Pam  0:01  
Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris, a former mimicker turned mather.

Kim  0:10  
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  0:17  
Because

Pam  0:18  
we know that algorithms are amazing human achievements, but they are not good teaching tools because mimicking step-by-step procedures can actually trap students into using less sophisticated reasoning than the problems are intended to develop.

Kim  0:31  
In this podcast, we help you teach mathing, building relationships with your students, and grappling with mathematical relationships.

Pam  0:37  
We invite you to join us to make math more figure-out-

Pam  0:42  
able.

Kim  0:43  
Hey, there!

Pam  0:43  
Kim! 

Kim  0:44  
I know you know what today is. 

Pam  0:46  
You

Pam  0:46  
know what? We should have some like celebration music, like, "AH! PWSHH! DING DING DING! LA LA LA LA!" 

Kim  0:52  
Yeah, yeah.

Pam  0:54  
Maybe our editor will throw us Craig, throw some like celebration music behind us

Pam  0:55  
right now! Woohoo! 

Kim  0:59  
Fireworks. It is such a great time. Can you believe that we have been at this for five years?!

Pam  1:06  
Wow! 

Kim  1:07  
Five years on the podcast. 

Pam  1:08  
Wow,

Pam  1:08  
it's like a small child.

Kim  1:11  
Oh gosh. Oh. No.

Pam  1:13  
No? 

Kim  1:14  
Oh, wow. I don't have the energy for that.

Pam  1:17  
Five

Pam  1:18  
years is unbelievable. And I give you a lot of credit for keeping this going. If this would have been only up to me, there's no way I would have been this consistent. Ya'll, we've had a lot of laughs, a lot of really important conversations.

Kim  1:30  
Yeah,

Kim  1:30  
and a lot of bloopers, and lots of mistakes in the intro, and a lot of me saying, "Wait, I'm sorry. I was looking at my window. I wasn't listening."

Pam  1:41  
Well, and me saying, "Wait, wait. I can't hear you. Wait, can I? Can you hear me?" And then we're like messaging back and forth in the in the audio program. Can you hear me? Can you hear me? Plug your audio in.

Kim  1:49  
Yeah. 

Pam  1:49  
Alright, so... 

Kim  1:51  
(unclear) celebration.

Pam  1:52  
...there you go. What are we going to do for this five year celebration of the Math is Figure-Out-Able podcast?

Kim  1:54  
Yeah, so for this episode, we asked people what were some of the important moments from the last 100 or so episodes that they felt like other people needed to hear? So, we do have the episode that is Start Here that is I think it's 156 to share with people like what are all the things that are Math is Figure-Out-Able that will get you a good view of what we believe. But we thought what are some other episodes that people need to know about?

Pam  2:23  
Yeah, so we have chosen a few episodes, and we're going to give you a little brief glimpse into those with maybe a few blooper reels flown...thrown in there. I just "flown in". 

Kim  2:36  
Yeah, that will be yours.

Pam  2:37  
I'm thinking about bloopers as we go. So, enjoy. Enjoy some clips from some very important episodes that we've done recently. And enjoy, enjoy. Here you go. Go for it. That reminds me, Kim, of times where people have said, "Hey, we kind of want like a list of the best questions to ask.

Kim  2:57  
Yeah, yeah. 

Pam  2:57  
And we've said, "I mean... That is a helpful..." Oh. "That is a helpful thing." Sorry, I was totally just unplugging my headphones, and I was trying to figure out why I was hearing crackling in my...

Kim  3:10  
We're such a mess today. 

Pam  3:11  
Today's a mess. Alright, I'm

Pam  3:13  
going to stop playing with the plug of my headphones. Where was I? Oh, yeah. People ask. Yeah, they ask for this like list. Well, and you and I have always kind of been a little uncomfortable with that because...

Kim  3:20  
Yeah.

Pam  3:26  
There are good questions. We can give you a list of decent questions to ask. I think the reason that we get kind of pausey and hesitant is it's you don't ask the same question at the same time to every student.

Kim  3:40  
Right, right.

Pam  3:40  
And really, you don't ask the same sequence of questions. That's probably the most important part of it. 

Kim  3:46  
Yes.

Pam  3:46  
That sequence of questions is going to depend on the student. 

Kim  3:50  
Yeah.

Pam  3:50  
Cool. So, I could also say there might be a time where you're interacting with a student and they're just kind of being obstinate.

