Pam  0:00  
Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris, a former mimicker turned mather.

Kim  0:09  
And I'm Kim Montague, a reasoner who now knows how to share her thinking with others. At Math is Figure-Out-Able, we are on a mission to improve math teaching.

Pam  0:18  
Because we know that algorithms are amazing. I was trying to decide if I was going to say historic or human because sometimes I change things up.

Kim  0:26  
Yeah, I know. I know.

Pam  0:27  
They're amazing historic human achievements, but they are terrible teaching tools because mimicking step-by-step procedures actually trap students into using less sophisticated reasoning than the problems are intended to develop and use.

Kim  0:39  
In this podcast, we help you teach mathing, building relationships with your students and grappling with mathematical relationships.

Pam  0:46  
Y'all join us to make math more figure-out-able.

Kim  0:50  
Hey, should we tell them that we were joking about last week's episode?

Pam  0:56  
Yeah, let's do, let's do. 

Kim  0:57  
Okay. 

Pam  0:57  
You boldly proclaimed your age to everyone. 

Kim  1:00  
Oh, yeah. Well, I don't care. Whatever. 

Pam  1:02  
I mean, I guess I could boldly proclaim I'm 10 years older than you.

Kim  1:04  
Yeah,

Kim  1:05  
I mean, it's a number, right? 

Pam  1:06  
There you go. 

Kim  1:06  
We're active, we're doing things. But after you were like "25 years, really?" I said, "Yeah, is that our silver anniversary? Like, what's the gift for that?"

Pam  1:17  
There you go. Well, we're... I think we're about to hit our five-year podcast anniversary. That's got to be. Is

Pam  1:24  
five years...

Kim  1:25  
Did we already hit it? I don't even remember. 

Pam  1:26  
Oh, golly. 

Kim  1:26  
There's so many. 

Pam  1:27  
Alright, well. 

Kim  1:28  
Like, a million episodes,

Pam  1:29  
Almost 300 episodes. We should have a party on the 300th episode. 

Kim  1:33  
Should we? 

Pam  1:34  
Did I just say 300? Is that a word? 300. 

Kim  1:36  
300? 

Pam  1:38  
Is it?

Pam  1:42  
Okay. 

Kim  1:42  
Okay. I think so. Are we having a party? Are we inviting people to the party?

Pam  1:47  
Oh. Hmm. Where will we be on the... You figure out where we're going to be on the 300th and maybe we'll have a team dinner?

Kim  1:55  
They don't care. So, like are you getting that thing done? 

Pam  2:00  
You and I

Pam  2:00  
will go have ice cream. Wait, I'll have ice cream, and you'll have?

Kim  2:03  
Chips and salsa. 

Pam  2:03  
Chips and salsa. Okay, there you go. Alright, it's a plan, it's a plan.

Kim  2:07  
Alright, sounds good.

Pam  2:08  
Golly. Alright, Kim. We recently

Pam  2:11  
have been at a couple conferences together. 

Kim  2:13  
Yep. 

Pam  2:14  
I went to tons of sessions where the point was to listen to kids. Do we believe in listening to kids? 

Kim  2:21  
Absolutely.

Pam  2:21  
Absolutely. Think it's super, super important. Now, to be clear, as a young teacher, I did not think it was important. And I did, like, think it was important to listen to kids, you know, tell me about their day, and...

Kim  2:31  
Yeah. Yeah, yeah.

Pam  2:32  
How their life was going, and the game. And I tried to go to kids' games and stuff. You know, like be involved in their lives. But as far as listening to their math? To me, math was about rote memorizing and mimicking, so there wasn't much to listen to. It was like, "Do you have it down or not?"

Kim  2:48  
"What problem do you need me to do again?" Yeah.

Pam  2:51  
"What are you

Pam  2:51  
stuck on?" But there wasn't a lot of, you know like, "How are you reasoning?" because I wasn't reasoning, so I wasn't listening for reasoning. So, we like the idea of listening to kids. Good stuff. 

Kim  3:01  
Yeah. 

Pam  3:01  
When we were talking about this podcast coming up. We're throwing around some ideas for it. I mentioned that I'd gone to some sessions on listening, and that I kind of wanted to talk about one of them. And you said, "Oh, was it this one?" And you mentioned the presenter's name. And I was like, "Oh, actually, no, not that one."

Pam  3:15  
Yeah, yeah. So, to be clear.

Kim  3:17  
Which...

