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FULL TRANSCRIPT

00:00:22:17 – 00:00:23:04
Peter Liljedahl
I ran it.

00:00:23:06 – 00:00:33:09
Kyle Pearce
In this episode, we bring back on the podcast for the third time the godfather of the Thinking classroom, Peter Linda Hall We spoke with Peter.

00:00:33:09 – 00:01:03:14
Jon Orr
Way back on one of our first episodes, Episode 21 of this podcast about how he built the components of the thinking classroom was also before he released his book called Building Thinking Classrooms. We then brought him back on episode 98. We talked about group work and how to choose tasks and what’s the optimal number for groups. And in this episode we bring Peter back on for that third time, and we’re going to talk about the three components of closing your lessons so students walk away feeling confident, connected to the learning that took place.

00:01:03:14 – 00:01:25:16
Kyle Pearce
All right, folks, let’s dig in with one of our favorite friends in the math world, Mr. Peter Liljedahl.

00:01:25:18 – 00:01:28:23
Kyle Pearce
Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pearce.

00:01:28:23 – 00:01:33:02
Jon Orr
And I’m Jon Orr, we are from makingmathmoments.com.

00:01:33:04 – 00:01:43:08
Kyle Pearce
This is the only podcast that coaches you through a six step plan to grow your mathematics program whether at the classroom level or at the district level.

00:01:43:12 – 00:01:57:00
Jon Orr
And we do that by helping you cultivate in foster your mathematics program like a strong, healthy and balanced tree. So if you the six parts of an effective mathematics program, the impact of your program will grow and reach far and wide.

00:01:57:06 – 00:02:23:20
Kyle Pearce
Every week you’ll get the insight you need to stop feeling overwhelmed, gain back your confidence, and get back to enjoying the planning and facilitating of your mathematics program for the students or for you district leaders, the educators that you serve. Hey. Hey there, Peter. Welcome back to the Making Math Moments That Matter podcast. First of all, we want to know where have you been lately?

00:02:23:22 – 00:02:43:06
Kyle Pearce
What’s been going on in your world? But I’ve also got to say, I feel like over the many district calls that John and I have been on over these past six months, your name, your work, whether it’s Betsy or they say thinking classrooms or they say Peter, it comes up so often. So clearly you have struck a chord.

00:02:43:06 – 00:02:57:09
Kyle Pearce
We know that it is definitely a movement and it’s a movement in the right direction. But the hard part is it’s still hard work. Teaching math is still hard work. So tell us, how are things going in your world? Where have you been and what have you been up to lately?

00:02:57:13 – 00:03:18:08
Peter Liljedahl
First of all, thanks for having me back. I don’t know if you noticed, but the first podcast I did with you was also the first podcast I ever did. Oh, so it’s always exciting for me to come back to this space. I love doing the podcast format. I do a lot of them, but there’s something about the Canadian content, the collegiality with this, the.

00:03:18:09 – 00:03:19:23
Jon Orr
Old cruise back together.

00:03:19:23 – 00:03:20:10
Peter Liljedahl
Yeah.

00:03:20:12 – 00:03:22:02
Kyle Pearce
Yes, that’s.

00:03:22:04 – 00:03:49:00
Peter Liljedahl
Where right now I’m coming to you from a place called Eau Claire, Wisconsin. And this is my last stop on a four week road trip through the US. Through is the wrong word. I’ve been criss crossing this country back and forth for four weeks. And wherever I’ve been, I’ve been all over. I’ve been zero D, Kansas, California, Texas, Colorado, Idaho and Wisconsin.

00:03:49:02 – 00:03:52:23
Peter Liljedahl
Just got here from Washington. I was also in Utah.

00:03:53:00 – 00:04:10:15
Kyle Pearce
How come you don’t sound like you’re out of breath? That’s what I’m wondering here, because I’m exhausted. John and I were in Houston last week and I feel like, man, those trips wipe me out now. And I can only imagine and know if it’s just that you’re just in such, such a zone. And yeah, it’s just you’re, you’re it’s not.

00:04:10:21 – 00:04:36:15
Peter Liljedahl
For you to relax. Although I usually catch up on email, but it’s my downtime. But prior to that, I’ve been also all over the world. This summer I was in Warsaw and I was in Oslo for the release of first the Polish edition of Building Thinking Classrooms and then the release of the Norwegian Edition. So there’s, I think, five or six languages in print now with plastic, seven or eight more to come next week.

00:04:36:15 – 00:04:37:19
Peter Liljedahl
I’m on my way to Australia.

00:04:37:24 – 00:04:56:09
Kyle Pearce
Congratulations, my friend. That’s pretty remarkable. Just like you said, it is spreading like wildfire. Maybe that’s too close to home for us Canadians with what’s going on right now. But it is a very massive achievement that you’ve had and continue to have here as more and more people dig in.

00:04:56:13 – 00:05:15:17
Jon Orr
Yeah, it’s a huge impact and I think it shows from the movement that’s happening is that folks are learning from your work, reading the book, but then quickly implementing and having success, which is changing students, right? It’s changing the experience that students are having in math classes and people know it and feel it. And that’s why it’s spreading by word of mouth, I’m sure.

00:05:15:17 – 00:05:38:04
Jon Orr
And, you know, before we hit record, you know, we were chatting about building, thinking, classroom conferences that you’re going to. But also you said usually the local place is doing all the organizing you’re attending and you’ve got your Hey, I’m coming. It’s going to be awesome. And you’re saying it’s such a great experience, but when you’re there and you’re talking with folks like, what are you hearing as some of the successes that teachers are having?

00:05:38:04 – 00:05:52:09
Jon Orr
I just named a few because those are the successes I’ve had, the successes I’ve had in the classroom. But also, what are some of the people are asking you the most I’m curious about? They’re going to ask you probably the same questions everywhere you go. I wonder what is that most ask question as well?

00:05:52:11 – 00:06:18:08
Peter Liljedahl
Okay. Wow, that’s a lot of stuff. All right. So first of all, let’s back up to success. I couldn’t be happier, of course, But one of the things I think is happening is that building thinking classrooms is almost becoming a frame that either could work is attaching itself to math education. There’s so much good work by so many good people out there that are doing things that are filling the space with resources to the great instructors.

