Desiree Harrison 0:00

In Episode 15 of the Kids Math Talk podcast, we began a discussion about the impact of labeling and ability grouping in mathematics, which are two unproductive practices that actually hinder growth and can destroy positive mathematical identities. Today, we continue this discussion by talking with researcher and author Peter Liljedahl about his new book - Building Thinking Classrooms (2020) - which focuses on unpacking practices that promote growth, community, engagement, and positive mathematical identities in order to promote student centered classrooms.

Desiree Harrison 1:07

Today on the Kids Math Talk Podcast, we have with us Peter Liljedahl talking about his new book, Building Thinking Classrooms in Mathematics Grades K-12: 14 Teaching Practices for Enhancing Learning (2020). So, welcome to the podcast Peter.

Peter Liljedahl 1:26

Thank you so much Desiree, it's wonderful to be here, thanks for having me.

Desiree Harrison 1:31

Of course. Part of the title of your book is the 14 Teaching Practices which might sound to some of our listeners, as, as a lot, but, the way that this book has been organized makes it so manageable, and so like you have those digestible chunks and each chapter evolves and you don't have to read the book in its entirety to start to see the big picture, which I so appreciate. And you have the, the FAQs at the end of every chapter because it is a mindset shift for a lot of educators and I really appreciate how you acknowledge that and you help continue to motivate us throughout the book, and um, acknowledge our concerns to say, you know, "just hold on, it's coming, just wait, trust this process, and try out this one practice and then come back." Cuz it's not that you have to do everything all at once and thank you for naming that claiming that because it's not always done in every text and educators need to hear that and need to read that and-

Peter Liljedahl 2:50

I appreciate that you noticed that and that you picked up on that because it was very deliberate to do so.

Desiree Harrison 2:56

The other section headings where it's just like toward a thinking classroom - I love that word toward because this is a journey and that, that also - like as I continued to read the book and I kept seeing that towards something, we're moving toward, we're moving toward, it reminded me of, um, one chapter in particular with the evaluation. And how that's always on the forefront of educators minds because we have a passion; we want to help kids get that same passion, but then we still have to think about the evaluation at the end of the day and grading and all of that.

You have these, these five different ways of gradually changing our practice and having that arrow moving toward. So I was just wondering if you could tell us more about how you got to that in particular, with the moving from focusing on work to actions, and all of those different practices.

Peter Liljedahl 4:00

So, initially, I have a story of how this was initiated in the introduction. And it was really, it was my reaction, to recognize. So I -for those people who haven't read the book, I spent time in 40 different classrooms, K to 12, observing students. So not observing the teachers so much. The teachers took care of the teaching. I was paying attention to the students and one of the things that I started to notice was that everywhere I went, I saw the same thing. Students were not thinking.

And as I started scratching this more and more and more, I realized that there was very few opportunities in the lessons that I was observing for the students to think. And not only that - that the actual institutional structures of classrooms in many ways were not allowing students the opportunity to think. So I started to really just experiment with - what are the things that we can change about the institutionally normative structure of classrooms, um, that would, that would at least afford the opportunity for thinking to occur.

And this was really very much - I was in the weeds - like it was, it was messy, we were experimenting with lots of different things. Eventually, it started to take form and structure, and, one of the ways that I got it to take structure was I went and spent more time in classrooms watching what teachers do. And this time I was focused on the teachers and I was focused on trying to categorize the distinct parts of a teaching practice. And it turns out that there was 14 of them. There are 14 things that every teacher does. And they do it in their own unique way, but there are these 14 things. Um, every teacher will give students some task to do. Every teacher will answer questions for students. Every teacher will have students give some sort of homework for students. Every teacher has students write notes - that's less true at the younger grades of course. Every teacher does evaluation.

These are the 14 sort of meta practices that everybody's individual practice is made up of. And that became sort of an organizational structure for us then when we were doing this research was asking ourselves, "Okay! So if every teacher has students do group work, is there a way to do group work that promotes more thinking than other ways?"

"If a teacher has students do some tasks, is there a type of task and a way to assign tasks that gets students thinking more?" and that really became the core of this 15 years of research into thinking classrooms.

So, so, that's sort of the emergence of how this came to be. The idea that it was, this, this, towardness, emerged after we had found the optimal, the 14 optimal practices, and I put quotations around optimal, because they're optimal within the space that we experimented, with the context, but once we found those, we also were keenly aware that no teacher could ever implement all 14 at once. Like it just is impossible! Um, not only only is that overwhelming from a professional perspective, it would overwhelm the students to have a teacher come in and just change 14 things on day one. So we spent a lot of time experimenting with, "Okay, so we know where we want to get to, now what's the journey to get there? What's the trajectory? How do we, where do we start? What's the first thing we do?" Um, and we learn things- there are really bad places to start and really good places to start. And this emerged this sort of pseudo sequence, which I talk about in chapter 15, but that then became the organization of the book because once we understood the way that, the best way for a teacher to implement these 14 things, I organized the book accordingly. So that as you said in the introduction there, that a teacher can pick up and read chapter one, and then go and do it. And then come back and read chapter two, and then go and do it. And, so, and each one of these things moves us closer and closer, and closer towards a thinking classroom.

