[00:00:00] Peter Liljedahl: Everyone can be mathematical, and being mathematical is a process. It's a verb. Given a rich opportunity to engage with others on an interesting activity, everyone can be mathematical. Whatever that looks like.

Episode intro

[00:00:16] Vanessa Vakharia: Hi, I'm Vanessa Vakharia, aka The Math Guru, and you're listening to Math Therapy, a podcast that explores the root causes of math trauma, and the empowering ways we can heal from it.

Whether you think you're a math person or not, you're about to find out that math people don't actually exist. But the scars that math class left on many of us definitely do. Oh, and don't worry, no calculators or actual math were involved in the making of this podcast.

Okay, so I know I always speak in hyperbole, so like you guys don't trust me anymore, and I don't blame you, but today I'm interviewing Peter Liljedahl. There, I just said his name without a single adjective before it, because he's that much of a big deal right now that no adjectives are even needed. 

Peter is the author of Building Thinking Classrooms, a book that's changing education as we know it, teacher by teacher, classroom by classroom. And in fact, the reason I had to get Peter on the pod is because over the past year, I literally couldn't escape him. Like seriously, every conference I went to, his name was dropped in every presentation I was in, regardless of presenter, regardless of topic. In fact, I even noticed teachers clutching his book under their arms, or like casually pulling it out of their bags when rooting around for a pencil. Like, he's a purse staple at this point. Bring your chapstick, water bottle, wallet and like a copy of Building Thinking Classrooms. 

I mean, half this season, me and the guests spend quoting him. Peter is everywhere. And as you'll see on today's episode, he should be everywhere because he's changing math education with one simple concept. Are you ready? Thinking. Just imagine if we taught students how to, wait for it, think. That's right, Peter is the math education hero we all desperately want and need right now. How's that for hyperbole? Okay. I've worn myself out. Let's get into it.

What's a "Thinking Classroom"?

[00:02:06] Vanessa Vakharia: Okay. Peter, welcome to the podcast. I can't believe you're here. I mean, we don't need everyone to know this, but I'll say it anyways. I've been boosting you up before we even hit record, because I'm such a fan. All of this stuff is happening because of you. Every conference I go to, somebody has a presentation on how to use your Building Thinking Classrooms in a different aspect of education, and I just think it's so cool. 

So, obviously I did my research and I read the book. 

[00:02:30] Peter Liljedahl: Okay. 

[00:02:30] Vanessa Vakharia: I read it. Yeah. And I wanna start with actually the most simple quote off your website, because it's so simple, but I actually think it's so complex. And that quote is, you say that "a thinking student is an engaged student". 

Right away I'm like, oh my God, that sounds so simple, but what does an engaged student look like? And really, let's back up. What is a thinking classroom and how is it going to produce this engaged student? That's two questions. You can start with the first.

[00:02:59] Peter Liljedahl: Okay. All right. so what is, okay, so what is a thinking classroom? Let's start out, let's come at it from this perspective. 

Building thinking classrooms is a reaction to the realization that students spend a lot of time sitting in classrooms not thinking. And this is an empirically deduced observation, I spent tons of time in classrooms observing what students are doing, what they're not doing, and so on and so forth. And the realization that students spend most of their time not thinking, has been documented. And building thinking classrooms is a reaction to that realization. It's a reaction in the way of trying to figure out how can we change this? How can we change this narrative? How can we change this truth? How can we reconstruct and reenvision what classrooms look like in such a way that students spend more time thinking.

And building thinking classrooms, the research and the book, is the emergence of these ideas. What a thinking classroom looks like, if you were to walk in on one, is that you would walk into a room and you would notice immediately that rather than sitting in desk, students are standing in groups of three, working at vertical whiteboards on a task. And that when they complete that task, they will be given another task, and if they get stuck on that task, they'll be given a hint, and sometimes they'll be too impatient to wait for the teacher to come and give them that extension or that hint, and they'll steal the hint or the extension from our neighboring group of students.

And if you spend enough time watching, you'll notice that the students are, through their engagement in these tasks, are moving through tremendous amounts of content with lots of conversation, deep understanding. if you were there at the very beginning of the lesson, you would realize that these groups of three are not strategically created. The teacher hasn't sat down and carefully decided who's gonna work with who. And they're not self-selected groups, that these groups are randomly selected, that students are picking cards or there's some sort of a digital team maker that's being used to sort them randomly into these groups of three.

And that the students are spending the majority of the time in the classroom in this very active stance, constructing understanding, co-constructing understanding, building, and making meaning with other students who are also building and making meaning. That's what a thinking classroom is.

[00:05:21] Vanessa Vakharia: I was wondering how you were going to even summarize an entire book in two minutes, but you did it actually, I'm nodding along, being like, yep, you've covered it all. Great. 

[00:05:30] Peter Liljedahl: That's because you read the book. 

[00:05:31] Vanessa Vakharia: No. I think from it, I think it's good because it's hitting on a whole bunch of the points, but this is such a crazy question, I guess, but why is it important?