00:06:18:10 – 00:06:36:10
Peter Liljedahl
Mike Flynn Everybody is filling this space with amazing work, right? Robert Kobilinsky And I think what building thinking classrooms is doing is it’s giving it a frame to hang some of these things on, not that they need it. There’s so much good work out there, but I think in some ways it’s become a synthesizing organ of the conference.

00:06:36:10 – 00:06:58:12
Peter Liljedahl
I went to an Indiana. It was unbelievable. Right. They reached out to us about a year ago and said, Hey, we’d love to have a building thinking classroom conference and sink your boots. I can’t think that that would ever work. There would be enough people that were interested in wanting to do that. We went through the process of them initiating the call and so on, and I was excited by it.

00:06:58:12 – 00:07:22:01
Peter Liljedahl
But there was a part of me that said, okay, I just can’t see it that many people would be that interested. Well, they had 925 people, 200 presentations, 128 presenters. I was on stage, I was busy, I was doing sessions, but I wasn’t the only one and I was just blown away. And why 925 Because the auditorium held 920.

00:07:22:01 – 00:07:25:08
Kyle Pearce
Seven and two security guards and that’s it. Yeah.

00:07:25:10 – 00:07:49:07
Peter Liljedahl
Yeah. And aside from the amazing organization by Indiana Learning and the local organizers in Franklin and just the synergy that people brought, I think one of the things that was really magical about it was everyone was talking about the same thing, which doesn’t happen when we go to Nancy and people are different. And it’s not that they were all talking about the same thing about they’re always thinking classrooms, right?

00:07:49:08 – 00:08:14:09
Peter Liljedahl
That was the structure around which the conversation was happening. But the thing I like the most was people were treating it like a problem to solve rather than a choreographed dance to master. So what are you doing with thin slices? Have you figured out consolidation? And I couldn’t be happier about that because I keep saying this A building thinking classrooms is a problem to solve, not a choreographed dance to which Peter is the only one who knows the moves.

00:08:14:11 – 00:08:37:01
Peter Liljedahl
I have research. I presented the research. The research continues to grow, but that transition from what we know we need to do to making it happen in your particular context needs to be problematize and it needs to be engaged in authentically. And that’s what I was seeing, people having these rich conversations, sharing their ideas. It was just such an amazingly supportive space.

00:08:37:03 – 00:09:01:06
Peter Liljedahl
What are the key questions? One of the questions everyone always wants thin slicing. How do we do more of that consolidation? How do I find time for that? What about notes, homework? And then, of course, a million assessment questions. And they come in different flavors. There’s the assessment question of what does assessment look like? And the minute you start talking and I go, I don’t want to know about that, or the people who are like, I’m there.

00:09:01:06 – 00:09:17:04
Peter Liljedahl
I’m trying it. I need some practical pointers on this. And that assessment is always has been and always will be a difficult part of teaching. We started by saying teaching math is hard work. It is hard work, assessment is hard work, and nothing we do is ever going to change.

00:09:17:04 – 00:09:37:11
Kyle Pearce
That’s the part that’s really for me interesting about you had already mentioned that it’s like a frame. I loved how you put that picture. It is like a blueprint, but a blueprints. Wrong, because the blueprint suggests it’s got to go like this and it has to go like that and it’s going to look the same way. And if I look at the blueprint, you look at the blueprint, it’s going to be exactly the same, which it’s not.

00:09:37:13 – 00:09:58:15
Kyle Pearce
But when you say frame, it’s like you’re in the sandbox and you get to do things a little different. Your castle can look a little different. But if you go too far outside the sandbox and maybe you’re starting to lose some of these elements and the interesting part is, is that that makes it so incredibly complex and big and there’s so many pieces.

00:09:58:15 – 00:10:23:22
Kyle Pearce
Just think of what you named the boat like then slicing, which is purposeful questioning and framing the questions and creating those problems strings and notes and homework and assessments like a complete other massive, massive idea. But yet everyone is flocking to the idea when you would think the opposite would be happening, right? If you told someone, Hey, if you come over here and you just like read this book, everything is going to be involved.

00:10:23:24 – 00:10:58:14
Kyle Pearce
That sounds too overwhelming for a lot of people, but yet it seems so the entry point so great. It’s like a great math problem, right? A great math problem has that low floor, but a massively high ceiling. And that’s sort of what was kind of popping into my mind right now is that you have this frame, this process that encompasses so many different elements from every math classroom that you could go down any rabbit hole you want and still have years left of work in practice and iterating to do as an educator to feel like you’ve really got a solid grasp on that.

00:10:58:20 – 00:11:06:06
Peter Liljedahl
Yeah, it’s funny. When I was first sitting down to write the book, I remember my editor saying like, you can’t put 14 in the title. Like, that’s just ridiculous.

00:11:06:07 – 00:11:11:07
Kyle Pearce
Not too many people like three. Yeah, three things and that’s all that matters.

00:11:11:08 – 00:11:31:08
Peter Liljedahl
I’ve maybe at the outset, but 14 I guess. Yeah. And I think that’s part of it is I think one of the strengths of building thinking classrooms. Not that other things that aren’t strong as well is that it’s really clear that we don’t do all 14 at once, don’t even try to do all 14 at once. But when you’re ready, as you said, when you’re ready, number five, Sarah, number six is there, right?

00:11:31:11 – 00:11:32:14
Peter Liljedahl
There’s more stuff to do.

00:11:32:20 – 00:11:47:17
Jon Orr
Yeah. And I think when people are latching on because it is an easy change to do some of the 14, right? Some of the 14 are really hard but some of the 14 are can be like, I can get into this right now and then I can start to make a change and see.

00:11:47:17 – 00:11:49:14
Kyle Pearce
And feel a difference. Yeah. Right away.

00:11:49:14 – 00:12:10:09
Jon Orr
Yeah. You feel the difference in the classroom. You actually get a different feeling when students are, say, up at the walls and you’re doing the work. What would you say? I sometimes worry about someone who says, I read the book, but I’m doing building thinking classrooms. And when you go in there, got their kids up at the walls and that’s the way they think it is, right?

00:12:10:11 – 00:12:28:06
Jon Orr
We’re doing building thinking classrooms. But what they’ve done and it feels like what they’ve done is they’ve like, here’s the work I was going to do and here’s the worksheet. Just go do it at the wall. We’re doing building thing in classrooms. And here’s the thing. It does feel different because your students are standing. They are talking about math.