Pam  3:17  
Yeah, go ahead. 

Kim  3:18  
Which means that there are a lot of sessions happening where people are talking about listening to kids. Hallelujah! That's fantastic.

Pam  3:26  
That's fantastic. And it got me thinking. One of the things that might be unique with us at Math is Figure-Out-Able, not like super unique, but maybe kind of unique based on all the sessions that we just went to, is that, yes, it's very important, super important, to listen to kids, listen to our students. But it needs to be about more than that.

Kim  3:49  
Mmhm. 

Pam  3:50  
What do I mean by that? So, it kind of felt like in a few of these sessions that we spent our time and effort kind of applauding listening to kids, but it didn't really help us know why we were listening, or, maybe more importantly, where to go from there. And I don't know if maybe giving a little bit of an example might be helpful. There was... again, everybody was talking about listening, in one session, we listened to a student's strategy, and I listened with an ear towards, "Okay, how would I model, represent that student strategy? What model would I choose?" 

Kim  4:33  
Mmhm.

Pam  4:33  
"Why? What do I know about this kid, so that, you know, I could choose a model." But as I was asking those questions, it wasn't so much choosing the correct model, as it was, what would be a model, based on what I've just heard this student do, what would be a model that might help them get more clarity around the relationships they were using, so that then they could go from there, nudge from there, do

Pam  4:58  
something...

Kim  4:59  
You're saying that was what the point was or that was not what the point was?

Pam  5:02  
That's what I was doing in my head. 

Kim  5:04  
Okay. 

Pam  5:04  
And so then when the conversation in the session was kind of stopped, as soon as people agreed what the kid had done, I looked around and nobody was modeling, nobody was drawing. I shouldn't say nobody, but most people weren't. 

Kim  5:18  
Yeah.

Pam  5:19  
For sure, the facilitators weren't encouraging it. Like, it wasn't a thing to do, and then we were just done, and then we went on and moved on to another student. So, what I felt, maybe that we just have this unique bent on, is that, yes, we want to listen to students, but toward an end. Like, oh, that sounds like because I'm going to now tell them what to do. It's not that. Help me,

Pam  5:40  
Kim.

Kim  5:41  
Yeah, I wonder if it has something to do with the creation of the Success Map that we believe in, that we are like... Maybe not that. I don't know. I mean, I feel like there's so much about the Development of Mathematical Reasoning and like kind of where we are in our journey. Like, we've thought very clearly about building numeracy and, like modeling student strategies. But in the combination there, it's about like we're going somewhere. It's like listening is great, but there has to be a deeper purpose.

Pam  6:14  
And the purpose isn't to say, "Okay, now I know what you're doing wrong, and I'm going to fix your steps." Or...

Kim  6:20  
Yeah.

Pam  6:20  
..."now I know what you can't do, and so I'm going to fill in the gaps."

Kim  6:24  
Yeah.

Pam  6:24  
Or... Like, right? Like, all those computer stuff things out there right now that sort of identify, quote unquote, gaps, and missing, and can't do. We're listening. What are students doing? What can they do? What assets do they have? But then we're not stopping there either. Now, we're saying, "Okay, based on that, how can I represent your thinking toward being able to then have a conversation about, "Ooh, like if you're Getting to a Friendly Number, can you also Add a Friendly Number? And if you're Getting to a Friendly Number, are you then thinking about adding the rest in a whole chunk?" And I just chose addition off the cuff. But what if I was writing the equation of a line between two points, and the kids trying to find the rate between two points and the student's using like a unit rate approach, where they're really thinking, "Well, if I back up this, and I back up that, can I..." You know or maybe they're using a non unit rate approach as sort of bigger chunks. Or maybe they're actually thinking about, "Well, if the line went through those two points here, but I could shift it there," more of a transformation approach. Once I kind of know what they're doing, if I know the major strategies, then I'm thinking about, "Okay, I know where you are, and I now have an idea of where I might nudge you next."

Kim  6:24  
Yeah.

Pam  6:24  
And maybe not even in the moment. But, Kim, as I said that, I'm really thinking with teachers. I'm thinking about our Success Map. And with students, I'm thinking... Is that what you're

Pam  6:24  
going to say? 

Pam  6:24  
Thinking about the Landscape of Learning

Kim  7:10  
Yeah, I realized why the Success Map popped in my head. Because when we work with teachers and we write content, a lot of it has to do with the people that are in front of us. Like, what do we know about them based on what they're doing, what they're saying, the engagement that we have with them all towards nudging forward through the Success Map. But when we're with students that we are also nudging, and it's with the DMR kind of in mind. And so, like (unclear).

