Math is Figure-Out-Able with Pam Harris

Ep 157: Building Thinking Classrooms

June 20, 2023 Pam Harris Episode 157
Math is Figure-Out-Able with Pam Harris
Ep 157: Building Thinking Classrooms
Show Notes Transcript

We want our students to be confident problem solvers who can think and reason through complex problems. In this episode, Pam and Kim highlight some of Dr. Peter Liljedahl's work on Building Thinking Classrooms to use student's natural inclinations to help them work better and more collaboratively. 
Talking Points:
It's about thinking, not mimicking

  • Thinking Tasks not mimicking tasks
  • Vertical Non Permanent Surfaces
  • Visibly random groups
  • It takes time for kids to accept working in random groups
  • Pulse of the room: Are student's opting out? What math are groups using?
  • The "how " is important, but so is the "what"

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Pam  00:01

Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able! I'm Pam. 


Kim  00:07

And I'm Kim. 


Pam  00:09

And you found a place where math is not about memorizing and mimicking, waiting to be told or shown what to do. But it's about sense making, noticing patterns, and reasoning using mathematical relationships. We can mentor students to think and reason like mathematicians. Not only are algorithms and step-by-step procedures not particularly helpful in teaching mathematics. But rotely repeating those steps actually keep students from being the mathematicians they can be.


Kim  00:39

We have a huge topic today. Super big. Big, big topic. Building Thinking Classrooms and Peter Liljedhal's work is super popular in education circles. He gets brought up quite a bit. And we have actually done quite a bit of his stuff, right? And have found success with his research and his ideas, and so we wanted to talk a bit about that today.


Pam  01:03

Yeah, excellent. Just recently in our state conference, the conference for the Advancement of Mathematics Teaching here in Texas, I was able to hear him again. I've heard him several times.


Kim  01:14



Pam  01:15

And the first time that I heard him speak, it was super interesting because his first chapter, and least when I've heard him speak...usually his first thing that he talks about, is how we're not thinking in classrooms. So, like his book is called Building Thinking Classrooms. And he talks about how what he saw when he went into these classrooms is mimicking, and it was really kind of... Kim, I don't know if you remember. I turned to you, and I was like, I looked you and I pointed, and I was like, "Has he heard me before?" I know that sounds maybe a little a little arrogant. I think the two of us were working kind of in tandem, or parallel. Maybe that's the word I want. Working in parallel on this idea of what does it mean to actually help students think and reason in classrooms and not mimic? And it was just kind of ironic that we were sort of using some of the same words and phrases to describe what we were seeing and what we knew could be true. So, completely agree with that part of his work, that take on education is that we don't want. I mean, the whole intro that I just read was it's not about rotely repeating steps, rotely repeating procedures.


Kim  02:24



Pam  02:24

We want students thinking. And what does that look like? And what are some of the things? I think he does a really nice job in his first chapter describing...maybe I'll even give it more than the first chapter...of describing some things that students do to look like they're thinking and not be thinking, ways students get out of thinking, and ways teachers kind of get trapped into promoting that behavior and the questions that they're willing to answer for example. I think he does a really nice job of bringing some of those things to light. He also, in his book, has a kind of four part framework, or this this chunk of 14 things to do that he suggests that you do kind of in these four chunks. So, there's these kind of 14 teaching practices. I'm not exactly sure what he calls them. I probably should have looked at that. 14 teaching practices, I think, that will help you create a thinking classroom. Many of which I agree with. Maybe not quite all of them, and what we can talk about that a little bit. At least not quite to the degree that I see some people implementing. But I thought today, we would spend some time talking about where we agree, the kinds of things that both Dr. Liljedhal and I would promote and think are very useful. And for those of you who have not done much with his work, just give you a little bit of overview of my understanding of at least some parts. I am not in this podcast episode attempting to represent him completely, so know that. I mean, he wrote a whole book ya'll, so. 