00:12:28:08 – 00:12:44:07
Jon Orr
As a teacher, you’re like, Well, that’s different than me just delivering. But there’s all so much more. There’s so much more that we have to do to get that deep learning that’s so important for students to make the connections. Is that question popped up or is like, has anyone brought that up to your retention to like, what do we do to help that teacher?

00:12:44:07 – 00:12:46:04
Jon Orr
Kind of like you got to take that next step.

00:12:46:08 – 00:13:11:01
Peter Liljedahl
I hear this from coaches a lot, actually. I think one of them even said they. Burdick realized their lesson, but that’s all they did. But I think, okay, they did that. That’s a step that’s an improvement. Hopefully they see some value in that and that value is enough to propel them into doing the next thing. And then I think next thing, I think a return on investment is important and anything that we try in our classroom, we’re willing to work hard, but we don’t want it to feel like our work is wasted.

00:13:11:07 – 00:13:33:02
Peter Liljedahl
So we want to see some return on investment. And if that’s giving a return on investment, but then how do we move forward? It’s funny because I’ve actually been working a lot on this lately, a lot around the closing of the lesson because you asked me, what are the successes that we’re seeing? So of course we’re hearing stories and we’re hearing lots and lots of stories of teachers.

00:13:33:02 – 00:13:59:16
Peter Liljedahl
I remember I was at campus, which is the big Texas math teacher conference this summer, and I was just walking down the street and this woman crossed the road and walked right up to me and said, this person new down, that’s telling you I implemented partway through the year in the units that I did thinking classrooms in my students scored well above state average on the standardized assessment and the units that came before I implemented.

00:13:59:16 – 00:14:27:08
Peter Liljedahl
They scored below these sorts of things. Stories about how you extended my career, these really positive, uplifting stories of student aspects and how they made the difference for an individual student or an individual teacher, seeing how student performance improved. And that’s always a slippery slope and difficult to measure. But the magnitude of these stories, but then, you know, we also have stories like I did it, it was fun.

00:14:27:13 – 00:14:47:02
Peter Liljedahl
The kids liked it. I didn’t see any improvement. And it’s like, okay, well, let’s dig into that story a little bit better. And often when that’s the story, what we see is exactly what you asked John, which is like, okay, random groups on vertical surfaces. And that’s all I did. And what that does is it creates a different space for meaning making to happen.

00:14:47:07 – 00:15:25:08
Peter Liljedahl
I think it creates a different experience for students, and students need better experiences. Learning aside, we need to improve the experiences of learners. They’re spending a lot of time in school 200 days a year, 13 years. That’s a lot of time. It’s the experiences aren’t positive. But how do we actually turn those positive feel good experiences into? Retained learning is an important step, and that’s why I’ve been spending a lot of time on the closing of the lesson on how do we transform that messy meaning making that in the muck, and then how does that then translate into something that the student can walk out of the room with?

00:15:25:10 – 00:15:37:05
Peter Liljedahl
But more importantly, when they come back in the room, they still with them as opposed to just drifting away and that being just an experience that happened in that moment in that space with that group. And that was it.

00:15:37:11 – 00:15:56:07
Jon Orr
Yeah. In the course that we were chatting with a bunch of teachers in our live Q&A session today, and teachers were wondering about boil down to consolidation, but really they were asking a different question. But when we dug deeper, it was the student who was leaving the classroom and they could sense that they didn’t know what the learning goal of the lesson was.

00:15:56:11 – 00:15:59:03
Jon Orr
They were in the muck, right? But then it didn’t.

00:15:59:03 – 00:16:01:07
Kyle Pearce
Lots of good thinking, lots of sharing. Right.

00:16:01:07 – 00:16:15:05
Jon Orr
And this is something we’re hearing from a lot of teachers who are trying to get students thinking, which is amazing. Right? We’re trying to get students thinking, but they get to the end and it’s either they ran out of time or they didn’t think about the end. It’s like, oh, we got them doing work. But then nothing. We’ve been calling it tying a bow on that, right?

00:16:15:08 – 00:16:31:08
Jon Orr
How do we tie a bow on it so that by the end of the lesson or by the end of the students walking out, they are feeling like, Wow, I know exactly what the purpose was today. And I now have these next steps to go and do. And when I come back tomorrow, I’m going to do that again.

00:16:31:08 – 00:16:45:07
Jon Orr
And I know by the end of class today I might be in the muck in the middle, but I know that my teacher’s going to bring it home for me at the end. And I think that part has been missed for a lot of folks. And I think that we’ve been chatting with lots about how to bring that home at the end.

00:16:45:10 – 00:17:08:09
Peter Liljedahl
So the metaphor I use is this We put them into groups, we get them thinking whether it’s a rich, deep task or it’s a thin slide sequence of tasks that get progressively harder. They’re making meaning. They’re in the they’re spitballing, right? They’re trying things, they’re putting it on the board. It’s working. Okay, let’s extend that thinking. Their ideas are converging, or maybe they’re not converging, but they’re finding synergy between each other.

00:17:08:11 – 00:17:30:06
Peter Liljedahl
Their ideas are moving them forward. They’re getting further into the task or further through the set of tasks. But their ideas are still floating. Their ideas are floating around loosely. And if the bell rings and they walked out of the room with those ideas still floating around loose, they’re likely to float away. Yeah, exactly. Yeah. And then they come back the next day and they’re like, Nope, never seen this before.

00:17:30:06 – 00:17:52:16
Peter Liljedahl
I don’t. You’re talking about Right, Right. And I think we’ve all had that experience. You and I took your attendance. You were here. We did this. I have photos. Right. But the purpose of a closing and I keep using the word closing as opposed to consolidation, because closing in my world includes more than consolidation, but it’s what is it that the closing does?

00:17:52:18 – 00:18:17:14
Peter Liljedahl
And you say tying a bow. What I say is that the closing is when the teacher helps the students organize and formalize their thoughts in such a way that they actually both expand their thinking, but also sort of sort them out, organize it in such a way that it pins down their ideas in a structure that they can then take with them.

00:18:17:16 – 00:18:49:00
Peter Liljedahl
So we’re going from that sort of free, floating, unorganized, informal ideas to more organized, formalized, structured ideas. And it can happen on its own. The students can certainly do it. And we have really good evidence that 60% of the students, 60 to 70% of its students, given the right experiences, can do that on their own. But the role of the teacher is to help all of them do it better, to help all the students achieve that same sort of formalized, organized thinking.