I am actually thinking of a lot of teachers and I think we can both think of those teachers who would be like, yeah I guess, but like, why do we need kids to think in math class? Like, why can't they just learn the algorithms and get through it like we all did? 

[00:05:52] Peter Liljedahl: Because we all did, right? We all got through it. And one of the things that there, there's two ways to think about this. Number one is, did we all get through it? Because the people who are standing there saying that are of course, by definition, the ones who got through it. The ones who became math teachers were the ones who thrived and succeeded in those environments. Right? 

But does that mean everybody thrived and succeeded in those environments? Like if we go out onto the streets and pick a hundred citizens at random and bring them into a room and interview 'em, how many would actually say that they were successful at mathematics and thatthey had a positive relationship with mathematics? And I suspect that number is very low, certainly less than five, right? That, that actually would label themselves 

[00:06:36] Vanessa Vakharia: Five in a hundred? 

[00:06:36] Peter Liljedahl: Thrived and enjoyed. Yeah. 

[00:06:39] Vanessa Vakharia: I, oh my God, I love it. Bold. But like, yeah, I kind of agree with you.

[00:06:43] Peter Liljedahl: Yeah. That's not to say that only five people got through mathematics. The vast majority get through mathematics. But how many of them would identify themselves as having a positive relationship with mathematics, and feeling confident and sure aboutmathematics? I think it's a very low number. And again, I'm not talking about the ones who, who squeaked through, but the ones who actually thrived. Right?

So, did that method of just, teach the algorithm and you'll learn it and then you'll get through it, actually produce the kinds of thinkers and learners that, that we want? So why do we need to do it? Because thinking is a necessary precursor to learning. If students are not thinking, they're not learning. Period. And if you have a classroom that doesn't get students to think, then they're not learning. They may be memorizing, they may be taking notes that they're gonna look at later, but in that moment, they are not learning.

Thinking is a necessary precursor to learning. 

And that is not a result that I am saying I was a first to claim. That has been known from psychology for a very long time, that thinking is a necessary precursor to learning. And then what building thinking classrooms does is build environments, constructs environments, that not only facilitates thinking, but necessitates thinking.

[00:08:01] Vanessa Vakharia: As you're saying this, of course, I'm nodding along, being like, yeah, that seems really obvious. But then I, at the same time, get so pissed off because I'm like, why do we know all this stuff, but yet, I mean, we're in different provinces, but at least you know, in Ontario and Alberta, and I know much of the states we're kind of like, hmm, no, no, no, no, no, we need to go back to basics, we need to go back to memorizing. Like what's going on where we're just ignoring all of the psychology.

[00:08:25] Peter Liljedahl: Okay, so I'm gonna speculate on this because it's, this is, I think this is a important question, but it's certainly not within the scope of my research, but I, my theory on this is that we forget to keep our eye on the prize, right? If our eye is on learning, if that's a goal, if learning is the goal and thinking is a precursor to learning, then we can, we can focus on thinking. But if performance is the goal, 

[00:08:56] Vanessa Vakharia: Hmm.

[00:08:56] Peter Liljedahl: If having students perform well on standardized assessments, if that becomes the goal, that's a different thing, right? Like good performance is a natural byproduct of learning. But that's only true if we keep our eye on learning. If we put our eye and our gaze and our focus on performance, then it's really easy to bypass learning, I believe.

[00:09:20] Vanessa Vakharia: I mean, so, I love it, but I almost feel like we're not even giving the thinking part enough credit. Because you do talk about this in your book, unless I misunderstood that, like ultimately, the performance we're seeking, would inevitably follow from a thinking cla, right? Like you do say that at some points. 

So like, tell us a bit about that because I actually think that's the, that is the biggest problem. What I'm gathering over the past couple of years, the biggest problem is people will be like, yeah, love it, cool, I mean, yes, we totally agree that we need kids to think and we need them to feel better and da da da, but what about assessments? Like, what about the test? What about the marks? 

Like, I was just in a classroom, actually I was in a school in New York, and I walked into their math class, their calculus class, and it was, I actually tagged you on Instagram, you probably don't see it cause you didn't follow me, but like, you'd be so proud, because the whole class, they had table groups, the entire classroom was vertical, non-permanent surfaces. They were doing all the things, and I was like, oh my God, I love this. 

But I gave a whole talk to the kids about, thinking and making mistakes in classrooms. That's a big thing I talk about. And afterwards, one of the girls came up to me and she was, cool, but like it's kind of bullshit what you're saying because at the end of the day, we're trying to get into Harvard and we need a certain mark. 

And I didn't really know how, and like the teachers too are kind of like, yeah, we like this idea of encouraging mistakes and thinking, but like they need these grades. Like how do you reconcile the two?

[00:10:44] Peter Liljedahl: Yeah. Well, I'm not sure that anybody can reconcile those two because we're coming at education from two very different purposes here, right. From the bottom up, what we're trying to do iscreate learning, and like I said, thinking is a necessary precursor to learning. So if we want to create learning as a byproduct, we have to start with thinking.