Kim  03:53



Pam  03:54

But I am going to try to give you the highlights that I kind of think are important, at least to consider at first. So, of his kind of 14 teaching practices that he would suggest that you try, again, he suggests that you do it in these four chunks, so that you start the first chunk, and then when that works, get that going, then you implement the next chunk. So, I want to start with that first chunk. In that first chunk, he's got three teaching practices he would recommend that you start in your classroom. One of them is, that you give students thinking tasks. Meaning, you don't give them tasks that they already know how to do, tasks that you've taught them to rote memorize the steps through, but tasks that they actually have to dive in and reason about. But you do that at vertical, nonpermanent surfaces. That's quite a mouthful. All that means is, that the surfaces are vertical. And they are erasable. So, he did some testing with where kids were writing with markers on horizontal surfaces like desks, and he found that students didn't engage quite as quickly. He put chart paper up vertically on walls, and because it wasn't erasable, he found that students didn't engage as quickly, or as much, or as collaboratively. And so, I'm not going to mention maybe all the things that he says about those. But he suggests that if you can put students up at these vertical, nonpermanent surfaces. So, vertical like a whiteboard or chalkboard. And so, that they're writing something that can be erased. And you put them in groups. But very specifically, he suggests that you visibly, randomly assign the groups, and that you change those groups up often. And he's going to be very clear that it will take a while for this to begin. But let me just maybe say that part again. So, you could picture in the classroom, where you've got places all around the classroom that have these vertical, erasable surfaces. So, you can picture whiteboards all around the room. You could picture chalkboards all around the room, or some kind of wipe book, flip chart all around. You know, something that students can write on and erase. You have visibly chosen random groups. So, what does that mean? That means that you've done something where kids can see that the groups are random. So, if you say, "Alright, today everybody, here are your groups," and you read them off, kids are like, "Yeah, you created those groups. You made them (unclear)


Kim  06:25



Pam  06:25

He thinks that it's super important for groups to be randomly chosen, and that kids believe that it's random. So, a way to do that is, as kids are coming in, you hand a card from a deck of cards. You know how many cards are in there, so that they'll split up into those groups evenly. And then, you say, "Okay, the twos are over here. The threes are over here. The sevens over there." they go to their assigned place. And now they kind of will believe you more that the groups were random. One of the reasons I think he suggests that groups are random is, that the students will begin to learn, or they'll.... What's the word I want. They'll accept the fact that the groups are random, and so they've got to learn to work with whoever they get because, "Nobody chose the groups to be this way, so I guess I'm going to have to be cooperative, like actually work." And he admits that it will take a while for that to happen, that it might take... I think he says a couple of weeks or more. 


Kim  07:22



Pam  07:22

Maybe a couple of weeks. Like two and a half weeks I think is the number I heard him say for kids to like, "Oh, this is going to be a thing." Like, "It's not going away, so I guess I better learn to work with you." 


Kim  07:32



Pam  07:33

You can picture. Kim, how many times in education is there this bandwagon thing? 


Kim  07:36

Oh gosh. Yeah.


Pam  07:37

(unclear) once or twice, right? I mean, kids are like, "I'll just wait you out. I'll wait you out away until you stop doing the thing."


Kim  07:44



Pam  07:44

So, you kind of have to get past that honeymoon stage. And then, he says students dig in. They dig in, and they will work together. He found that if you put him at these vertical surfaces, students will write faster, they'll pick up that marker, they'll write, they'll they'll start getting their ideas out. He also... One of the things I thought was super interesting is when I heard him say that if students are sitting at desks, maybe in groups, and they're supposed to be working together. That to opt out of the work, they will lean away from the group. And if the room is like a typical room, and kids are kind of sitting all on their desks and there maybe in groups, to lean out of that group is not very noticeable. Nobody's going to be able to sort of tell that they kind of leaned out of the group. But if you have students around the room, all standing at these vertical surfaces writing, if a student is going to lean out of that work, then they kind of lean into this middle of the room where there is no one. And that's way obvious. Like, if you want to stick out, then you've opted out. In other words, opting out puts you in the limelight that kids don't necessarily want to be in.


Kim  08:56



Pam  08:56

And so, instead of opting out of the work, in order to kind of blend in and not stick out, they'll actually lean into the work, and they'll actually be doing things. Because at a moment's glance, you can look around the room and see who's got stuff up on their board.  If there's nothing on a group's board, that might be a little bit of social pressure to start working. If you've leaned out of the work, the kids can see that. They can see that you're not involved in that. There could be some sort of social pressure to kind of like. So, what he's suggesting is you can kind of use the dynamics that are naturally occurring in class to promote thinking. Like, let's promote kids digging in and getting the work done.


Kim  09:11



Pam  09:38

So, those are interesting things to start to try to put in your classroom. And I think they are enticing. And that's maybe too strong of a word. Help me Kim. It's desirable? No. An attractive! That's the word I was looking for. It can be an attractive thing for someone to say, "Hey, do these things, and it'll fix everything." 


Kim  10:00



Pam  10:00

Like, "Do these things, and check it out! Everybody's going to be thinking. Now, we've tried some of this, Kim.