00:18:49:02 – 00:19:08:06
Peter Liljedahl
But also for those students who are able to formalize and organize their thinking on their own. So also expand their thinking, thinking to realize that, yeah, you have a way of thinking about this, but there’s multiple ways of thinking about that. Let me show you some of those and let me help you put those into their slots so you have a richer thinker understanding of the concept.

00:19:08:06 – 00:19:26:13
Peter Liljedahl
And there are three practices that help us do that. Consolidation is one of them. Note making is the other, and then check your understanding questions. And that’s not to say that we need to do all three, but all three contribute to that process of turning the disorganized to organized and the informal talk channel.

00:19:26:15 – 00:19:56:09
Kyle Pearce
I love it. I’m so happy that you articulated that because I was going to ask you that. I wanted to really get explicit and I wanted to get structured, as you just said, because I don’t want anyone walking away kind of going like, So what is the difference between a closing and a consolidation? And you were saying it’s more than just the consolidation and I think you nailed it in terms of all three of those things are so important and how they happen may look and sound a little different, depending right on the scenario, the students, the approach potentially.

00:19:56:11 – 00:20:17:15
Kyle Pearce
But I really like that because I think oftentimes and I think this is happening more times than not, not only are we not doing as a whole, we’re not doing a great job with consolidating, but then we’re also not formalizing it, right. Giving students some sort of structure or working with them to build that structure right. It can be facilitated.

00:20:17:16 – 00:20:46:07
Kyle Pearce
Some teachers are like, Are they just supposed to make their note on their own? And you’re like, You can allow that to happen, to give them the practice, but then we probably need to come in and sort of help to ensure that that structure has been formalized. Because how many times, not just in math class, but just in everyday life where something resonates with one person, You assume it’s resonating in the same way with someone else, and then you have a conversation like, Oh, I totally didn’t know that’s what you meant by that, or I totally missed it.

00:20:46:13 – 00:21:06:07
Jon Orr
Remember that movie idea that we had talked about for a while? I don’t really share this with you, Peter. There’s something called it sounds harsh or not vulgar, but it’s called the dumb Viewer Effect. It was something that our nineties TV shows did at the end of these hour long, you know, mystery dramas. You were doing things along the way and you were, as a viewer, piecing things together.

00:21:06:07 – 00:21:08:01
Jon Orr
And this mystery word, oblivious.

00:21:08:01 – 00:21:12:04
Kyle Pearce
John Weird, I think we call a little bit softer on that. But you’re right. You call it.

00:21:12:06 – 00:21:15:05
Peter Liljedahl
All those you miss all the clues and all the hints.

00:21:15:09 – 00:21:16:04
Kyle Pearce
Exactly.

00:21:16:04 – 00:21:25:06
Jon Orr
There is a character that would come in. Exactly, exactly, exactly. A character would show up and go, what I missed or something like that. And they would just state all the things that.

00:21:25:08 – 00:21:29:11
Kyle Pearce
Thank goodness that guy showed up. Otherwise, I have no idea what was happening in this episode.

00:21:29:13 – 00:21:44:16
Jon Orr
It’s kind of like that’s happening in the class. Prolog though I think I taught like this for a while when I was consolidating is you think that because you witnessed, you saw different things happening from different groups around the room or you heard a kid say it to somebody. They didn’t actually formalize it in terms of generalizing as well.

00:21:44:16 – 00:21:52:09
Jon Orr
So it’s like you have to make it very clear. You have to be that person who is like, the person walks in the room. We have to summarize it all up so that you.

00:21:52:11 – 00:21:56:17
Kyle Pearce
Know, the person this teacher is that person that goes, Here’s what.

00:21:56:18 – 00:22:10:00
Peter Liljedahl
Happened. But there’s new out there because we also don’t want to make it so that the students don’t have to do any of that much. And just waiting for us. Right? Right. That’s true. Space. Yeah. We’re just closing the door on those last few.

00:22:10:02 – 00:22:15:24
Kyle Pearce
They’re like, he’ll be back with the photocopies. Say that the Peter your portable story it’s like not I. He’ll be back. He’ll be back.

00:22:15:24 – 00:22:24:14
Peter Liljedahl
I’m waiting for your appointment. About Heard one student say it. So we assume everybody saw it even worse than we saw it. So then we assume that everyone sees it.

00:22:24:18 – 00:22:26:18
Kyle Pearce
It’s our confirmation bias, right? You’re like.

00:22:26:18 – 00:22:27:17
Peter Liljedahl
Oh, gosh.

00:22:27:17 – 00:22:33:09
Kyle Pearce
That’s what I was looking for. It’s like they must have got it. Meanwhile, they might be completely oblivious to it, right?

00:22:33:13 – 00:22:51:09
Peter Liljedahl
And one of the things I’ve been saying a lot lately is we have to stop using ourselves as proxies for what’s good for the students, because who are we? Who are we as math teachers or teachers in general? We are the survivors. We are the Thrivers. We’re the ones who got the gold stars and the praise and the grades.

00:22:51:15 – 00:23:11:07
Peter Liljedahl
We’re the ones who learn how to play the game of school, played it well, liked playing it, and then we became teachers and it’s a game that has a lot of losers. And always assuming that just because something worked for us doesn’t make it a proxy for something that works for all our students. And that confirmation bias is so dangerous because when we look at a student who’s doing it, they’re us.

00:23:11:07 – 00:23:19:05
Peter Liljedahl
But I want to get back to this idea of the notes In my research when I originally did the research, I haven’t really said this very often, but the original research on.

00:23:19:05 – 00:23:22:13
Kyle Pearce
This is insider information, right? Only found here.

00:23:22:15 – 00:23:40:20
Peter Liljedahl
The original research on the note taking was just so bad. Not the research, but the results were so bad that oh my goodness, this is just a waste of time. It’s the data is just telling us everything negative is happening here. And in fact, our first intervention around notes was to just do no notes.

00:23:41:01 – 00:23:45:11
Kyle Pearce
So tell me more about that. Was that when they did it themselves or when the teacher did her own.

00:23:45:15 – 00:24:05:13
Peter Liljedahl
Or it was in that sort of irate you, Right. Yeah. And watching the students and just watching how disconnected they were and how cognitively absent and how many mistakes were in the notes, few students look back at those notes and just what a time suck it was out of that valuable short period of time. Teachers are complaining we don’t have enough time.