Pam  3:58  
Right. Where they're like going to wait you out until you tell them what to do. And in that case, we might, as teachers... That might be the time where we get the most like, "Oh, let me just tell you what to do." You know like when the kids like, "I don't know. I don't know.

Kim  4:14  
Yep, yep.

Pam  4:15  
"Just tell me what to do." So, we also might want to kind of parse out when you're dealing with a kid who's just trying to wait you out until you just use a funneling pattern of questioning. And maybe we can talk about, like, Kim, how you could... In fact, Kim, how would you handle that?

Kim  4:32  
I mean, so much of it is dependent on the relationship with the student, right? Like, that's kind of the first thing is, you know, how do we get to this place where they're so focused on the answer. Have I done something to indicate that I'm focused on the answer? You know, what's their background in mathematics? 

Pam  4:49  
It

Pam  4:50  
might be the beginning of the year where they come to you, they've all kind of had that as their background. 

Kim  4:55  
Yeah, yeah. Well, but it

Kim  4:56  
could be. You know, it has happened that it's, you know, it's on me, and so I have to really think about what do I know about the student and try to enter into a place where they have access to something, right? I don't I think kids when they're seemingly obstinate, when they're like, "I'm just going to say something," most of the time it comes from they're trying to regurgitate something they think you want or they're kind of checked out a little bit because we haven't accessed what they know. And that's kind of the whole point of questioning to me is let me get to where you are that you know something about this. And instead of like shove you along, let me like dig into a conversation with you and guide you, and partner with you, and have a conversation with you, so that we can make connections together. 

Pam  5:44  
Yeah,

Pam  5:45  
so know your content, know your kids. You're sort of thinking everything you know about that student, and then you're using that to enter into the conversation. 

Kim  5:57  
Yeah, for sure.

Kim  6:00  
"Now, I realized it isn't so much about solving math after learning from you

Kim  6:04  
both." 

Pam  6:04  
Wait, wait, wait. Sorry, I'm reading along with you. 

Pam  6:06  
Oh. You're reading. You're not supposed to read.

Kim  6:08  
Well, I'm just reading along with you. 

Kim  6:10  
Okay.

Pam  6:11  
Okay, but... 

Kim  6:11  
Yeah?

Pam  6:12  
Sorry, I'm actually wondering if maybe we can have Craig cut that a little bit. Can you go back to...

Kim  6:20  
You know, if we're saying we want kids to be thinkers, then maybe we need to examine some of the compliance that we have in our classrooms.

Pam  6:30  
I mean, and, Kim, you're a massive questioner. 

Kim  6:32  
Yes. 

Pam  6:33  
We work together, and so I'll say, as a mathematician and as a teacher, one of the most valuable... How do I say this? You are super valuable to me because you don't let me get away with anything.

Kim  6:49  
Which is tough, right? It is definitely tough because when I question, it might feel like somebody's saying, like, "Oh, you think I'm wrong." And it's literally about having (unclear).

Pam  6:58  
I mean, sometimes you do. Sometimes, you do.

Kim  6:58  
I mean, sometimes. But really, it's about I want to understand. 

Pam  7:04  
And

Pam  7:04  
often we push each other for clarification and for like meaning what we say and not just kind of offhandedly whatever. And meaning what we say, but also being heard the way we intend to be heard. 

Kim  7:19  
Mmhm.

Pam  7:19  
Those are two different things, I think. 

Kim  7:20  
Well,

Kim  7:21  
and really, it means that you're you're examining things really deeply and like you're not saying something on the fly, but you've really thought about a situation, and it matches up with your beliefs, and it matches up...

Pam  7:33  
With integrity. Mmhm.

Kim  7:35  
Yeah.

Pam  7:35  
Yeah, yeah.

Pam  7:36  
And you and I both, that's important to both of us. 

Kim  7:38  
For sure.

Pam  7:39  
So, we're both questioners. But we kind of want to turn the conversation a little bit to this idea of compliance and what does it mean to be compliant? Because you kind of said, you know, there might be some things like safety where we need kids to be compliant. You kind of said our society is a little bit compliance driven, and that might be... We might take that a super negative, but I'm going to say there are some places where compliance, I think, is important. Maybe not blind compliance. Maybe... 

Kim  8:09  
Yeah. I think

Kim  8:10  
people have different what they're okay with in their lives for compliance or not. And so, I don't know that we're going to suggest like how much compliant each person should be.

Pam  8:10  
Yeah.

