualizes, and temporalizes things.
Let’s juxtapose that against a classic word problem. Mary went to the store to buy some eggs, milk, and cheese, right? Eggs are $3, milk is $4, and cheese is $5. How much money will Mary need? Well, the answer to that question is: apparently she doesn't need any money because she already went to the store!
So that story is depersonalized. Who is Mary? Like, is Mary a child? Is she my age? What's she doing buying cheese? Like, what child my age buys cheese, right? The story is also completely decontextualized. How far is this store? And the story is de-temporalized and we really don't care about it. We just want you to care about the numbers in the story.
Storytelling is doing the opposite. The narrative comes out in the mathematics and how problems are solved.
Now, why did 'story' not make it into my book? I had enough data to show that it could have been. Why was ‘story’ not the 15th pedagogical practice?
MSM: How do visual solutions promote a thinking classroom?
PL: I'm a huge fan of visual solutions. But it's not just visual. Let's call it register-specific solutions, right? What are the comfortable mediums through which a student can articulate their thinking and their solution that are specific to them? For example, this tension between chronological and logical is really about register. Students are much more adept at communicating in chronological ways and logical ways.
How can they communicate their thinking not just in terms of the solution but how can they communicate their thinking to each other when they're working together? And you know text isn't going to be it. Symbolic may not be it. We have to think about this as multi-modality. And it's what the student themselves use as a medium to help cue up their own thinking.
MSM: Which Building Thinking Classrooms practice do you believe has the most impact?
PL: Depending on what we're talking about, it's a different answer, right? I think that formative assessment is one of the most powerful tools we can give students to help them with their own learning. I often say if you do nothing else in my book, do that because the greatest inequity in education is not the inequity between students, it's the inequity between the teacher and the students. Why should teachers have all the knowledge of what students are capable of? We need to put that power into the hands of the students.
But I still hold that the most important practice is using visibly random groups when implemented consistently. What visible random grouping does is communicate to students that we believe in all of you. We think you're all capable. And it communicates it through our actions, not through our words.
What random groups does is it builds community and community unlocks empathy. And when that happens, we start to see that real collaboration doesn't actually begin until students care as much about their peers' learning as their own learning.
When that happens, we can actually get on with the learning. It is the engine that drives everything.
MSM: What is one of your favorite stories about how the Building Thinking Classrooms practices transformed the classroom?
PL: I have so many. I'll tell a story about Alex. Just a little over 10 years ago, I presented at the Canadian Math Education Forum. It was a collection of teachers, mathematicians, math education researchers and leaders. So, Alex is a math teacher. Alex was at the forum for the very first time I presented on Building Thinking Classrooms.
Alex talked to me after the session. At the time he introduced himself as being three years away from retirement. That was 2014. I saw him about three months ago. And he's now three years from retirement! It's been fun for me to hear those stories. Like, I was going to retire. And now this has given me that life.