00:24:05:15 – 00:24:09:23
Peter Liljedahl
I know we don’t have enough time, but you just wasted 25 minutes doing notes and no one’s looking or.

00:24:09:23 – 00:24:11:12
Kyle Pearce
Paying attention to when they’re writing it.

00:24:11:13 – 00:24:32:06
Peter Liljedahl
Right? So it was better to do no notes, right? It was one of the few times in our data where actually not doing anything was better than what was happening. Now. And we’ve got a bunch of time back. We weren’t wasting the kids weren’t disengaged, right? And we just photocopy notes or put them online and the kids could have them.

00:24:32:10 – 00:24:59:02
Peter Liljedahl
But getting back to this idea of closing is a winning formula. It’s an organic response. No, making plays a role in the note, making an opportunity for students to sit down and think about what happened today and then to organize what happened today into some sort of a structure in the book, I shared some ideas and we can just have the kids write a note to their future forgetful self, or you can use one of these graphic organizers.

00:24:59:04 – 00:25:18:00
Peter Liljedahl
And that data was pretty good. We went from 20% of students being cognitively present when they write notes to 60 to 80%. That is a huge win. Statistically, that’s a huge win for equity. Why is it’s not such a big win? Because that means we still have 20 to 40% of students who are not having access to that experience.

00:25:18:02 – 00:25:44:08
Peter Liljedahl
Right. And yes, they can download notes and yes, we can hand him a photocopy. But the act of making notes as a closing activity, as an organizing activity, was missing for these students. And often it wasn’t that they couldn’t access it, they just chose not to teach. We’ll make that choice, right? Adults someday. Yes, but kids will make bad choices and they will make choices that are counter to their best self-interest.

00:25:44:10 – 00:26:05:17
Peter Liljedahl
And we know that’s what happens. And so for me, it was back to the drawing board even after the book came out, because if I have 20 to 40% of the kids who are opting out of this activity, and I know that this activity is valuable for their learning, we got to do better just because students make bad choices doesn’t absolve us of the responsibility to do better.

00:26:05:20 – 00:26:22:10
Peter Liljedahl
It’s back to the drawing boards and playing with the language and playing with it. And in May, a new structure emerged. Finally, there was a new structure. Last year I played with it for a long time, but again, we were having this opt out and then May came around and I was playing with this one thing and it was starting to show real promise.

00:26:22:10 – 00:26:39:18
Peter Liljedahl
I ran it and 22 different classrooms, grade two to grade 12 personally and 22 different classrooms. It landed every single time everything was involved. Every student participated, every student got something out of it and it was like, okay, now I’m getting closer to what it is I want.

00:26:39:20 – 00:26:59:22
Kyle Pearce
So I am so curious what that looks like and sounds like. Because before you go there, I want to just reiterate what I heard you say and it makes so much sense, right? We know that getting students to do this metacognitive process of thinking it through and you could see why some would opt out, though, right? Because we don’t like thinking.

00:26:59:22 – 00:27:15:24
Kyle Pearce
Thinking is hard. And it’s fairly obvious that it’s like after I already did a bunch of thinking, right. So now it’s like I already did all this thinking and now he wants me to do more thinking, which we know is good. I know a lot of things are good for me that I don’t do, or sometimes I do and I shouldn’t do.

00:27:16:01 – 00:27:24:17
Kyle Pearce
So what is this new structure? I’m actually curious. What were you tinkering with and is it the same different modified version or a smooshed together version?

00:27:24:18 – 00:27:40:20
Peter Liljedahl
I’ll share that with you. But I think part of the reason that students are opting out, you’re right. Thinking is hard and now there’s more of it. But I think also education has somehow created a situation where not having is more valuable than not making it.

00:27:40:20 – 00:27:58:08
Kyle Pearce
Absolutely. I’m going to check that book and make sure that you’ve got all the pages in the right order and all for good reason or I shouldn’t say for good reason for out of the goodness of the heart, the teacher thinks it’s in their best interest. But yet I used to post the notes online for a long time as well.

00:27:58:08 – 00:28:15:08
Kyle Pearce
And like you had said, I kind of came to that conclusion. I’m wasting my time writing, which was true. I post them online, but that was also not really any better. But I got time back. But it was a net zero in terms of benefit, But I got more time where I was able to do more math.

00:28:15:12 – 00:28:24:19
Peter Liljedahl
And parents love. By the way, parents love it when you put notes on it and there’s something to be said for that because then they feel that they can participate in their child’s learning.

00:28:24:21 – 00:28:27:07
Kyle Pearce
Or it’s like you haven’t fully missed it. All right.

00:28:27:09 – 00:28:52:01
Peter Liljedahl
Right. And it’s a great absence. Someone is away and so on. Yeah. All right. So what’s the new structure? So first of all, what is the impetus for this new structure? So one of it was we still having kids after the other one was a couple of realizations. One was structure is important. We talked about that and this idea of despite the fact that the kids have been mucking about, I still want them to walk out of the room with some structure.

00:28:52:01 – 00:29:16:08
Peter Liljedahl
So I wanted the notes to have an opportunity for me to provide some structure. There is also the incredible value of examples worked. Examples in math can carry a lot of understanding in the way we construct them, but also the way we look back at them over work. The example could really carry a lot of understanding in all the things we tried previously or that were in the book.

00:29:16:08 – 00:29:39:18
Peter Liljedahl
That wasn’t enough focus on work examples. But there’s also this idea that counterbalancing the structure is also choice, because one of the things that is a really strong indicator that someone is cognitively present or one of the things that really necessitates someone to be cognitively present is if they have to make a choice, they have to select, they have to sequence when they’re making choice.

00:29:39:23 – 00:30:04:00
Peter Liljedahl
Cognitive presence is sort of hand-in-hand with that. So it’s not just structure, it’s also choice. So the jumping off point was actually sort of a Cornell model of notes, which is an example is in the book. It’s four quadrants. In the four quadrants that we tried in the book was sort of like, here’s our definitions, here’s our formulas, here’s an example, here’s something like a non example.

00:30:04:02 – 00:30:23:05
Peter Liljedahl
Yeah, we labeled the four quadrants, but that was sort of a jumping off point. But I started to play with this in relatively rapid succession and settled on a structure that works really well. So you’ve got to picture four quadrants clockwise from the top left to the bottom, left and right, which if you’re teaching geometry or trig, you hate that number.