Kim  8:10  
But I think we're saying that we would agree with each other that there are times where compliance is important. 

Pam  8:28  
So,

Pam  8:29  
maybe let's parse out today. We're going to kind of wing this a little bit. Where is compliance important for us or not important for us in...

Kim  8:36  
Yeah, in a classroom. 

Pam  8:37  
Yeah, we could do lots of things, kind of in other places, but let's focus on math teaching a little bit. Or maybe just even teaching. 

Pam  8:42  
Yeah.

Pam  8:43  
So, Kim, I know you told me a little bit about...  Reunitize. And that is a skill that we need. It's a... It's a pat. [Pam clears throat] Sorry, kid. Craig, um, get rid of that

Pam  8:56  
please. 

Kim  8:58  
We have talked about this before on some episode, and maybe more than one, that Problem Strings are an art, that there's a nudge, that they're going somewhere, there's a purpose. And I know that some teachers, right now, are thinking about a Problem String, and they're going, "Wait, but like I let my kids solve it however I want or however they want. And even though there might be a goal of the string, they can still solve it however they want. And that's true. They, you know, on their paper, at their desk, whatever, can solve however they want. But the conversation is not about a bunch of different strategies. As you go through the Problem String, there is a focus and that the direction that the teacher's headed the conversation supporting that goal. It's like in a Problem Talk, it's there's different conversations about different kinds of strategies. And in a Problem String, the conversations more narrowed.

Pam  9:56  
Especially if you're trying to develop a strategy.

Kim  9:58  
Mmhm.

Pam  9:58  
If you're trying to develop a model, the conversation can be... 

Kim  10:01  
Yeah.

Pam  10:02  
You can ask for lots of different strategies because you're trying to really get good at the model. 

Kim  10:07  
Right.

Pam  10:07  
Or a big idea. But in this Problem String, we're really trying to focus on a strategy. 

Kim  10:11  
Yeah.

Pam  10:12  
Or building some relationships that kids can use. Then we're going to  focus the conversation. Not demand what kids do on their paper, but focus the conversation. Yeah.

Kim  10:22  
What's

Kim  10:22  
really nice about a Problem String too is that you're giving kids the opportunity to do lots of different things. So, in this particular strategy, or in this particular string, the work that was on a ratio table had a strategy of Over that you were going for. But there was still some really nice conversation, or in my head there was conversation, about doubling, about scaling, about times 10, about quarters. Like, all of those things were in my head as I was doing this work. And because there are multiple problems in a Problem String, I'm doing more math than in a Problem Talk where you ask me how I solved that one problem that one way. I might be a Kim who's sitting on the carpet and as the kids are talking, I'm staring at the numbers, and I'm thinking about lots of other ways I could solve it. But I might not be. I might be a kid who solved it one time, and then that was the whole thing.

Pam  11:16  
Mmhm. 

Kim  11:16  
So, you get more math, more done in the same amount of time. 

Pam  11:22  
Yeah,

Pam  11:22  
all the mathing that you just mentioned that we get out of that Problem String experience, compare that to the mathing or not that we got from a kid solving the problem using the algorithm. Even if we had them solve 15 or 20 problems using the algorithm. The kinds of mathing that would happen as they're doing that versus the kind of mathing that's happening as we're taking kids through a Problem String like this. They're getting lots of answers in both cases, but the amount of mathing that's happening is significantly different. 

Kim  11:55  
Yeah. 

Pam  11:55  
Look what we get from mathing.

Kim  11:57  
Yeah. And because kids need more and more and more experiences to really make sense of what's happening around them, the more that we can do with them that's meaningful, the better for sure.

Pam  12:10  
And giving them those meaningful experiences with constant feedback. Like, in a Problem String if I'm doing 1-29, Odd lots of problems, maybe I'm getting correct answer feedback, but that's it. In a Problem String, I'm getting lots of feedback on my thinking over and over and over again. High dose of patterning. Alright, cool. ...found a place where math is not about memorizing... Whoops, yeah, it is. Wait. Oh, my gosh. Not about memorizing. I'm like, "Wait, do I mean that? What do I mean? Okay. It's not. I was thinking about the fact that you were laughing right before (unclear).

Kim  12:50  
I know, I'm sorry.

Pam  12:51  
And when you said, "And I'm Kim," I'm like, "Oh, that was really super serious. Okay. And you found a place where math is... I don't even know anymore. 

Kim  12:59  
It's not about memorizing! 