So, the structures really emerged out of this sort of empirical research into this.

Desiree Harrison 8:38

Every chapter, it just made so much sense to me. And, like, you were saying, it's about the students, not about--they are the center of this work, not the teachers, and that's something also that you don't, um, often see in a professional development book or professional learning book - it's usually about what the teacher needs to change because of the teacher, but I really liked how - "Oh, this makes - this is going to help my students the most, so let me go and change that. And the idea about the rubrics and making them more visual based because we are visual learners was, that, that made so much sense, cuz I know when I first started in the classroom, I was actually a middle school science teacher and I had rubrics, and people around me weren't using them, but they were relatively new in our building, but they weren't picture based and they were very wordy and I think like you said, nuanced and just it wasn't - looking back on it, "woah, what was I doing?" But I mean I didn't, I didn't know then what I know now, but just, just sitting down and listening like you have done for so many years, just listening to students can make all the difference.

Peter Liljedahl 10:00

Yeah, and can I jump in on that? So, one of the things that we learned around evaluation and grading, and assessment was that how teachers interpret and understand things is very different from how students interpret and understand things. And if we want to use rubrics, for the purpose of helping students become better learners and better navigators of their own learning, then we have to use rubrics that communicate more clearly to students, than communicate more clearly to teachers. It turned out they were very different. So that I think is what you're picking up on there- is that all that work in those chapters is about - how do we actually construct and use rubrics that make sense to students rather than making my grading easier.

Desiree Harrison 10:52

Yes. We always so, you always hear that teaching is a selfless act, but then we have to continue to make it selfless in all the different areas in which we are interacting.

Commercial Break 11:05

I'm taking a quick break, to remind Kids Math Talk listeners about all of the math professional development books that are available through Corwin Mathematics at us.corwin.com. Many of the authors of some of the latest titles have been guests on this very podcast. Search for Teaching Math At a Distance, Activating Math Talk, and also the book referenced in today's podcast, Building Thinking Classrooms, to get you started. Want free shipping? Of course you do! Then use our special code, K-M-T-S-H-I-P, that's KMTSHIP, all caps, at checkout. Now let's get back to the interview.

Desiree Harrison 11:56

So, something else- I've been hearing about you and your wonderful work for years and year and, so, like, I was saying to you earlier, before we started, DACTM (Detroit Area Council of Teachers of Mathematics) analyzing all your research and with some of those colleagues, I kept hearing VNPS, NVPS, and I was like, okay, I'm not really sure what VNPS means, but now I know what it means, the Vertical Non Permanent Spaces, and something that I realized when I was still in the classroom, like right before I became a coach I was a 3rd grade teacher, and I realized I was trying - like I did not have the language, did not know your research at that point - but I was trying to get kids to do this, to, like, stand up to write on, um, to write on our cabinets, but then I was told that I couldn't do that. So, I went back to the desks - the regular desks, the regular, like sit down and let's write in a notebook, but can you please tell us about this VNPS and the progression of this.

Peter Liljedahl 13:16

Coming back to what I said before, so every teacher gives students something to think about and then they usually give students collaborative groups to think with - and now the question is - Where are they going to do their work?

And one of the most enduring institutional norms is that students will work by writing in their notebook. They'll sit at their desk and write in their notebooks. And the question is, "Is that really the best place to do the work, if we want students to start thinking?"

And, so we experimented with lots of different ways - like who would like that that would make a difference? That whether they're writing in their notebook, or they're writing on a piece of flip chart paper- does it really matter?

It turns out it matters a lot. And when we started experimenting, what we discovered relatively quickly, is that if we get a group working on a thinking task, standing a a whiteboard. Working on a vertical whiteboard, we get way more thinking out of them. they think for longer, more of the students are thinking. And there's a whole bunch of other by-products. Like we get - they're more enthusiastic, they're more collaborative, they're more communicative, they have more perseverance. Like, all of these things start going through the roof if we get them up on a vertical whiteboard.

And that was - we ran some controlled experiments on that and it just kept coming back. That this was by far, the best workspace to have students do their thinking.

Now, teachers are infinitely innovative. And very few teachers have enough whiteboards in the room to be able to get all of their students working on whiteboards. So, teachers started finding, ah, hacks. So we learned very quickly that we can have students writing on windows, or the side of a filing cabinet. We could have students write on vinyl picnic table covers, or that sort of of cellophane that you wrap flowers in or make gift baskets out of. All of these work just as well. All they really need to be is vertical, and erasable. And that's when the terminology shifted from whiteboards to vertical non-permanent surfaces. Because it wasn't that it was a whiteboard. It was that it was vertical, and it was erasable.