00:30:23:08 – 00:30:24:14
Jon Orr
That doesn’t work anymore.

00:30:24:15 – 00:30:45:01
Peter Liljedahl
But psychologically, that’s the way our mind works. Yeah, yeah. Top left and then clockwise. Okay, so the top left corner quadrant is a sort of fill in the blank structure. It’s here is an example, but I’ve partially solved it. There’s some boxes I want you to fill in, and there’s some other things I want you to fill in.

00:30:45:01 – 00:31:06:06
Peter Liljedahl
Maybe there’s some terminology I want you to put in place, but it’s sort of like I build the frame. I indicate what things I want you to add on to the frame. That’s my opportunity to provide structure. Quadrant to top right hand corner is a worked example, but I’m going to tell you what the example is. So I’m going to give you the task that I want you to turn into a worked example.

00:31:06:12 – 00:31:14:11
Peter Liljedahl
So it’s called example one, and it’s usually slightly more challenging than the worked example that was in quadrant one.

00:31:14:11 – 00:31:15:14
Kyle Pearce
But now they’re doing it.

00:31:15:14 – 00:31:35:00
Peter Liljedahl
They’re doing it first. A lot of freedom on how they want to make it look and so on. But I’m telling you what the task is. Quadrant three, which is the bottom right hand, is example number two. But you have a choice here. You choose what you want. Example two to be. So here we go. Now we’re selecting the freedom, the choice.

00:31:35:00 – 00:31:42:01
Jon Orr
So it’s a blank box and it’s like, Hey, you can pull one from the wall that you did earlier. It’s just you fill in what you feel like you need here.

00:31:42:05 – 00:32:03:10
Peter Liljedahl
I might put a structure in. I might say something like, I want it to be this type of question. Yeah. Or I might want the answer to look a certain way, but you have a choice as to what to pick. I just want to make sure that what you’re picking fits from a range of choices. Not that you’re all of a sudden going back and doing two digit addition in the middle of a multiplication unit or whatever.

00:32:03:10 – 00:32:03:24
Peter Liljedahl
You know what I mean?

00:32:03:24 – 00:32:05:04
Kyle Pearce
Exactly. Yeah.

00:32:05:06 – 00:32:25:02
Peter Liljedahl
So there is some parameters, maybe hemming it in here, but still choice. The bottom left hand quadrant is called Things to Remember. That’s a completely blank box, but it’s called Things to Remember. And this is your opportunity to record what was meaning for you from the lesson, the things that you want to carry forward, the things that you think are important.

00:32:25:07 – 00:32:42:16
Peter Liljedahl
Maybe the things that were real sticking points for you that when you figured it out, you felt really good about it. And it’s how you want to articulate that in your own words. So those are the four quadrants, and if you pay attention to it, what you notice is the top two quadrants are structure, because on the bottom two are choice examples.

00:32:42:16 – 00:32:59:04
Peter Liljedahl
On the right hand side and so on. So it kind of carries this ability to have all of the pieces that we want. But here’s the thing. They do it together in groups at the whiteboard. So at the end of the lesson, we may have to a consolidation, we may not. Maybe we feel that up. See, you know what?

00:32:59:04 – 00:33:02:07
Peter Liljedahl
I’ve been checking in with every group. They all know what they’re doing. I don’t.

00:33:02:07 – 00:33:03:03
Kyle Pearce
Know. You’re ready for.

00:33:03:03 – 00:33:25:02
Peter Liljedahl
Consolidation, but we’re moving straight to this note making. So I draw up the structure I put in the fill in the blank one, indicate what the task is in quadrant two and label quadrant three. Example Two things to remember in your groups. You’re not going to produce this at your board. And it is every single time we’ve done this, the energy level in the room kicks up a notch.

00:33:25:05 – 00:33:47:19
Peter Liljedahl
It’s really interesting to see. And I think part of it is there’s an element of, okay, I can do the first quadrant. There’s this mastery space that they’re in there enjoying the mastery experience of being able to showcase what it is they know in an example why, and then select thing. Example two ensures that they’re going to have success because they get to pick it.

00:33:47:24 – 00:33:52:17
Peter Liljedahl
And then the things to remember the conversations are so unbelievably deep. What they’re talking.

00:33:52:17 – 00:33:59:18
Kyle Pearce
About, you only have so much room. So I want to make sure what I put here matters right instead of just everything.

00:33:59:21 – 00:34:01:10
Jon Orr
They’re drawing on the whiteboards.

00:34:01:12 – 00:34:01:21
Peter Liljedahl
Yeah.

00:34:01:22 – 00:34:14:24
Jon Orr
This note is their value in taking it away from there. Like what you were saying. Parents love to have it in the binder, the having of the note. So it’s like, am I taking a picture of it? Or if you’re taking a picture, it, it’s lost in picture land. What’s not going to.

00:34:14:24 – 00:34:30:22
Peter Liljedahl
So there’s a couple of ways that this works. So some teachers will take pictures of three or four representative ones and upload them. Students will take their own pictures. Some teachers take pictures and print them out and give them to the students the next day. But we’ve also played with and I would say that this is not so.

00:34:30:22 – 00:34:49:08
Peter Liljedahl
If we do this in primary three, we’re doing just the top two quadrant. When we move into the other grades we’re moving into. Okay. So the note making was actually more important than the note having right? Kindergarten teachers don’t care if kids have notes. Grade 12 teachers care a lot, and then it’s almost a linear progression throughout there.

00:34:49:08 – 00:35:06:03
Peter Liljedahl
So if you’re a grade three teacher, you may value the note making more than the note having. But if you’re a grade 12 teacher or a grade 11 teacher, the note having is also really important to you. So in no spaces we played with this idea, okay, you’re going to do it in your groups. And that’s when 100% participate and 100% have access.

00:35:06:03 – 00:35:09:13
Peter Liljedahl
And then you’re going to sit down at your desk and you’re going to make your own.

00:35:09:15 – 00:35:35:11
Kyle Pearce
The part that I love about this is what I’m hearing and some of the struggles that we’ve had, conversations with teachers who are like, I’m just not sure how to do note to my forgetful self or my future forgetful self and and really exactly what you’ve articulated here. And it’s been so clear in my mind that not only is it helpful for the students to have the structure, but it’s also important for the teacher to have the structure in their mind of like, what do we need to do here?