Pam  8:13  
We're saying DMR. Developing Mathematical Reasoning framework.

Kim  8:16  
Yes. 

Pam  8:16  
Yeah, that landscape.

Kim  8:17  
So, we're kind of always... Those two are so ingrained in all of our  conversations and in our minds, that we're nudging. Yeah. 

Pam  8:26  
So, all that

Pam  8:27  
to say it's not... Listening isn't... It's important. It's necessary. But it's not sufficient. Like, we have to help move forward, I think. I think that's... Yeah. And maybe somebody's going to say, "Sure, but the sessions you went to, they were focusing on listening first."

Kim  8:44  
Yeah.

Pam  8:44  
"Then we can move forward from there." Okay, okay. I was just aware of like it seemed to happen a lot where listening kind of... It was kind of presented as that's the goal.

Kim  8:53  
Yeah. 

Pam  8:53  
And that's like a goal on our path.

Kim  8:56  
Yeah.

Pam  8:56  
I don't know. Does that metaphor kind of help?

Kim  8:58  
Yeah, yeah, yeah. It seems similar to when teachers make the shift from there's one way to solve problems to let's let kids solve problems kind of in varied ways. Then sometimes it feels like we see classrooms where anything goes and just let the kids solve problems however they want, and there's no sophistication conversation. There's no nudging towards particular strategies. So, you know, it's a necessary starting point to say we want kids to solve problems in more than just traditional ways that we were grown up in. But, so it's a necessary starting point, but then we have to help them develop sophistication. We can't just say, "However you want to solve it. Good for you. Yay." So, I see some similarities there. So, we're listening to kids because it's in service of moving them forward, not just for the sake of listening. It also

Kim  9:57  
needs... 

Pam  9:57  
In the same way you're saying, we're asking kids to solve the problem using what they know, their own way, but not because that's the end. That's not the end goal. 

Kim  10:06  
Right.

Pam  10:06  
The end goal is okay now we know what you can do, and now let's help you shift forward. Let's help you grow and develop more sophisticated.

Kim  10:16  
Yeah, I see some some parallels there where...

Pam  10:18  
Yeah, that makes sense.

Kim  10:19  
...we're listening for a purpose. And we're letting kids solve problems, but we're also guiding and nudging. It also kind of reminds me of in coaching. We just mentioned the Success Map. But we're thinking about, you know, when I'm working with teachers, and I'm engaging with them, and I'm listening to them, I'm thinking about like a specific move that I can use or a specific thing that I can coach on within this framework to nudge them forward. I'm not just like watching them teach. I'm watching for specific things, and I want to engage with them in conversation about like a next move. What's the next move that we can make? Because their goal is to become better teachers. Their goal is to like learn and grow. Anyway,

Kim  11:09  
so... 

Pam  11:10  
Hey, that reminds me of that session you went to that Sam Otten did and the work that I've read recently where... So, Sam Otten, he's the... Help me. The what do you call it? 

Pam and Kim  11:24  
Math Ed podcast

Pam  11:24  
guy, yeah. Moderator? The host of? Host. There we go. Host, there's the word I was thinking for. 

Kim  11:29  
We don't

Kim  11:30  
have one of those, so we don't know.

Pam  11:33  
He does a great job on the Math Ed podcast. But some of his work that he's doing is about these small nudges for teachers.

Kim  11:41  
Yes. 

Pam  11:42  
And so I would say he's diving in to see what teachers are doing. But not... That's not the end, right? It's not the end goal. Okay, now we know what you're doing. The end is what would be a really good nudge, a next nudge that could just make a little bit of forward movement? We're interested to see more about that. I think that's an interesting idea. 

Kim  12:04  
Yeah. 

Pam  12:04  
So, you're kind of comparing all of these ideas of not just doing something for the sake of doing it, but always towards then growth and development from there.

Pam and Kim  12:13  
Yeah.

Kim  12:13  
Yeah.

Pam  12:14  
Yeah, nice.

Kim  12:14  
It kind of also reminds me of I went to a session at... Gosh, I don't remember if it was SM, NCTM or SM about Affirming Learning Walks. And I think I mentioned that on that episode how much I loved that idea of just loving on teachers and being in their classrooms and saying like, "Man, this is really going well."

