Building thinking classrooms in mathematics

A conversation with Peter Liljedahl

Most efforts to reform or improve mathematics education in the last several decades did not question the traditional structure of the classroom: teachers at the front and students sitting at desks. Based on 15 years of intensive research in K-12 math classrooms, Peter Liljedahl discovered that if math teachers were going to help students think and not simply mimic the teacher or disengage from the lesson, the structure had to change.

A professor of education at Simon Fraser University in British Columbia, Liljedahl published the results of his research in his 2020 book, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning.

For the last two years, the Olympic athlete (in canoeing) turned math teacher turned education professor has been traveling to school districts in the U.S. and Canada, training teachers on how to bring thinking classrooms practices to their schools.

Phi Delta Kappan spoke with Liljedahl about disrupting classroom norms, how to tell if students are thinking and not mimicking, and why his training resonates for teachers.

PHI DELTA KAPPAN: Your book was published in 2020 during the pandemic. How do you think that affected the response?

LILJEDAHL: The book on face-to-face teaching was released in the middle of a lockdown during the pandemic. At the time, I thought it was a disaster, but in hindsight, I think it may have actually been a great timing, because as they were going back to face-to-face teaching, teachers wanted something different.

There is something else going on, too. Math education for the last 50 years has been on a journey. The field has been trying to revolutionize and revise the way teaching and learning happens in the math classroom. There’s been a concerted effort from the entire community of math educators everywhere — everyone is working on this. There have been all these amazing initiatives going on. Teachers all over the world are trying to revise their practice and change things.

But in every initiative one nonnegotiable has been that the normative construct of a classroom will remain unchanged. Maybe we’re going to do small things, like collaboration or technology integration. But the assumptions that the teacher is going to be standing, the students are going to be sitting, the teacher is going to be writing on the board, and the students are going to write in their notebooks have never really been challenged.

The problem with these institutional norms was that when students walk into a classroom that looks like every other classroom, they’re going to behave the same. Even if you’re doing something really progressive or interesting or innovative, the students are behaving the same. Then Building Thinking Classrooms comes along and says, “Hey, maybe we can just change the way things happen in the classroom a little bit,” and suddenly, the floodgates open. These other amazing initiatives are easier to implement. Prior to that, they were swimming against the current of institutional norms. Thinking Classrooms showed teachers how to transform the workspace of the classroom, and then the other things they were trying to do became easier.

KAPPAN: How did you become interested in doing this research?

LILJEDAHL: While I was doing my Ph.D., a teacher named Jane contacted me. She wanted me to come in and help her implement problem solving in her classroom. Problem solving [a teaching method that encourages students to solve complex problems by integrating knowledge and perspectives from different areas] was on the horizon in our curriculum in British Columbia and Canada. Jane was a generalist middle school teacher, and she had worked on pretty much every aspect of her practice except math, so she asked if I could help her. I spent a week in her classroom trying to help her implement problem solving, and it was disaster after disaster after disaster. Jane was tenacious, but in the end, we finally decided this wasn’t working.

But then I spent a lot of time observing in her classroom, just trying to understand what happens in her space that made this not work. And what emerged from those observations was a realization that her students were not thinking. They were busy. She kept them very busy, but they weren’t thinking, not in the way we know students need to. There was a lot of mimicking, a lot of “I do, we do, you do.”

Those observations turned into a project where I visited 40 different K-12 classrooms in tons of different settings. I kept seeing the same thing: kids not thinking. We talk about teaching, and we talk about learning, but there’s a facade that students project toward a teacher that includes all these other activities, in addition to learning. I turned my observations into an empirical study, which revealed that only about 20% of students are spending 20% of their time thinking, and the other 80% are spending their time moving between behaviors, such as stalling, slacking, faking, and mimicking. The vast majority — 50% — were mimicking. This research was 20 years ago. Just last year, a researcher redid that research in some settings in Australia and found almost the exact same percentages.

When I did my research, everywhere I went, classrooms conformed to a really narrow sense of institutional norms that were largely unchanged in the last 170 years. If everywhere I go, I see these institutional norms, and everywhere I go, I see students not thinking, then if I want students to think, I’m going to have to break these norms. How do we break norms and see if it has an impact on student thinking?

Building Thinking Classrooms came from 15 years of research into trying to find a set of practices, a set of things that we could do differently inside our classrooms. We’re still going to stay inside the four walls of the classroom. We’re still going to stay on the same bell schedule. But what are the things that we can do differently inside of those walls in that time to increase student thinking, get more students thinking, get them thinking for longer?

KAPPAN: What does a thinking classroom look like?

LILJEDAHL: The book is called Building Thinking Classrooms. It’s not called Shazam: You Have a Thinking Classroom. You have to build it. We start building with the first practices in the book.

First, we need a thinking task, where the students really have to think, and where mimicking is not possible. The second thing we need to do is to give them someone to work with, and that comes in the form of a collaborative group. The big thing in Building Thinking Classrooms that the data revealed is that those groups must be chosen at random, they have to be visibly random, and they have to be small groups — groups of three were optimal. Students are going to pull a card that determines their group and then they’re going to work on vertical whiteboards. They don’t have to be whiteboards; they just have to be vertical and erasable.