00:35:35:11 – 00:35:53:11
Kyle Pearce
Even though most teachers grew up taking notes and they grew up giving notes, so you would think that you’d be an expert at it. But it’s almost like they’re in this new world. They’re like, Well, I can’t do anything that I did before. It’s got to be completely different. And then it’s almost like they can’t see how that would come here.

00:35:53:11 – 00:36:13:23
Kyle Pearce
But what you’ve done is you’ve taken some of the most important parts, a typical note that a student would take. Again, not an effective way to do it would have some of the key pieces you want them to know. It would have some worked examples. Now there would be less ownership, of course, as we know. But the part I really like about this is that you’re bringing the work to examples in.

00:36:13:23 – 00:36:35:22
Kyle Pearce
We know work examples are important, but bringing them in after the learning has already happened gives students the opportunity to truly engage with them. Whereas in that note, taking world teachers would try. We’ve all tried to get students to say, Hey, Tommy, help me out with the next line of this exam. And the students are like, I know the math I got to do here.

00:36:35:22 – 00:36:45:13
Kyle Pearce
I still don’t get the point of what’s happening in here. It’s very different. It’s very clear that they can see this progression and it’s definitely going to resonate in a much more effective way.

00:36:45:17 – 00:37:08:21
Jon Orr
I’m already imagining spinoff activities with the example too. We’re all going to create our own everyone cover up your example two Don’t show the other groups. Your example too. We’re going to unveil it. Who’s got a hard example too? Who’s got an easy example too? Let’s make an example to and challenge the group beside us to see if they can do example two It’s almost like you’ve got this built in.

00:37:08:23 – 00:37:28:02
Jon Orr
You’re going to have all these different example tools around the room and if you cover up, if they build it and it’s like, I’m going to cover up the solution to example two, but I’m going to come up with the problem. You’ve now just built in the full purposeful practice for the next stage. Right now move around the room and do example to from everybody else and you’ve got that practice built in and.

00:37:28:02 – 00:37:50:13
Peter Liljedahl
One of the things we have to be aware of that example too, is so there’s this old Carl Sagan quote, An absence of proof is not the same as proof of absence. And just because the group pics are relatively easy. Question for problem two example two doesn’t mean they can’t do more. It didn’t occur to them. Maybe they wanted to do something more challenging, but they couldn’t picture what that would look like.

00:37:50:15 – 00:38:11:19
Peter Liljedahl
And so seeing someone else’s example two is like, Oh, that’s what we wanted. And this is actually what we see when we transition the students into the Deathstroke. You now make your own note. What they do is you kind of tend to copy their own groups, quadrant one in quadrant two. When they get to quadrant three, they start looking around the room going, Ooh, I like that problem to that example to better or I like that one.

00:38:12:00 – 00:38:20:19
Peter Liljedahl
And then they pick a different one that they themselves had done. And then when they get to the things to remember, they start looking and picking from friend groups. Yeah, I like the.

00:38:20:19 – 00:38:21:23
Kyle Pearce
Good stuff, you know.

00:38:21:23 – 00:38:39:01
Peter Liljedahl
And like that point and what we’re doing here is we’re creating access. Lots of students can participate in this. What I would caution the teachers away from is it’s really tempting that the next stage is, okay, now you’re just going to sit down and do it on your own right from scratch. You’re not going to do the group stuff first.

00:38:39:03 – 00:38:59:11
Peter Liljedahl
And now we’re back to 20 to 40% of students opting out. And that’s not what we want. Unless you’re teaching grade 12 calculus. Maybe you want the kids to get to that stage, but that would be the exception to that. I would say that for everybody else, let’s give them the rich, meaningful experience of not just note making in dialog with other students.

00:38:59:13 – 00:39:01:23
Kyle Pearce
That makes a ton of sense for sure. I really like that.

00:39:02:04 – 00:39:22:06
Jon Orr
Yeah. And you always provide such insightful ideas for folks to use in the classroom, and this is just another one. I love that you thought about this area as a need for folks in built upon what you’ve published, and I know that I think you’ve got it to come out in a future edition with an update, which is going to be amazing for people.

00:39:22:06 – 00:39:36:21
Jon Orr
And every time we chat with you, Peter, we always learn something. And I think it gives us energy. I think I don’t know if you can tell, but it’s like every time we chat with Peter, I’m like, I’m going to run right into the classroom right now and try all these things too. And so I definitely want to thank you, Peter, for joining us here on the podcast.

00:39:36:21 – 00:39:46:18
Jon Orr
But before we sign off and let you get on with your world tour, what would you say is a big main message? You want to leave the teachers who are listening to this with today?

00:39:46:20 – 00:40:05:23
Peter Liljedahl
I think what I said earlier, the only thing in classrooms is a problem to solve, right? It’s not a dance to which I hold the choreography. Every classroom is different. Every time I go into a classroom, I see teachers doing things differently. And it’s still a thinking classroom, right? You got to make it work, but always work. The problem always work the problem.

00:40:05:23 – 00:40:25:07
Peter Liljedahl
And I think the most important thing is we got to always balance the things that make our job more efficient against the things that make learning better. And sometimes we have to find efficiencies just in order to be able to keep going. But always ask yourself, is this an efficiency that benefits me at the detriment of student learning?

00:40:25:09 – 00:40:52:18
Kyle Pearce
So well said. And I think it’s so important. And actually, Peter, we were chatting through email earlier this week about what we should do at the upcoming summit here, but I feel like we’ve got our teeth into this idea. I love it. I love how we’ve structured this idea. We’ve given people a vision of what that closing looks like, that it’s not only are we in need of improving as a whole around consolidation, but also that that’s not the end of the lesson, that there’s still more to it.

00:40:52:20 – 00:41:10:05
Kyle Pearce
And I have a funny feeling that as we get closer to the summit in November, that some friends might have a session where I’m going to guess that this idea might come back to the forefront. So we want to thank you so much for spending some time with us here today. We know you’re extremely busy. Again, not out of breath.

00:41:10:05 – 00:41:34:22
Kyle Pearce
I don’t know how it’s possible, but we so appreciate you on behalf of the math community, the math moment maker community for coming back to your podcast Roots, as you said, it being the first podcast that you’re on. And we always love the. So where can people find you now? I know they’ve heard it before on past episodes, but where is the best place for them to find your work besides your book building thing in classrooms?

