Pam  00:01

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

Kim  00:07

And I'm Kim.

Pam  00:08

And you have found a place where math is not about memorizing and mimicking, waiting to be told or shown what to do. But it's about making sense of problems, noticing patterns, and reasoning using mathematical relationships. We can mentor students to think and reason like mathematicians do. Not only are algorithms not particularly helpful in teaching mathematics, nor fun, but rotely repeating steps actually keep students from being the mathematicians they can be.

Kim  00:38

Absolutely. So, last week, we started talking about kind of a big topic, right? Building Thinking Classrooms. And you shared what you think about Peter Liljedhal's work and how we had done some of the things. And you get asked about his work all the time, and how your work fits together. So, today, we're going to talk a little bit more about maybe how you are a little different. Is that a fair way to stay that? 

Pam  01:05

Yeah, I think so, I think so.

Kim  01:06

Little bit. 

Pam  01:07

In just a very professionally, respectful way, I'll just make some suggestions about I think the best ways to maybe implement Dr. Liljedhal's work. By the way, Kim, I'm going to just compliment you on saying his name. Do you know how many people I've worked... I'll be talking to people, and they're like, "You know that Lil..." I'm like, "Guys, it's not that hard. Lil-ya-doll." Now, Dr. Liljedhal, you can tell me I'm saying it wrong, and I will then happily apologize because I hope I'm not.

Kim  01:35

Right. 

Pam  01:36

Alright, so let's dive into maybe some nuances of kind of my perspective on the best ways to use his first three teaching practices. I do want to talk more about his other four chunks. He has four chunks of things. I want to talk about the other three at some point, but I'm going to hang with that first set of teaching practices in this episode. So, something really important. If you have not listened to the last episode, you're going to need to listen to that before this one because I'm not going to re-explain stuff. So, something really big to consider. I think that people that are on the BTC, Building Thinking Classrooms, sort of bandwagon are telling you to do vertical, nonpermanent surfaces in visibly, randomly chosen groups all the time. We are saying, some of the time. 

Kim  02:27

Yep. 

Pam  02:28

So, let's dig into that a little bit. Do I like the idea of putting my students in my university classes, participants at workshops, students in classrooms up at vertical, erasable surfaces, giving them thinking tasks, and asking them, separating them, splitting them, putting them in visibly randomly chosen groups? Yes, when it's appropriate. And so, I would say that's very appropriate when we give them the thinking tasks that he just suggested. That's part of one of his first pillar of things is that it's got to be thinking tasks. However, he suggests that it's with non-curricular tasks, that you do that at the beginning of the year because if you do it with regular math tasks, kids will do what they've always done, and they'll try to mimic, and they won't dive in and think. But if you give them non-curricular, sort of not the kind of questions they're used to looking at. If you give them those non-curricular tasks, they'll look around, they're like, "Wow, this is really different." You know like, "We're standing up. We're at these whiteboards. We only have one marker. He or she clearly put us in this randomly chosen group. And this is kind of an interesting problem. It doesn't look like the math problems that we're used to solving. Maybe we could reason through this." And kids will dive in, and they'll they'll think, and they'll help each other. And it's kind of they're interesting problems. It doesn't look...because you're at vertical, non permanent surfaces...or feel...you're in these randomly chosen groups...like the math that they've done before because you're doing different, then the math looks different. And so, because of all that together, kids are kind of willing to dive in and do some thinking. Then, you kind of do this switchy thing where once kids are thinking, then he says, "Now, just give them a math tasks." Just give them normal math tasks, and because they're like, "This is what we do here," they'll continue to think about those math tasks. I think he probably has a point. I think it probably works just fine to do that. I don't think you have to do that. In other words, the "that". What's my "that"? I don't think you have to start the year with non-curricular tasks if you start the year with really good, rich curricular tasks. So, when you give them that really good, rich curricular tasks, put them up at the vertical nonpermanent surfaces, randomly choose the groups, give them the one marker, and say "Go," but give them a curricular task that's interesting. It doesn't look like the ones that they were rote memorizing their way through the year before, but it could actually be the curriculum that you teach. Now, that's not easy to come up with what those tasks are. It's one of the things that I work on and other really good people I know. Kyle Pearson, John Orr are working on that. We've got a colleague in Norway. I totally just swallowed the throat lozenge I had in my mouth. Sorry.

Kim  05:13

[Kim laughs] I'm sorry.

Pam  05:14

Good heavens. James, I know your name. Do I know how to pronounce his last name though? James... 

Kim  05:19

Oh, we already butchered that once.

Pam  05:21

(unclear). You're going to... He'll tell me if I totally.

Kim  05:24

I think that's right. 