This is a massive revision to the way a classroom normally functions. In the institutional, normative structure of school, the teacher says, “Let me show you how to do it. Now you do it.” That sets up mimicking. In a thinking classroom, the teacher says, “I’m going to give you a task. You’re going to have to think about it, so I’m not going to do it first.” That’s different from what students are used to. Getting them standing and working on a vertical whiteboard like this is a big departure. When you walk by a thinking classroom, there’s no mistaking it, compared to when you walk by a classroom where the students are sitting at their desks.

KAPPAN: Why is random grouping important?

LILJEDAHL: The normative structures that teachers use are either strategic groups or self-selected groups, and you need to disrupt that. Randomness was pretty much the only other thing we could do, so we experimented with randomness. It had to be visibly random, and for it to work better, it had to be re-randomized about every 45 to 75 minutes. So now we ended up with these visibly random groups and we got an empirical result that is reproducible.

When we used those types of groupings, students went into their groups willing to offer an idea. That was the big data point. When we used strategic groupings or self-selected groupings, 80% of students went into those groups either unlikely or highly unlikely to offer an idea, because they knew that their role was to follow. But after three weeks of randomness, 100% of students were going into their groups either likely or highly likely to offer an idea.

Now the question is: Why? Well, there were a whole bunch of things going on. One, they didn’t know what their role was. So they were not going in predisposed to follow. Another one was they had greater self-efficacy in these settings. They said things like, “my teacher thinks we’re all capable. Otherwise, they wouldn’t do random groups.” Whereas, when we were doing strategic grouping, the students knew exactly what role you were casting for them. “My teacher thinks I’m not very good. That’s why they’re putting me with so-and-so.” And then they just lived down to those expectations. It became a self-
fulfilling prophecy.

KAPPAN: And students being vertical?

LILJEDAHL: Kids are used to sitting and working at their desks. How do we innovate on that? We could have them work on big flip chart paper at their desks, or whiteboards at their desks. Then we can try those vertically. We tried all these different things. Having them stand and work at the vertical whiteboards was by far the best, and was a reproducible result. It was transformative.

Why is this such an optimal workspace? What is it about the fact that it’s erasable? Turns out that students don’t feel at risk when it’s erasable. They’re more likely to start. They’re not worried about making mistakes, so that we can get onto that behavior of thinking bigger. When they were working on, for example, vertical flip chart paper, there was a “non-start” behavior where they said, “We don’t know what the answer is yet, so we can’t put anything down.” They were afraid to write anything unless it was perfect. But it couldn’t be perfect unless they wrote something. And it created this sort of negative feedback loop.

But then why vertical? Why was it so much better than having [the workspace] horizontal? When it was horizontal, somebody owned the work because it was oriented to them, and everybody else was looking at it sideways, so there was sort of a clear leader. When it was vertical, everyone was oriented toward it the same way. They had more of a shared perception of the work, that it’s ours. When it was vertical, they could see other groups’ work, which promoted knowledge mobility. When they got stuck, they had access to other ideas. When it was vertical, it was easier to teach, and the teacher was more aware of what was going on: “I don’t have to wait for that quiz on Friday to see if my students understand. I can see right now who understands and who doesn’t. I can push in with intervention, directly and immediately where it’s needed.”

But all these things were eclipsed by one interesting piece of data, and it took a long time for this data to emerge. I would interview the students, and it felt like there was something else happening. And finally, it started to reveal itself. Students said, “Well, I can’t hide when I’m at the whiteboard.” You dig deeper into this, and it turns out that when students are sitting, they feel anonymous. The further they sit from the teacher, the more anonymous they feel. When students feel anonymous, they are more likely to disengage. And the more anonymous they feel, the more likely they are to disengage. Standing up took away that anonymity, and not in a way that made students feel exposed. I’m not anonymous, and I’m not invisible. If I’m not invisible, I’m less likely to disengage. This was a huge shift.

KAPPAN: What are the teachers doing in this classroom?

LILJEDAHL: You have to plan differently for a thinking classroom, because you have to think about how to launch the task and what sequence of tasks to give the students as they’re ready for them.

Once the lessons are up and running, they’re doing what I call working the room. They are monitoring and intervening with support and extensions. That support can be as minor as a hint, but it can also be stepping into this group and providing a little bit of direct instruction. It’s a very effective form of differentiation. What do students need right now? So, this group needs a hint. This group needs to talk to another group. This group needs a little bit of direct instruction on this, and this group needs an extension. You’re managing that space for about two-thirds of the lesson as the students are working at the whiteboard.

We cover tremendous amounts of content. When I co-teach with a teacher, we lay out all the topics that they have to teach that week. And we usually get through anywhere from three to five lessons of content within a thinking classroom lesson. Because the kids are thinking, so much learning can happen. When they’re not thinking, everything is difficult. It takes a long time, and they don’t retain it. The baseline data showed 20% of students are thinking for 20% of the time. Imagine how hard teaching and learning is in a space like that, versus where 93% of students are thinking for 100% of the time. Just think about how much more learning can happen in those spaces.

This article appears in the December 2024 issue of Kappan, Vol. 106, No. 4, p. 32-35.