So, that was this vertical, and non-permanent being erasable, turned out to be really, really, really, powerful. And now, we didn't understand why. We just knew that that's what was comping out number one in all the measures. We spent a lot of time doing theoretical work around this; trying to understand why is it that it's working so well. And there was a lot of little things that emerged. Ah, things like, well, when all the students are standing a a whiteboard, all the students are staring at the work in the same orientation. This was not true when we had whiteboards on a table. There was always some student looking at it upside down. It turns out that when everyone was up on a whiteboard, if they needed to borrow an idea-that was what one of the kindergarteners students once said - "I'm gonna go borrow an idea." They could just look around and get ideas from other students. It was easier for them to gesture, they were talking to each other in a different way. But, all of these things were relatively minor contributions. What turned out to be the most significant, and it took a long time to get at this, is it turns out that when students are sitting, they feel anonymous. And that when students feel anonymous, they disengage. And that's both a conscious and a subconscious act. So, they are much more likely to disengage when they're sitting than when they are standing. And if they're sitting far from the teacher, they're more likely to disengage. And we have verified this through lots of different experiments.

So really, what was happening was when we were getting the students standing, they weren't feeling anonymous, they were less likely to disengage, and so they were more engaged, more focused, more energetic, and more enthusiastic in their work. So, it's one of these acronyms that emerges in education, we love acronyms, this one's VNPS.

Desiree Harrison 17:38

So, I wrote down the idea of what you said the kindergartner said, that I'll borrow the idea, 'cuz I think that that's such a beautiful way of thinking about it, instead of, "Oh! You stole my idea!" Which we sometimes hear kids saying. But inviting collaboration and saying that we're all working - we're all really working together. No one's stealing from one other person. We're building upon ideas. Or being inspired by somebody's else's ideas is much more powerful to think about.

And you were talking about engagement and having - I'm thinking about how much that word has emerged since remote learning has been happening. It's always been with us, but I've never heard so many people talk about engagement before. And thinking about disengagement and how to keep kids engaged beyond keeping their camera on or anything like that. But you were talking about not feeling anonymous, and that reminded me of one of the chapters in your book about the keeping the flow going. And thinking about the ability versus challenge. So, can you speak to this idea of flow.

Peter Liljedahl 19:00

Sure. So, engagement is one of these. So, let's start - Engagement is one of these words that everybody intuitively knows is a powerful thing. It exists in lots of curriculum documents. Your principal at school probably uses it three times every time they talk about something. Engagement is just something we know is inherently good. We want our students engaged.

And for me, engagement became a really important thing because I made the observation that when students are thinking, they're always engaged. And when students are engaged, they're always thinking. So, engagement and thinking travel together - they're not quite the same thing, but they're always together. And if you think that you have students who are engaging without thinking, they're actually being entertained, rather than being engaged.

And engagement is really, really important. And disengagement, of course, is the antithesis to thinking. So, the question then is - How do we create engagement, if engagement requires thinking?

So, there is a Hungarian born psychologist, he works at the University of Chicago. His name is Mihaly Csikszentmihalyi, and he became, about 40 years ago, became interested in something he called the optimal experience. The optimal experience is this experience when we are so engaged that you don't want to disengage, right. And we see this in our kids, like, twice a year, right, like the bell rings and kids are so engaged they don't want to go out for recess or whatever. But he became really- so obviously this idea of optimal experience has powerful educational implications and so he studied people he thought we most likely to have optimal experiences, and he studies them for a long time until he gathered enough data. And then he started to notice some patterns.

And he noticed for example, that every time someone's having an optimal experience, they lose track of time. They become less self-conscious, they stop doing the activity as a chore and they start doing it for the sake of doing it.

He noticed that there was immediate feedback on action. He noticed that-and this is the most important one - he noticed that every time people were having an optimal experience, it was a perfect balance between the ability of the doer and the challenge of the task. And he represented this in a graph, but we don't need to have the visual here. We just need to talk about three special cases.

So, special case #1 - Let's say that there's an imbalance and the challenge of the task is much, much greater than the ability of student. Well, we know, we've seen this happen. This is when students are going to become frustrated.

And now let's say conversely, that the ability is really high and the challenge is really low. Well then the students are going to become bored.

So those are, sort of, two extremes. And now, let's talk about when they're in balance.

So this is when there's a nice balance between the challenge of the task and the ability of the student. This is where the optimal experience happens. This is where engagement happens.

This is where, what he started to call flow, happens.

So flow is this band on this graph where there's this perfect balance between the ability of the doer and the challenge of the task. And it's a really important place for us to think about as educators. Because it turns out that in our classrooms, there's really only three spaces students can be in, in this balance point - within this relationship.

Either they're frustrated, or they're bored, or they are in flow, in this balance.

And, so, if we're not maintaining the balance, we're either frustrating or boring our students.

And neither of those is helpful for thinking or learning.

So that kind of puts it on us - How do we create this balance?

And then, of course, this is complex because not all our students are the same. So, we've got 25 students who are all in different places and we're trying to create this balance. And not only that, when students work on something, their ability increases, so now we have to increase the challenge as their ability increases. And we have a word for this in education - and it's called differentiation, which is our ability to meet the learner where they are and to keep them engaged as their ability increases. Except when we think about differentiation through the lens of flow, we kind. of land in a different set of practices than if we think about differentiation through classic means.

But that's sort of what flow is. Flow is ultimately, trying to construct and maintain a balance between the challenge of the activity and the ability of the students. (25:53)

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