Kim  10:07



Pam  10:07

So, both in workshops that we give where we're in person.


Kim  10:11



Pam  10:12

And also in my university classes.


Kim  10:13



Pam  10:14

I have put students up at vertical, nonpermanent surfaces. You know again, vertical, erasable surfaces. I put them into visibly randomly chosen groups. Another thing I didn't mention is you give them one marker for the group, so they have to kind of share the marker. Not everybody's... A reason for that is if you give everybody a marker, they can all just start writing on the board, and they don't have to be cooperative in any way. So, if there's only one marker, then there's more conversation about what goes up on the board, who's going to be writing it. Before something maybe goes up there, they're kind of agreeing or, you know, they're kind of encouraged to look at each other's work. Because what are you going to do while you're standing there while someone else is writing? Oh, How did I start that sentence? Oh, yeah. So, we've done some of that. And I don't know, Kim, if you want to like. What have you found? Like, (unclear) flop horribly? 


Kim  11:04

Oh, gosh, no. Like, I was going to say that you've been saying "students", but I think that these behaviors that he described are absolutely true with adult learners as well. Right, we see...


Pam  11:15

That's true.


Kim  11:16

When we're working in a workshop, and we see teachers want to disengage, I love as a teacher, you can glance around, and you're like, "Oh, let me go to that group, this person." Because it's kind of on the outskirts of the room, right? We're not looking at a pile of kids in the middle. I love the vertical, nonpermanent surfaces around the room because you can see at a quick glance, like who's engaged, and who's not, and who's working, and who's having conversation. It just makes it really nice to be able to take a pulse of the room at a glance like you mentioned.


Pam  11:49

Oh, can I add to that? Don't forget anything you were going to say. So, not only a pulse of engagement, but also what kind of math is happening? 


Kim  11:57



Pam  11:57

Like, I can look at these surfaces. I can't peer over kids heads to see what's happening on their on their table or their desk, but I can look around the room...teachers are kids...and I can see on these vertical surfaces, "Oh, that groups working on this. And that groups kind of this. Or that groups really stuck. Or that groups..." 


Kim  12:13



Pam  12:14

And that pulse is super helpful. I hope you didn't forget the other thing you were going to say.


Kim  12:18

No, no, no. I was just going to say it helps you to make decisions as a teacher of groups to visit, and in what order, and what the conversation is going to be about as you're crossing the room to have conversation with them.


Pam  12:29

Nice, nice. So, ya'll, we jumped in, and we tried some things. We did find that people will pick up a pencil sooner. Or I guess it's really a pen if they're on this nonpermanent surface. We did find that teachers would dig in and work a little more cooperatively sooner and more cooperatively. We did find some some things that made enough sense that we continue to do that kind of work sometimes in workshops. And maybe I'll start off saying, or maybe I'll continue this, this idea of, we wholeheartedly support his idea that we want to create thinking classrooms.


Kim  13:09



Pam  13:10

We might push back just a little bit on how often or... Yeah, I'll just say. How often we do the vertical, nonprofit surfaces, visibly, randomly chosen groups. And we'll also talk a little bit about what those thinking tasks look like. But maybe the biggest thing that I want to just say in closing today for this episode is, I think that he's done a super job. And we only talked about three of his teaching practices. And we'll talk more about the rest of them in future episodes. I think he's done a really, really good job of talking to us about how. How we can create thinking classrooms, some sort of things to do. And I think a lot of teachers have found that, like I said earlier, attractive. That it's like, "Oh, I can do that? That I can do. I can do that." 


Kim  13:54



Pam  13:54

"And that will change? Bam!" And so, I think that's super helpful. If I may offer, I'm absolutely about the "how", but I'm also about the "what". And I mean by that, I'm also about what you teach, the mathematics, the way we mathematize. That it's not the same mathematics that were in traditional textbooks where it's about mimicking procedures. That there's more to when we say "know your content, know your kids," there's more to "know your content" than many of us had from our own experiences. And so, next week, in the next episode, we're going to dive into how we differ a little bit, in some ways, from what Peter Liljedhal says, and maybe some things that I would not use his work for. So, hear me clearly everybody. I'm not denigrating his work at all. I'm suggesting that there are some places where we might de-emphasize some of the things he said, and maybe do things a little bit different sometimes. But love the idea of creating a thinking classroom. I think he's on some really good ideas. Alright, ya'll, thank you for tuning in and teaching more and more Real Math. To find out more about the Math is Figure-Out-Able movement, visit Let's keep spreading the word that Math is Figure-Out-Able!