So that's what my focus has been on. Let's start with the thinking. Let's get the students thinking, let's get 'em thinking together. Let's get 'em thinking individually. Let's get 'em thinking about powerful mathematics. Let's get them thinking. And then the learning will be a byproduct. Performance will be a byproduct.

But we're also coming at education from this other perspective, which is, and when I say we, I mean a lot of other people, not me, but like we as a society are coming at education from this idea of education as some sort of a gatekeeper. That education is the pathway through which we will enter into adulthood and into productive and profitable adulthood. 

So, so now education is a gatekeeper. So K to 12 education is a gatekeeper to get into a good post-secondary and post-secondary is a gatekeeper to get into productive and profitable careers. Right. And when we think about it like that and we keep focusing on the performance aspect of it, it really changes the game. 

Process vs Outcomes

[00:11:59] Peter Liljedahl: You know, I, I'm gonna dredge something up from a long, buried deep past. I used to be an athlete, I used to be a high performance athlete. 

[00:12:06] Vanessa Vakharia: What?

[00:12:07] Peter Liljedahl: And 

[00:12:07] Vanessa Vakharia: Like what? What sport? 

[00:12:09] Peter Liljedahl: I, I was a canoe paddler. I 

[00:12:10] Vanessa Vakharia: That is so Canadian.

[00:12:13] Peter Liljedahl: Yeah it is so Canadian, I know. 

[00:12:14] Vanessa Vakharia: Stop it. 

[00:12:16] Peter Liljedahl: First ever Canadian championships I raced at, was on Center Island in Toronto. So, 

[00:12:22] Vanessa Vakharia: Oh my God. Okay. We're gonna need pics or it didn't happen, but yeah, continue with the analogy or whatever it was that you were getting at.

[00:12:28] Peter Liljedahl: But anyway, so a huge part of sport is about trying to fine tune, it's all about performance, right? It's about performance, because that, that is what sport is. But, how do we achieve the performance? How do we get to a point where we can achieve desirable outcomes? And you know, there's a whole part of that, which is honing the body, right? Honing the body. Training, training, training, building up endurance, strength, anaerobic threshold type stuff. There's all of that. 

But once you've done that, there's also the psychological. And entering into that sort of sports psychology world, one of the big standards, one of the things that really stands at the center of effective sports psychology is are you gonna focus on the process or are you gonna focus on the outcome?

And when you focus on the process, the outcome will come. It'll be a byproduct. If you focus on the outcome, it may come, but there's no guarantee of it. And from a athlete perspective, focusing onprocess was way more productive for me than focusing on outcome.

When I would go into a race and all I thought about was my race plan and my race strategy and my preparation and the things I needed to focus on, I would have way better results than if I went into a race focused on winning. You don't get to decide if you win or not because there's eight other people in the race who are gonna decide whether you are gonna get to win or not. You can only focus on yourself. You focus on yourself, and you have the best outcome you possibly can.

Winning is a possible outcome, but that's got a lot to do with how well you perform and how well the others perform on that day as well. 

I had my best outcomes when I focused on process, and it's the same thing in education. 

[00:14:07] Vanessa Vakharia: I personally really needed this pep talk. So yesterday I was trying to hit a note in the Pink Floyd solo. Do you know that the part I'm talking about the like what? No. Oh my God, actually, wow. Delete. 

[00:14:19] Peter Liljedahl: You gotta tell me which song.

[00:14:21] Vanessa Vakharia: The Great Gig in the Sky. It's like the famous solo. It's like this famous like, David can actually sing it better me than me. The point is, who cares, the point is this, is that I was trying to do it and using all my vocal techniques and I couldn't get the note, and I kept being like, oh my God, and David's like, stop it. I was like, how can I even tell that any of this practice is working? And he's like, because you're practicing. So like no matter whether you eventually hit that note or not, you are going to like build some sort of skill. And if you're only focusing on success being, if you hit that note, you're gonna miss all the little successes on the way, right? Like, I'm working on my vocal technique, I'm working on my breath control. Maybe I'll never get that note, but it's the journey versus the destination thing.

So first of all, I needed that pep talk. Thank you so much, Peter. But also,I really think that is so important in math. You can't, I'm reading this book, something about like, being comfortable with uncertainty or something like that. It's like "needing to know for sure". And the idea is like, okay, so with math, let's say we are focused on the thinking and all of like being in a flow state and curiosity and feeling like you're just in something and you're doing something. Regardless of whether you're that person or you're the person who's memorized every algorithm, you can't know for sure how you're gonna perform on the final test. Like, you can't know, right? You can't know what's on the test, you can't know how you're gonna feel that day, all that stuff. So like, focusing on what you can control, which is the process, in the interim, you're being present and you're focusing on what you can control in the situation and what you can get out of it.

[00:15:41] Peter Liljedahl: Yeah. And, and it's about bringing your best self to that space, right? Like 

[00:15:47] Vanessa Vakharia: Yeah. 