Pam  05:25

So, he's really super interested in at least collecting really good, rich tasks. Cathy Fosnot has amazing Rich Tasks I think. Anyway, there's some places that you can get Rich Tasks. I don't think it's trivial to come up with curricular Rich Tasks. But I do you think it's possible. I've definitely written some, especially in our. Well, in all of our Building Powerful Mathematics workshops, we've got Rich Tasks we would suggest. So, that's a thing. You clearly heard me last episode and this episode say, we do put our students and the teachers we work with up at vertical, nonpermanent surfaces in these randomly chosen groups, and we do these curricular Rich Tasks and get students thinking. One thing that I would slightly differ on is, if you can find, and create, or share with each other, or get for me or other good people really good Rich Tasks, then you don't have to start with non-curricular Rich Tasks, so that would be a place where I would slightly differ. And you know what, Dr. Liljedhal, maybe you would agree with me. You're like, "Well, yeah, If you can find a really good one, go for it. They're just hard to find." So, maybe we agree on that. Another thing, though, that I think maybe we... Maybe I'm actually kind of sure we might disagree a little bit on is, that's the only time that I would put students up at those vertical, nonpermanent surfaces in those randomly chosen groups. There are other things I would do in classroom teaching, and one of those huge things I call Problem Strings. So, if you've listened to the podcast for longer than about 15 seconds, you've heard me do Problems Strings lots. I love Problems Strings. I think they're a super effective way to help cinch things, to help introduce things, to help refine things, ideas, concepts, strategies. Really good way of teaching. And I think I'm just going to state, I believe Problem Strings are best done whole group, with students at their desks. It doesn't have... I was going to say with something to write on, with. But it doesn't have to be nonpermanent, doesn't have to be their notebook. It could be either of those. But Problem String success hinges on the discussion between each problem and the modeling of the teacher between each problem. One of the things he suggests is that you de-front your classroom, meaning there's not this teacher at the board and the sage on the stage, and all the thinking happens with the teacher, and the kids are just mimicking. And so that's one reason why you put them around the room at these vertical, nonpermanent surfaces. And I'm totally cool with that when kids are doing those Rich Tasks at those vertical, nonpermanent surfaces in those visibly, randomly chosen groups. But when we're doing a Problem String, I think the teacher is at a board and the students are at their desks. And I don't know that it has to be the front of the room. I think it could be any one of those now, vertical, nonpermanent surfaces you have around the room. So, when you do a Problem String today, you could do it at this whiteboard. And when you do a Problem String tomorrow, it could be at that whiteboard. And when you do a Problem String the next day, it could be over there at that. And when students come in, you could just say, "Hey, today, orient your desks. I'm going to be here." "Today, it doesn't matter where the desks are because you're at vertical, nonpermanent surfaces doing a Rich Task." But today, right now? Right now, orient your desks because I'm going to be right here and we're going to do a Problem String." "Hey, for this Problem String, everybody oriented? Yep, the desks are there. Cool. Everybody ready? Here's the first problem. Do the first problem." Alright, now, I'm going to choose someone to share their thinking for that first problem, based on what I've seen as I circulate, based on questions I ask. I'm going to represent that thinking in such a way because I know where the Problem String is going, and so I'm going to orchestrate a final display by starting with that very first problem and representing it with a purposely chosen model. I might have a kid say, "Well, I did it on an array." And I might go, "Okay, tell us what you did, though, with the numbers. Where did you chunk them?" And then, I might still put those values in a ratio table because I know where I'm going with the string. Know your content, know your kids. I know the content, I know the goal of the lesson, and so because I know that, I'm going to say, "Yeah, but how did you those chunks? Ooh, I'm going to put those chunks up in these equations." I'm going to choose the model, because I know where I'm going. Then, I'm going to say, "Does everybody understand Kim's strategy for that one? Can somebody restate that strategy? Does that make sense? Okay, everybody's good on that one? Alright, cool. Next problem." Everybody solves it. Alright, now everybody solves it however they want, and I'm going to encourage them to think and reason however they want, and I'm going to say, "Okay, cool, cool." Based on where I know I'm going. I don't say that out loud. But based on where I know I'm going, I look around, or I ask certain questions. I choose someone to share. I represent that thinking in such a way. Now, depending on the string, I might choose two students to share. We might compare the strategies. It depends on the Problem String. But I'm representing the thinking, and I'm orchestrating a conversation. "Okay, ya'll, but so and so in the first problem did this. Why did so and so in the second problem did that? Do those have anything in common? Oh, did the numbers influence how they chose that? That's interesting. Well, based on that, I wonder how you might think about this problem." And now I get the third problem. Again, they can solve it any way they want, but I have been nudging certain relationships by what we're celebrating during the conversation and the modeling, the representing of the thinking, the making the thinking visible. I'm subtly nudging kids to consider relationships they might not be considering while they're solving the problems. Next problem. Same. We keep going. And by the end of it, we're having a conversation about a certain set of relationships that are leading towards a certain strategy, model, or big idea. And I'm not going to pretend that we've cinched it, that everybody by the end of the string is doing it, but everybody by the end of the thing is considering it, they're thinking about it, and we've started to create those mental connections. If you do that Problem String in groups at those vertical, nonpermanent surfaces, chances are super high that students will solve those problems the way they are inclined to solve them the whole time. Because there's not that conversation, and that nudging, and that making thinking visible happening in between to give them other ideas, to help them think about other things. Does that make sense, Kim?