Pam  12:35  
But wait, Kim, an Affirming Learning Walk, doesn't that mean that... Is this a non-example? Because is this where you go in and all you do is just give them affirming positive?

Kim  12:44  
Well, I mean, I think there's something right about naming things that you see that are going well, but I think that if I were doing Affirming Learning Walks, I would be very... Like, I would be looking for things that are going well that I want to encourage more of. So, you know, I think you can say all kinds of nice things, positive things. So, I think that even in that kind of coaching, or that kind... It's not even coaching. That kind of situation where your goal...

Pam  13:15  
Interaction?

Kim  13:15  
...is to lift the teacher up. I think you could even be specific and choosy about...

Pam  13:22  
Intentional.

Kim  13:23  
Thank you for that word. Things that you want to hype up. Things that you want to say, "Man, like more of that. You're doing an amazing job already." But like, let's call out that thing that's going so well because it's making a big impact.

Pam  13:38  
You know, completely out of Math Ed for just a second. I was listening to a podcast the other day about relationships, and it was sort of marriage advice. And it was like, if you like something your spouse is doing, tell them. Like, 

Kim  13:49  
Yeah, right. 

Pam  13:50  
Be grateful for that thing. Like, reinforce the thing that you want to see more of. So, I hear you saying in an Affirming Learning Walk, even though you're not noticing things for improvement out loud. You're not like stating those things. The things that you notice to affirm could be the things that you are encouraging to see more of. 

Kim  14:07  
Yeah.

Pam  14:08  
That's nice. I like that. Hey, could it also be similar to... Think models for a second.

Kim  14:15  
What kind of models? 

Pam  14:18  
Well,

Pam  14:19  
I'm thinking specifically about... Well, I'm all over the place. Let me start with manipulatives. I remember Gail Burrell when she was the NCTM president forever ago. I'm dating myself. Where she said, her President's Message, "Where's the Math?" Because she was seeing manipulatives all over the country as she traveled around, but she was like worried that the math was getting lost. And I think she had a really good point that we might sort of understand people to say, "Use manipulatives. It's the bomb. And they will magically learn math." We're not saying manipulatives are bad. But they're not the be it, end all. It's not the... The goal isn't for kids to use manipulatives. The goal is to use those concrete materials to help kids develop mathematical relationships and connections, so that they can then develop more mathematical relationships and connections.

Kim  15:12  
Can we clip that? Can we clip that and put it everywhere? Yeah. Yes, yes, please.

Pam  15:17  
So, then I would also say that's true with like an area model. I think when you were pushing me on which models, I think if you are saying do a jump strategy with a number line or do a box method, the potential is there that you're seeing that as the end goal.

Kim  15:38  
Mmhm.

Pam  15:38  
That the end goal that kids are making jumps or the end goal that kids are drawing squares. I think the end goal is for kids to be developing relationships that are about linear measurement, and friendly numbers, and place value, if I'm on a number line. And I said linear measurement. So, what do you... Square measurement? Area measurement? Like, two-dimensional. There, that's the word I want. Two-dimensional measurement with area, but also, again, friendly numbers and bigger chunks of area as they're really growing multiplicative reasoning. So, the end isn't for kids to do a thing with manipulatives to get an answer. The end is to use those concrete materials or those models to help kids learn and grow. Does that fit?

Kim  16:19  
Yeah, for sure. Yep. 

Pam  16:21  
Nice.

Kim  16:21  
I think when we were chatting, there was also this bit about listening to students, about if your point... So, we've been talking about mathematical reasons to listen. But also I want to name that if your point for listening is about creating community and helping students have a voice, even then it's not just, "I'm going to watch you as you talk, and I'm going to listen to you as you talk." Like, I think even in the space where it's not about listening for mathematics necessarily, you're listening for a purpose. Like you're listening to say, "Okay, there's where they are. And I want to help engage more. Like, I want to help them have a more often considered voice. I want to have a more connected voice to the rest of our group." So, even then, whatever your goal is, it has to be in service of more than just...

Pam  17:19  
Could I say you want it to allow their experience, their humanity, their voice, their personality, their presence to influence you.

Kim  17:32  
Yeah. Yeah, thank you.

Pam  17:33  
To matter to you, to connect with you. 

Kim  17:39  
Yeah.

Pam  17:40  
That it's... Yeah. 