[00:15:47] Peter Liljedahl: And again, putting results in its rightful place, right? Performance and results are outcomes, they're byproducts. It's even in the word, when we think about the word outcome, it's what comes out of the preparation, the work, right?

The power of collaboration

[00:16:06] Vanessa Vakharia: You're right, a hundred percent. But it's like, are we in the weirdest spot in education where it's like we know, the like, and I'm using air quotes, but like the right thing to do. Like we know what we really need, like we really actually need kids to like grow up in a world where they feel capable of raising their hand, of taking a risk, of thinking outside of the box.

Like, climate change doesn't need you to memorize a bunch of algorithms, it needs you to think of a creative solution and be like, you know what I mean? Like, it's like that kind of stuff, but like, yet, is there still this weird thing where it's like, okay, great, you can do that all you want into the classroom, but if they're not taught to perform in a way that's meaningful for them to actually become a scientist, we're screwed.

[00:16:42] Peter Liljedahl: Yeah. So one of the things that I often say is that it's a lot easier to get a student to university than it is to actually prepare them for university. And, if we think about that, it's like getting students to university has been reduced to just marks, right? And if I'm the teacher in the classroom, I actually have a tremendous amount of control over the kinds of marks you're gonna get. I can get you the marks that you need to do to get into university. 

Is that gonna make you prepared for university? I had a master's student, uh, named Nina Bach, she did this really nice thesis where she interviewed students who had just finished calculus one at university. So they had just finished, and she asked one question. And the question is, what do you know now that you wish you knew coming outta high school, that's gonna help you to be successful. 

Not one of 'em said that I wish I knew logarithms better. Nobody said that, nobody said, I wish I had better command of trig, right? They said things like, I wish I had better time management skills. I wish I was better at thinking outside the box. I wish I was better at persevering. I wish I was better, and this is the key one, I wish I was better at finding people and making connections with people who I could learn with. 

[00:17:56] Vanessa Vakharia: Hmm. 

[00:17:56] Peter Liljedahl: Like remember the study cubicle? I went to SFU for my undergrad degree. SFU is not a huge school, maybe 35,000 students. There was study cubicles everywhere. Every floor of the library had them, every corridor in the university had them. They were absolutely everywhere. And I lived my life in these study cubicles. 

When I now teach at S F U, I know where there's 11 study cubicles. All the rest are gone. They've all been replaced with collaborative spaces, spaces where students go to make meaning together.

And one of the things I've learned, because I have spent time in university lectures just observing, is that, by and large, a lot of those university lectures, especially the first year ones and the second year ones, those lectures are not places where you go to learn. It's where you go to learn what you have to learn. 

[00:18:46] Vanessa Vakharia: Hm. 

[00:18:47] Peter Liljedahl: And then you go away and you learn it. But you need, you need to have people to make meaning with, to learn this stuff.

[00:18:55] Vanessa Vakharia: It's funny, like, so I,failed grade 11 math twice and then I was sent to this quote unquote school for misfits. And the whole vibe of that school, it was in an office building at Yonge and Eglinton in Toronto, and it was where I developed my love for learning math for a variety of reasons, but one of them was, once I discovered that I was kind of good at math and I liked it, I became the class tutor. And what we would do is every single day we would go to Coffee Time, we would light up a pack of cigs and I would teach everyone math, we had the best time. Every kid from the kid who thought they could never understand a single thing to the kid who kind of got it, we would be having the best time ever, drinking way too much coffee, like helping each other out.

And it became this fun thing we did, this fun social thing and actually, I mean, we obviously don't smoke anymore, okay? It's not cool guys. But at my tutoring center, the whole vibe, it's all pink velvet couches, open spaces, whiteboard walls. And kids are always like, oh my God, we can actually talk about math in here. You know, like, everyone will jump on a problem and try and figure out a way to solve it. But the craziest part is now it is 2023, and that is still very rare. 

Like you're right, like you're talking about S F U and how it's changed, but a math classroom hasn't really changed, right? Most math classrooms, where our students come from at least, it's still like rows of individual desks, it's very teacher focused, But, I think that's so, so interesting what you're saying, because we've said forever, like the style of teaching and learning you're talking about has actually been used in the humanities way more traditionally than it has been in math. Right? 

[00:20:29] Peter Liljedahl: Yeah. 

[00:20:30] Vanessa Vakharia: And maybe now, with the idea of thinking classrooms, again, if you were taking away from it being outcome-based to it being like, let's just talk about math and learn together in that thing, maybe that does open up space for that style, right? Like, if no longer we're competing with one another for the best mark on some tests and we're not supposed to share, maybe that opens things up.

[00:20:47] Peter Liljedahl: Yeah. And that's, this is one of the big differences we're seeing in thinking classrooms. When that empathy unlocks, and when you were talking about those spaces where you were smoking and drinking coffee and making this work, is that there was, it was oozing with empathy, right?