Kim  11:41

Yeah, absolutely. I mean, I think so much of it in a Problem String is about reflection, and nudging, and conversation that you're the guide, right? Like, you are crafting the conversation based on an end goal, and you drop things along the way to make it become something within the kid's zone of proximal development. Like they're aware of the thing because of the hints that you've laid or that other students have laid along the way.

Pam  12:11

And it's interesting when you say "drop things", I think you mean "drop in". Like things that you lob out, things that you purposely, hints you give. But you also drop things, meaning that kids might be doing something that's fine, but it's not helping where we're headed, and so you de-emphasize it. You literally drop it. Like a student might say, "Hey, but I want to share my strategy." And you might be like, "I believe you. Not now." And then, you move on. 

Kim  12:38

Yeah. Yes. Yeah. 

Pam  12:39

Like, we very politely say, "Mm, during a Problem String, I choose who shares because I'm moving the math forward." Were always with an eye towards making sure that all students are being supported, and presented, and promoted a sense makers. Like, we're always with an eye towards making sure that we're giving students what they need to be successful. So, we're not choosing the... In fact, it's funny, Kim, we're not choosing necessarily the "right kid" or the "brightest kid" or the "quickest kid", right? We're often choosing the kid who will maybe make the conversation a little muddy, so that in the cleaning up of the conversation, in the refining of it, in the clarifying, everybody learns more. If we call on the kid with the most clear explanation. Then, if that's what teaching is, let me get the most clear explanation out, and oh, we're done. Then, why didn't I just say it? Why go through the whole? Because we would suggest that's not learning. That's not what gets us the most bang for our buck.  So, we are suggesting that putting kids up in visibly, randomly chosen groups at vertical, nonpermanent surfaces with rich curricular tasks is a fantastic thing to do when you are doing those Rich Tasks. In my kind of curriculum, that happens two maybe three times a week, where we're doing those rich things, and then we're going to follow up with a congress. I think... Yeah, I'm going to talk about that later. We follow that with what we call a Math Congress after Cathy Fosnot, where we have a conversation about that Rich Task. That's happening maybe two or three times a week. 

Kim  14:17

Yeah.

Pam  14:18

More often than that, we are doing Problem Strings, which are kids in a whole group, at their desks, where the teacher is focused on, "I've got an outcome here to move the math forward." I'm nudging, I'm celebrating certain things, so that certain patterns today are the ones that we are fussing with. It's not like I'm slapping kids hands and saying "No, not that. No, stop that." Not at all. I'm just like we said, letting some things drop, and I'm dropping in things, so that certain patterns, relationships, and connections are the ones that are paramount for that day, and that we're creating more and more sophisticated thinking for that  particular day. 

Kim  14:57

Yeah, and the exciting thing for the listeners is that it's not an either, or. You can have both. You can do both. And you should do both! It's not, you know, "Which path do I have to pick?" 

Pam  15:10

Absolutely.

Kim  15:10

They just have their own importance, for their own moments, at different times.

Pam  15:15

Absolutely. So, definitely not saying, you know, "Chuck, that Building Thinking Classrooms book." No, I think there's some wonderful things in there.

Kim  15:22

Yeah. So valuable.

Pam  15:22

Especially. Very valuable. And we'll talk about more of them in his other three chunks of things. I think there's definitely some more value to be had in those pieces. But for today, I really wanted to focus on, if you believe in Problem Strings, then I don't recommend that you do those at vertical, nonpermanent surfaces with visibly, randomly chosen groups because they won't have the punch you can have if you do them, well, at all. They'll fall flat, and then you'll get frustrated, the kids will get frustrated, and we won't develop the math. And then, you have the potential to throw it all out. And I don't want you to throw it all out. Like Kim just said, I want you to use Peter Liljedhal's first first chunk there, when it's appropriate, with good, rich curricular tasks. And I want you to do whole class, teacher in charge in the right way.  Facilitating the learning towards a goal, representing thinking, crafting careful conversations, purposeful conversations, when you're doing things like Problem Strings and other instructional routines that are very helpful parts of a good balanced math curriculum. Alright, that was kind of fun. Hopefully, I did that justice. If anybody thinks that I kind of didn't do something justice, I'd love to hear more on your take. Keep in mind that we're going to talk about at least some of the rest of his points that deserve some some uplift for all of us. Highly recommend that we all build thinking classrooms. It's just maybe how we do it and which parts that we're going to kind of fine tune a little bit. And then, remember, I'm also about the "what". That there are major strategies. It's not just some random collection of whatever kids do. It's also not the algorithm. There are specific things we need on the landscape of learning that we need to develop in kids and we need to know what those are. We need to know our content and know our kids in order to really teach math that is figure-out-able. Alright, Kim do anything to add or is that good? 

Kim  17:19

So good. Yeah. 

Pam  17:21

Cool. Alright, ya'll, thank you for tuning in and teaching more and more real math. To figure out... To figure out. To find out about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. Let's keep spreading the word that Math is Figure-Out-Able!