Pam  13:01  
It's 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. That's what it is. Yes. We can mentor mathematicians as... No! Not the one I want!

Pam  13:18  
I'm just going to skip that line. Not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keep students from being the mathematicians they can be. Alright, we're keeping this one because I want you to know we re record that intro every time. I got to hug my grandson twice this weekend.

Kim  13:40  
That's exciting. 

Pam  13:41  
That made things good. Yeah.

Kim  13:42  
Super fun.

Pam  13:43  
Yeah, he's so cute. He will... He will, um... How do I even say this? He will join me in doing things for longer than I think any of my kids ever did. Like, he and I made cookies last night, and he'll just, you know like, grab the... He's 15 months old, ya'll. He'll grab the measuring cup, and we'll dip it in the flou, and we'll pour it in, and then we'll dip it in the flour, and we'll pour it in. And last night, I lost track of him, and all of a sudden, I looked at him, and he had his hand in the flour, and he had it all over his face. I was like, "Oh, hey." Anyway,

Pam  14:14  
oh, he's just brilliant. Yeah. 

Kim  14:15  
I think I forget how old he is and that he's doing stuff like that. I picture him still tiny bitty.

Pam  14:20  
Oh, he's so cute.

Kim  14:21  
So cute, so cute. 

Pam  14:22  
And both of them are, I just see one a little bit

Pam  14:24  
more often.

Kim  14:25  
Yeah.

Pam  14:25  
Yeah.

Kim  14:25  
Oh, I actually see your other one more on Zoom.

Pam  14:28  
Because you

Pam  14:28  
see him virtually, yeah.

Kim  14:29  
That's hilarious. Okay. Alright, well, I have a super, super... Ooh,

Kim  14:37  
I can't wait to hear which one. Yeah, so in this book, you have a section about math distortions.

Pam  14:42  
Ah.

Kim  14:43  
And I think... You know, I've heard bits of this over time.

Pam  14:48  
Mmhm.

Kim  14:48  
But I think that it will really resonate with people like never before. And the first time that I had a chance to hear you speak about these distortions in this particular way was at NCSM. And typically, I know like what your presentation is going to be. And no disrespect, but I kind of like half listen because I've heard (unclear).

Pam  15:12  
You help me create. You know like, I run it by you usually. Make sure. Yep, mmhm. 

Kim  15:16  
But

Kim  15:16  
listen, I don't know why. I don't know why I didn't know what you were going to say this time. But I remember like you starting to talk, and I heard you say something that I was like, "Okay, I know what she's going to do here," but you described these distortions differently than I ever had. And I just got to tell you. Like, when you started, I kind of looked up, and I just looked at you, and I like sat up. And I remember sitting up and leaning in. And I can't remember who I was sitting next to, but I looked at them like, "This is... Like, wait, I'm hearing something new I haven't heard before." And the people in the room heard it so well as well. I remember like just feeling the silence in the room because it was such like the story, and the connection, and the way that you described what I'm going to ask you to share today just... It just made sense in a way that other things, I think, like people maybe have kind of heard. And so, I hope that you'll share today about the math distortions. 

Pam  16:24  
You

Pam  16:24  
know, I remember that particular NCSM presentation because in that silence that you're talking about, somebody went, "Huh. Yeah. And I kind of zeroed in. And I was like. You know, I heard the noise, and I was like, "What?" And that person goes, "It's just so good."

Kim  16:41  
Yeah. I think it... Because you have. You've kind of talked about these distortions in a different way. And this time, it just hit differently. It just hit differently for me. It hit differently for the people in the room. So, I think we should talk about that today.

Pam  16:56  
Cool. So, maybe I'll just mention. The book is called Developing Mathematical Reasoning - Avoiding the Trap of Algorithms. 

Kim  17:03  
Yeah.

Pam  17:03  
It has been a labor of love. And I'm going to give Cameron, my son, some credit. He had heard me talk about kind of I think the way that you had heard me talk about these distortions before, and I would talk about them as perspectives. In fact, we may have a podcast or two where I have talked about perspectives.

Kim  17:22  
Mmhm, yeah.

Pam  17:22  
Yeah. And he said, "I don't think you should call these perspectives, because that makes it sound like valid, and good, and we should, you know like, I don't know, honor that people have this perspective kind of on life." And he goes, "But these aren't perspectives. These are distortions." And I was like, That's so good! Yeah. So, yeah, in the book, just overall, I've poured a ton of learning and thinking to help math teachers and leaders really realize that algorithms can trap students. I know we sort of start the podcast that way.