And kids have a tremendous capacity for empathy. And what does empathy look like in collaborative settings? It's when the students start to care as much about each other's learning as they do about their own. And this is one of the things we're seeing in thinking classrooms, these random groups, vertical surfaces, it's unlocking the empathy. It's no longer about that competition for marks. It's about learning. My learning and your learning. And we all should be able to learn and have access to learning.

Levelling to the bottom

[00:21:31] Vanessa Vakharia: So one of the things you talk about in thinking classrooms is that leveling to the bottom concept. Do you think that kind of is part of what you're talking about here?

[00:21:40] Peter Liljedahl: You're talking about the consolidation, about how we consolidate from the bottom? Yeah.

Consolidation from the bottom is a very teacher directed activity, but it's about recognizing that students are in different places. And originally when I did the research that was called Leveling from the Bottom, and it was so problematic having that title, because I had to always explain what I meant by it. And the title came actually from how it juxtaposes with Alan Schoenfeld's work from like 1985, forever ago. He did this research on, how students work in classrooms and how they problem solve and so on and so forth.

And one of the things he identified was that a really common phenomena that happens in classrooms is what he called leveling to the top. 

[00:22:26] Vanessa Vakharia: Mm. 

[00:22:27] Peter Liljedahl: And the idea of leveling to the top is that the teacher's gonna ask the students to do something. And you know, I'm gonna demonstrate, demonstrate, demonstrate, and now I'm gonna turn to the class, I'm gonna say, now you try one. The teacher has now demonstrated how to do this, and now they're gonna turn the, the responsibility over, the opportunity over to the students to now, their job is to try to recreate what they've been shown how to do. And there's a couple of interesting phenomena that he noticed, but I'm gonna layer in some of the phenomena that I noticed as well.

So the teacher turns to the class and says, now you try one. And the first thing I noticed was that the average amount of time that the teacher gives is four minutes and 22 seconds. And that's just from sitting in countless classes, watching how much time is given. And there is an average, of course there's an average, four minutes and 22 seconds.

But what was more interesting is that's not what the teachers are paying attention to. What are they paying attention to is, what is the threshold, what is the number of students that they want to be done before they, they bring closure to that activity? And it's around 30%, right? 

Because when 30% of students are done, when you pass that threshold, now you're having to manage the people who are done, who are now off task. Right? And 30% is a pretty critical threshold around that. So this is observational. It's not theoretical, it's just observational. The data shows that when the teacher says, now you try one, that they wait for about 30% of the students to finish. And then they go over it. 

Now, here's the deal. I asked you to do this question. I need you to know how to do this question because I'm gonna ask you to do another one that's gonna be harder. You need to know how to do this one before you can do the next, right? So I'm,I'm asking you to solve for, uh, the hypotonus on a right angle triangle, and I need you to know how to do that because the next question I'm gonna ask you to do is solve for the shorter leg. And so on and so forth, so there's this sort of leveling up that's happening. 

But when the teacher decides they're gonna go over this task, by and large, what Schoenfeld noticed was that the teacher levels to the top, which means I want you to get to this point, so let's go over it at this point, right? And I'm waving my hands around here, but if I want you to get to a certain point, that is the point that I'm gonna go over it at. And he called this leveling to the top. And the idea is that we believe that by doing that, I'm gonna lift all the students, because only 30% are finished, I'm gonna lift the other 70% up to that level by showing them how to do it.

But it doesn't work. Right? It doesn't work, and it doesn't work for a bunch of different reasons. One of which is, for the majority of the students, that's way outside their zone proximal development. Like if they didn't understand how to do it on their own, you telling them how to do it doesn't actually help them understand it, it just gets them to see how to do it, right. 

And the other reason is if it did work, if just showing kids how to do something worked, I think we'd all be in a very different place right now. Right? You wouldn't be running a tutoring service. If telling kids how to do something worked, we wouldn't need tutoring centers, we wouldn't need Khan Academy, we wouldn't need, uh, remedial courses. All our students would be performing well because we're really good at telling kids how to do stuff. Like we're really good.

[00:25:54] Vanessa Vakharia: Yeah. Yeah. Like, it's weird. I'm feeling better and worse as this talk continues. Like, I'm like, I'm like, oh my God. Yes. But like, uh.

How thinking classrooms enhance equity 

[00:26:04] Vanessa Vakharia: Okay. We obviously have a million things to talk about, so I wanna just get to a couple heavy hitting things that I really wanna ask.

The first is, I mean, this is a podcast about kind of math trauma and math therapy generally, and you've said a lot of really interesting things and one of the things I'm wondering is do we think, I mean I obviously think the answer is yes, and I'm sure you do too, but do we think this idea of switching from a outcomes based classroom, so being like, Hey, this is what success means in this classroom, it's actually a certain mark, and if you don't get it, you're out, versus a thinking classroom, how do we think that has uh, the ability to reach the students that feel the most left behind? 