Kim  17:41  
Because then you're

Kim  17:42  
going to do. I think my point is you're going to do something about that. You're not listening just to say, "Okay, high five. I heard you." It's to learn more about who they are. Like, this is so embedded in know your content, know your kids. If you're listening to them, it is about knowing them and knowing how to position them, either mathematically, like with what they know and where you're going to head with them, or listening to them mathematically as a community member, so that you can bring them more into the fold, or capitalize on the experiences that they have.

Pam  18:20  
So, is this also parallel to some of what we see with when people do Number Talks or they try more investigative inquiry kind of tasks? 

Kim  18:31  
Yeah. 

Pam  18:31  
Where they might say, "Okay, who wants to share?" And anybody who wants to share, shares.

Kim  18:39  
Yeah.

Pam  18:39  
And sort of as if the purpose is to share. 

Kim  18:43  
Yeah.

Pam  18:44  
And we would say that's not the purpose. 

Kim  18:49  
Yeah.

Pam  18:49  
That's not the end. We're not done then. It's kind of like all the things that we've just talked about. We're going to have kids share, but in service of a purpose. We're going to be intentional about building the mathematics. And at the same time, being equitable and making sure that we're positioning all students as learners. You know, I'm reminded. I heard Cathy Fosnot give a talk in one of the virtual summits. I don't remember which one, and I only actually heard part of it. But part of what I heard was she said, "There's a difference between a Number Talk and a Problem String. Many Problem Talks or Number Talks were designed for talk." And she said, "That's not enough." And I'm just paraphrasing. I'm sorry I'm not quoting her exactly. But something about I just remember her saying, "It's not enough for the purpose to be about talk. We have to actually build the mathematician, build the mathematics." 

Kim  19:35  
Yeah. 

Pam  19:35  
Like, help build the mathematics and help the mathematician develop. And I've had some pretty hard conversations with some advocates of having all kids share, where they said, "No, no, no. You have to have all kids share or you're not honoring all kids as learners, and you're not..." What's the other word I want? Like, you have to let all...If a kid wants to share, you have to let them share. And I would say that because I've allowed, I've encouraged, kids to use their own strategies to solve the problem using what they know to reason, and communicate, and think, and work together, because that was the starting place, I have honored their work. I have honored where they are. And that is a great, necessary starting place. But then that's not the ending place. So, now in the share, I'm going to actually, deliberately, intentionally choose students who will help move the mathematics forward for the group. 

Kim  20:39  
Yeah.

Pam  20:39  
And there might be times where I'm working individually with kids or in small groups where in that moment I have a specific student share that maybe I wouldn't have share in front of the whole group for whatever reason, so that they get a chance for their work to be honored and their work to be celebrated and valued. I want to bring all, I want to position all kids as sense makers. And sometimes people hear me say that I'm going to choose a specific student or students to share, and they think what I mean... There's a word that is that. They think what I mean. They Intuit. They...

Kim  21:12  
Assume? 

Pam  21:13  
Assume. Thank you. They assume, because of prior experience, that I mean I'm going to choose the most clear kid, the quickest kid, the kid who looks like they're the best, or the smartest, or whatever. When, in reality, I'm rarely going to choose the kid who I think is going to give the most clear explanation, because if I believe that learning happens when you get the most clear explanation, then I would just give the most clear explanation. 

Kim  21:36  
Yeah. 

Pam  21:37  
So, if I believe that the more learning occurs when I put you in a position where I invite you into sense making, and I invite you into relationships and to make connections, and I'm very deliberately and intentionally creating those situations with purposeful numbers and purposeful problems. If all of that is happening, then that is the right conditions for students to really make, and strengthen, and clarify mental mathematical relationships, so that then they are built. They're developing as mathematicians, and we're moving the math forward.

Kim  22:13  
Yeah. So, we started the episode by saying the idea of even listening to students was maybe something that you didn't do as an early teacher because you didn't know. So, is listening a great step forward? Absolutely. It can absolutely feel like something to do. We want to create community. We want students and teachers to be good listeners of each other's ideas. And we want students to have voice, and agency, and identity as a mather. But we can also do that with the goal of moving forward. We can actually move the math forward and help the mathers develop into better mathers in our classes.

Pam  22:53  
Oh, that was so well said. Nicely done. So, yeah, listen, absolutely, and for a better purpose, a bigger, better moving forward purpose. I should have just let you finish. Alright, y'all, thanks for tuning in and teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. And thanks for spreading the word that Math is Figure-Out-Able!