00:41:34:22 – 00:41:36:09
Kyle Pearce
Where can they get in touch with Peter?

00:41:36:13 – 00:41:54:23
Peter Liljedahl
Well, I’m not hard to find. If you’re looking for me for an email address, I think Twitter hashtag thinking classrooms are at P.G. only at all the website building thinking classrooms. It’s under construction right now, but the old pages are still there. And one of those is where I’m going to be giving presentations that are sort of open access.

00:41:55:01 – 00:42:24:06
Peter Liljedahl
A lot of presentations I do are close to the district, but those are open places. And of course, there’s a new set of books coming out soon called Math Tasks for the Thinking Classroom. And the first one is going to be K-2 five in the next one following a month or two later is going to be the 6 to 12 edition, and it’s going to have all these new ideas about consolidation and but wrapped around kind of what a lesson looks like, a wrap around how we use a task, how we launch a task, how we scaffold a task, and then how we close a task.

00:42:24:10 – 00:42:41:21
Jon Orr
Love it, love it. Looking forward to that. And what we’ll do is when those come out, we’ll go back and update the show notes page here with all the links so that folks can find those if they’re listening in a year or so or whenever they grab this episode to listen to. So, Peter, thanks so much And we look forward to, again, presenting with you at the summit in November.

00:42:41:21 – 00:42:43:00
Peter Liljedahl
Yeah, I’m looking forward to.

00:42:43:05 – 00:42:47:09
Kyle Pearce
Absolutely safe travels and looking forward to seeing you in person again sometime soon.

00:42:47:13 – 00:42:49:24
Peter Liljedahl
Well, I’ll see you at Oceana in Kingston for sure.

00:42:49:24 – 00:43:14:01
Kyle Pearce
There you go. Take care. All right there, friends. John, always a pleasure to bring Peter back on the show. Something that I was unaware of was that this was the first podcast show that he was interviewed on. And since then, he’s been on very many, many podcast interviews and I’m sure even radio and television interviews in some cases.

00:43:14:01 – 00:43:36:11
Kyle Pearce
So it’s great. What an honor for us to have Peter there also to be able to call him a close colleague and a close friend. And every time we have a conversation, you said it in the episode, you said how you always seem to learn something new. And we talk about this all the time, whether we’re doing a math mentoring moment episode or whether we have a guest on, we’re always learning.

00:43:36:13 – 00:43:55:22
Kyle Pearce
But you would think after having Peter on so many times, having so many with Peter in person and on Zoom calls when we were preparing some of our joint sessions that we’ve done in the past, you would think that that learning would stop. But every single time we always managed to dive down a bit of a rabbit hole.

00:43:55:22 – 00:44:20:20
Kyle Pearce
And today talking about that idea of the closing and having Peter sort of look at it as something larger than just the consolidation was really interesting. And for me, what I immediately saw and this is where I think and why we get along with Peter so well, is because our view, while our frame, as he called it, may be a little bit different in how it came be.

00:44:20:20 – 00:44:49:14
Kyle Pearce
There are so many similarities and I would argue that yeah, the math moments framework that we use fits nicely in the building classroom frame, which is why both you and I use so many of those practices from thinking classrooms. And something I want to really highlight is just the importance of those three parts of the closing that consolidation, having that opportunity for students to kind of user metacognitive skills to kind of reflect and create that note.

00:44:49:16 – 00:45:12:15
Kyle Pearce
And then also having those follow up prompts, those are things that we do in our make math moments, problem based units in every single lesson we’re doing that process. We’ve never called it the closing, but from now on it’s like, maybe we should be using that language. And I really loved it. So when I looked at the tree of our math class program, I was thinking about two big ones here.

00:45:12:17 – 00:45:37:15
Kyle Pearce
One is, of course, the pedagogy piece, right? Which is going to be the branches of your tree. Of course we’re talking about teacher moves and all the pedagogy. But I think even more important here is that we honed in on the roots of the tree. The math content is at the core, just like the roots of the tree are one of the most important systems in the tree.

00:45:37:15 – 00:46:02:22
Kyle Pearce
They to be there in order to nourish the tree and the mathematics needs to be there in order to nourish your math program. If we go in and we try to implement any of those 14 practices from building thinking classrooms and there isn’t real strong math content at the forefront, then none of those moves are going to add up to anything worthwhile.

00:46:02:22 – 00:46:10:09
Kyle Pearce
And it was great to hear Peter kind of articulate that just in a different but similar way to how we have in past episodes.

00:46:10:11 – 00:46:28:15
Jon Orr
Raise summary there. Kylan. I don’t think I have anything to add. So folks, if this is the first time you’ve listened to this episode, you maybe saw Peter’s name in the title and you’re like, I got to listen to that one. I know that some of you are out there listening for the first time, then welcome and hit that subscribe button so that you can listen to more.

00:46:28:15 – 00:46:52:00
Jon Orr
And we encourage you, if you have have listened before or maybe feel so inclined on your first time, to give us that rating and review on Apple Podcasts or on Spotify hit us up so that you can leave that review. It will help the show. It’ll help other educators find this episode specifically, I’m sure, so other teachers can listen to Peter and his unique insights that you’re not reading in his books.

00:46:52:02 – 00:47:09:15
Jon Orr
So please rating and review Also show notes, resources and transcripts head on over to make map on Sky Sports Episode 249. That’s episode 249. And you can get all of those and plus any links we shared here in this episode.

00:47:09:18 – 00:47:37:01
Kyle Pearce
Hey friends, as we mentioned, the virtual summit. Peter’s going to be back with us. And once again, we’re going be on with Peter doing a joint session. Always so much fun, so much learning, not just for us, but also, of course, for you. It is a completely free event this year in 2023, we are looking at November 17th, 18th and 19th, a completely free live virtual summit.

00:47:37:06 – 00:48:01:19
Kyle Pearce
We have ten featured speakers and a lot of other speakers that have amazing ideas to share, head over to make math moments dot com forward slash summit and you can register for that event, make math moments dot com forward slash summit and we will see you in our session with Peter. All right math moment maker friends until next time I’m Kyle Pearce.

00:48:01:19 – 00:48:03:01
Jon Orr
And I’m Jon Orr.

00:48:03:03 – 00:48:05:23
Kyle Pearce
High fives for us.

00:48:06:00 – 00:48:10:06
Jon Orr
And a high five for you.

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