[00:26:40] Peter Liljedahl: Uh, okay, so let me just rephrase the question a little bit. Because it's not just about the re casting it as outcomes versus thinking. It's just how can a thinking classroom, a different physical structure, a different environment, actually give more students access to learning? 

This is actually one of the things that I've been exploring a lot lately because, you know, there's this huge push for equity in education these days, both in Canada and the US. It'd be nice if we could say thatthat push and that focus has been there for a very long time. But it's really at a crescendo right now. Everybody is talking about how we can create equity. And then comes along Building Thinking Classrooms, which wasn't designed to do that at all. Building Thinking Classrooms, all of that research was entirely about how do we get students to think, and how do we get more students to think, and how can we get students to think for longer? And I guess by the mere fact that the research is about trying to get more students to think, and thinking is a necessary precursor to learning, that somehow building thinking classrooms is creating greater equity.

But then, I started to think very closely about thinking classrooms and in what particular ways does it do this? And one of the things that I came up against was this understanding or this challenge around equity, because I would talk to teachers all the time and I'd say, so what are you working on? And they'd, they're like, I'm working on equity. And I'd say, okay, so what does that look like? What does that mean for you to be working on equity? 

And it was really difficult for a lot of teachers to articulate this. Think about Ontario, where they've just destreamed their curriculum, right? And one of the main reasons to destream the curriculum that has been articulated is that we need to create greater equity. So I'm talking to these teachers, and this idea of equity is, at some sort of a visceral level that everyone understands it, but at sort of an actionable level, it's hard for teachers to imagine what it is I'm supposed to do different, right? I consider myself equitable, I'm fair, I, you know, all of these things. 

One of the things I started to really realize, that for me, equity is an outcome and it's a goal. My goal is to create equity. And if I achieve that, then the outcome will be greater equity. But what's my day-to-day work? What is it that I do on a day-to-day basis to try to achieve this goal? And I realized that the day-to-day work, is to try to create access. And how do we create access, how do we give more students access to education? 

And when I think about building thinking classrooms through that lens, a lot of things start to emerge as creating more access. Everything from using low floor tasks, a task that everyone can start, that creates greater access. Right? 

Having, for example, students stand up and work. Now, how is that, how is standing and working at whiteboards creating greater access? Well, the work is oriented the same for everybody. If they were sitting down, there's only one person who has that privileged position where the work is oriented towards them. Everyone else is looking at it sideways or upside down. That seems pretty minor, but it's still greater access. The work is oriented the same for everybody. They can see each other's solutions. That's greater access. They have more access to more ideas. 

But one of the things that was really interesting in our research is one of the reasons that revealed itself to be so effective was actually not at all about the students standing and had everything to do with the consequences of having them sitting. Because, and it, took over two years to get at this result, it turns out that when students are sitting, they feel anonymous. And the further they sit from the teacher, the more anonymous they feel. And when students feel anonymous, they disengage, which means that the students who are sitting, the ones who are further away from the teacher, are more likely to disengage. And now they have less access to learning than the students who are sitting near front. 

Now, a lot of those students chose to sit at the back. That was their choice, but they still have less access. The mere fact that they're sitting in rows is creating inequitable access to education and learning on that day, because the students that are further from the teacher are more likely to disengage. Getting 'em to stand up gave everybody the same access because nobody was invisible. 

So it's these subtle things like this in what ways is thinking classroom greater access. Consolidation from the bottom is about starting where everybody got to and working your way up instead of leveling to the top like Alan Schoenfeld talked about. It's all of these little things. It's a self-assessment that gives everybody access to what it is that is actually trying to be achieved here, right? It's all of these little things that are sprinkled throughout thinking classrooms. Not by design, the design of thinking classrooms was to try to create more thinking, but I think as a byproduct of that, there are these opportunities for creating more access that are emerging out of these practices

What shapes our relationship to math

[00:31:47] Vanessa Vakharia: Ugh, amazing. And I mean, the whole time I'm sort of thinking too, your idea that this is all about thinking, just the fact that you're encouraging thinking means, I think, that you're encouraging all ways of knowing. If that is the purpose, if it's to think, I think you mentioned this somewhere, but I don't wanna put words in your mouth, that like everyone thinks. We think from different perspectives and in different ways, and especially in a math class where collaboration is encouraged, the more ways you can think about something gives you a greater advantage. So it's almost like everyone's participation is valued. 

I think maybe we said this at the beginning of the podcast, but for sure, for me, through Math Therapy, like my whole goal is to simply just help people develop a better relationship with math. I don't care if you're faster, I don't care if you're getting a better mark, I don't care if you can add fractions, I just want you to feel like better. Literally, like whatever that means. Like a smidgen better, right? 

And because also too, thinking about equity, and maybe this seems a bit far reaching, but mathematical knowledge forever and always has been framed as the superior knowledge. Like it's a thing that makes you smart even though like, we know that's bullshit, right? Like it's just math, who cares? 

But I can get off stage after shredding a sick solo and no one will call me smart, but I'll tell them I'm a math teacher and they're like, you must be smart. And I'm like, what the fuck? I just like shredded a sick solo in your face. You know what I mean? Like there's hierarchies of knowledge. 

So allowing more kids to feel better in math, I think is enabling more kids to simply feel more like they belong, like they have more worth in the world, period. 

[00:33:16] Peter Liljedahl: Absolutely, and this is, I don't talk aboutthis around my work, around thinking classrooms, but adjacent to my thinking classroom research, I spent 20 years doing research in affect. That is one of my primary research areas in math education is I study affect. What students believe, what their attitudes are, what their emotions are, what their identity is, and how they see themselves in the future, their relationship with mathematics. That's been my research staple for 20 years. 

[00:33:43] Vanessa Vakharia: That's wild. I feel like I need all of it. Where do I find it? I don't wanna read any academic papers though. Can you just write it in, in layman terms. 

[00:33:51] Peter Liljedahl: No, that's all written in academic speak. 

[00:33:54] Vanessa Vakharia: Ok, no thanks.

[00:33:55] Peter Liljedahl: But it's, what's, what's so interesting and powerful about that is if we think about affect as this positive thing that you're talking about, and that we want students to have this positive relationship and this positive identity with mathematics, and just think about how hard that is to achieve for you, like you're, these students you're working with, you got pink couches and coffee and you got, and you're wanting them to have this experience, right? Like it takes a lot, tremendous amount of work. 

The flip side of that coin is just think how easy it is to ruin that. 

[00:34:25] Vanessa Vakharia: Yeah.

[00:34:25] Peter Liljedahl: Think how easy it is to get students to become disaffected with mathematics.

And once a student feels at risk, once they feel that they are hurting, that their emotions are trending towards a negative, the door just closes. There isn't any learning going on there, right? And this has been proven over and over and over again, that when students approach mathematics with negative affect, they're just not learning. Right? When they are fearful of mathematics, when they are fearful of anything. 

And when you trace back students' autobiographies around their experiences with mathematics, there's so many similar stories and the stories are this. I used to like math. I used to be good at math. And then at the end of the story is, I'm fearful of math. I don't like math. I, you know, I'm glad I'll never have to take another math course in for the rest of my life. 

But where was the transition? And almost always that transition is some amount of speed coupled with public shaming. Like somehow those two things together are just the key pivotal moment where students transform their identity and their relationship with mathematics. And then there isn't, they're no longer grasping to learn, they're grasping to survive. Right? They're grasping to get out of this lesson with the least amount of emotional and social damage possible. That's not a recipe for learning. 

[00:35:53] Vanessa Vakharia: I, it is so funny you just said that, the reason I was laughing is not because like that's funny at all, but because I was just putting notes together for an episode I'm recording just on my own about math trauma, I literally crowdsourced this on Twitter, and I was like, the most common themes are speed and public shaming. 

Like, I literally just wrote that out because you, you always hear that, right? It's like mad minutes in front of the class or it's a teacher picked on me and I didn't have, anyways, we could go on. 

We have to wrap up because time is just flying by. I need to ask one question though, that I'm just dying to know before we get to the two final questions, they're just like, super fast. 

Does Peter have haters?

[00:36:27] Vanessa Vakharia: Have you faced resistance? Like are people like, uh, like cancel Peter Liljedahl, like, no thinking? Like I feel like with any amount of fame, right, there's always the haters. Like, do you have haters?

[00:36:41] Peter Liljedahl: I don't know if I have haters. I haven't encountered haters per se. I would,I'm sure they're out there. I'm hoping they're not. I, I hope that thinking is something that everyone can get behind. 

[00:36:52] Vanessa Vakharia: You would think, you would hope, yes. 

[00:36:55] Peter Liljedahl: You know, like, and recognizing that we all, no matter what side ofhow you approach this issue you come from, that we all want our students to learn. And I think that's universally true, every single math teacher I've ever met wants our students to learn mathematics, right? And that's without a doubt. And every teacher educator I've ever met and every researcher I've ever met, everybody wants students to learn mathematics. And I think the people who write the standardized assessments want students to learn mathematics. I think we all want students to learn mathematics. 

And I think it's not too hard to accept the fact that we need our students to think. How we achieve that, I think there's a lot of discussion and differences around, but I think we can all agree that we want our students to think. 

So I don't know if there are haters, but I have encountered resistance less so of late. Usually when I give a presentation now, people want to be there and so on and so forth. But you know, every once in a while I do a workshop in a situation where people have been forced to be there and they're having to hear messages that they don't want to get behind and so on and so forth.

So you, you encounter resistance, but that resistance isn't from a place where I don't want students to learn, I don't want students to think. That resistance is coming from a place of, okay, this is not how I do things, this is not how I was taught how to do things, this is not how "we" do things, this is not how it's always been done. The resistance isn't that there's necessarily a disagreement behind the common goal. I think the resistance is just, sometimes change is hard.

[00:38:21] Vanessa Vakharia: God, that's so like nice and kind of you. Very understanding, very empathetic. Modeling what you preach. 

Q1

[00:38:28] Vanessa Vakharia: Okay. Time for the two final questions. Are you ready? Yes, you are. 

What is the one thing, I mean, this seems very trite in the context of our conversation, but you have to answer it. What is the one thing you'd like to see change about the way math is taught in schools?

[00:38:41] Peter Liljedahl: Uh, elimination of standardized assessments.

[00:38:44] Vanessa Vakharia: That's me clapping. That's the clap. 

[00:38:46] Peter Liljedahl: I think we need to re professionalize teachers and trust the teacher as the professional to be able to make a judgment of what a student knows and what they don't know. The teaching profession is a professional profession, we need to get back to that. Every time we impose standardized assessment, it deprofessionalizes teachers, it causes us to have to narrow our curriculum and our focus. And it focuses us to emphasize outcomes rather than the process. 

[00:39:08] Vanessa Vakharia: Mm-hmm. Snap. snap, snap, snap. 

Okay. 

Q2

[00:39:11] Vanessa Vakharia: Final question. What do you say to someone who says, Peter, I'm just not a math person.

[00:39:17] Peter Liljedahl: So I, I think. Yeah, that's a tough question. And the reason it's a tough question, and you might appreciate this, Vanessa, is that you probably get people who say to you that they're just not musical. And you'll say, oh, yes you are, you just haven't had the right experiences and the right teaching and the right this and the right that and you would probably continue to say that for the rest of your life until you actually try to teach me music. And then you would realize that, that, that everyone is musical, with the exception of Peter Liljedahl. I have a great, a great appreciation for music. I have a difficult time being able to recreate the tempos and the melodies, 

[00:40:00] Vanessa Vakharia: That's jazz. That's just called Peter, you're fine. 

[00:40:04] Peter Liljedahl: Okay. I'm just improvising. Okay. That's all it is. 

But what do I say to someone who says that they're just not mathematical? I say, you haven't had the right experiences. Everyone can be mathematical. Everyone can be mathematical, and being mathematical is a process. It's a verb, 

[00:40:22] Vanessa Vakharia: Hmm. 

[00:40:23] Peter Liljedahl: That's what being mathematical is. It's what you have experienced in your life is a whole bunch of mathematics as nouns. And you have learned that you are not good at mathematics as a noun, but everyone can be mathematical. Given a rich opportunity to engage with others on an interesting activity, everyone can be mathematical. Whatever that looks like.

[00:40:48] Vanessa Vakharia: I, I mean, just, I'm just deep sighing because I loved it. "Math as a verb." 

And also I have to say, I just interviewed Deborah Peart, her whole thing is the Mather movement and it's turning math into a verb, which is "to math". So like her whole thing is stop calling people Mathematicians, call them Mathers because everyone is doing math as a verb. 

Outro

[00:41:10] Vanessa Vakharia: This has been so fun. I can't believe we did it. I can't believe we met. I can't believe we're both Canadian. I can't believe you used to be a professional paddler and honestly, you're changing the world. This is so cool, and I think you're great.

[00:41:25] Peter Liljedahl: Thanks, Vanessa. I think you're great too, and I'm going to correct this great egregious oversight of not following you on Twitter.

[00:41:33] Vanessa Vakharia: Oh my God. This is actually a huge deal. Are we still recording? Yes. Okay. This is a big moment. This is a big moment for me. Thank you so much. Peter Liljedahl has followed me on Twitter, everyone. I don't know, I, have you? Have you? I'm gonna check.

[00:41:46] Peter Liljedahl: I will, I, I'll do it right now. 

[00:41:48] Vanessa Vakharia: Bye. 

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Episode outro

[00:41:50] Vanessa Vakharia: Okay. What a guy. I mean, what a guy. Who is this guy? Is it just me or are you also stuck on like the whole pro canoe paddler thing? Like how many lifetimes has Peter Liljedahl even lived? His vision for math education is becoming revolutionary and okay. Seriously, just last week I was at a conference and a presenter said, I've turned my classroom into a thinking classroom, like it's just in the vernacular of every educator now. 

How crazy is it that all this time, no one in curriculum design or education thought about what it means to teach students to think? I mean like what? I have a lot to think about. And yes, I did that on purpose and I know you probably do too. And guys, I can't emphasize this enough. If you're an educator, get yourself a copy of Peter's book. Trust me, I don't even like reading that much and I loved it.

If something in this episode inspired you, please tweet us @maththerapy, and you can also follow me personally @themathguru on Instagram, Twitter, and TikTok. 

Math Therapy is hosted by me, Vanessa Vakharia, it was created by me and Sabina Wex, and it's produced and edited by David Kochberg. Our theme music is by Goodnight Sunrise.

And guys, if you know someone who needs math therapy or just needs to hear someone else getting math therapy, please, please, please share this podcast, and rate or review it on whatever podcast app you use. Those things actually make such a big difference for us. I'm determined to change the culture surrounding math and I need your help, so spread the word. Until next time, peace, love, and pi.

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