Kim  17:51  
Yeah.

Pam  17:52  
But we really dive into details and kind of help teachers go, "Oh, that algorithm. I can see how that does." We outline some traps that kind of hit all algorithms. We've said before. Algorithms are amazing human achievements, but they are terrible teaching tools. 

Kim  18:07  
Yeah.

Pam  18:08  
Yeah, so when... Would you consider that there are people out there who can see the shark a little bit easier? Let's just sort of use this as a metaphor for a second to say that there are people who have natural talents, I think, out there. You know, some people play basketball easier. Some people run. Hint, that's you. Like gazelles. You know like,  we all have natural talents, and inclinations, and interests that sort of makes some things come a little bit easier for us. That doesn't mean that I can't run.

Kim  18:45  
Right.

Pam  18:45  
I don't know that I'll ever be as good of a runner as you, but I can run if I put the time and effort into it. So, that there are some people out there who saw patterns and put them together to make more math. Like, they were out in the world, and they had a low dose of mathematical patterns, and they used them, and they put them together. And then all of a sudden now, like more math becomes apparent or useful to them, and then they can put those patterns and relationships together, and then more math. And they mess with those relationships. And then one of the things as they were messing with these mathematical relationships is they dug deep and they generalized. They were like, "Oh, check it out. Like, if I line these numbers up, I can actually add these numbers in columns because there's this place value thing happening. But that's after they've really explored and messed with and really created mental maps and connections and relationships. Then one of the things. Not the end goal. But one of the things they do is that they create algorithms. They create generalizations that could allow people to operate on stuff. Those procedures can help people get answers. And, ya'll, historically, that was super important. The algorithms that al-Khwarizmi...I pronounce his name wrong, I'm sure...came up with in the, I think 600 700 a.d. They were super important because they allowed shopkeepers. You didn't have to be trained in the abacus anymore. You could just actually do the sums and the figures yourself to keep track of your your finances in your shop. That was super important. But just mimicking those steps of an algorithm to get answers? Again, super important. But that's not really doing the same processes that mathematicians, the same mental actions that those mathematicians were doing as they were creating those mental relationships and creating those generalizations. Would you consider that then teachers and textbooks took those steps and somehow that's what gets taught? So, again, if everybody can think of this kind of a magic eye image. You're thinking about those dots and everything. Here's the analogy, be a student in a classroom and be in that moment where we're learning something where students often get kind of stuck. Like, maybe it's long division. Maybe it's fractions. Maybe it's solving proportions. Or like solving equations. What? Like, pick a pick a moment where students often kind of get stuck in mathematics. Maybe it's memorizing their multiplication facts. You know like, whatever. And could you be a student who is sitting in that class and the teacher says, "Alright, everybody. Ready? Does McDonald sell cheeseburgers? Here are the steps of long division algorithm. And you could be a student who has, for whatever reason, you can just see a few, get a low dose of patterns, and you're like, "Whoa! Like, that's really cool! I could see that shark!"

Kim  18:45  
Yeah. 

Pam  19:00  
"Like, I just... I see there's relation." And you start playing with the relationships. And you can kind of see what's happening behind the scenes. And you're like, "Wow, I could see the shark! Why is the teacher making me write down squiggles?" Like, because the teacher is like, "Here are the steps that you do.  And now, you got to do this." And the kid's like, "No, like, I can just... I see what's going on here, and I can just see that..." Pick a problem. 4 divided into 364. They're like, "Well, I can just see what's happening. Like, I can think about how many 4s are in 360, and then there's only one more 4 left over. You're going to what? You're going to make me write all these steps down?" The students who, with some low doses see the shark, in that moment, they're like, "Why are you making me write down all these squiggles?" Do you have that student in your class where they just come up with an answer, and you're like, "Yeah, you got to show your work. And they're like, "Really? I really have to show my work?" Because they can just see the shark. And then, let's be clear, they might not even know what worked to like really what their brain was doing because it certainly wasn't the steps that you were just trying to get them to memorize. So, we might have some students that do that. But then be some other students in the class where the students might go, "There's supposed to be a shark there? I don't... I just see a bunch of squiggles and dots and stuff." And the teacher says, "Alright, start doing these steps. Memorize these squiggles." And the students are like, "Oh, that's math. Okay. Math is memorizing these squiggles. This is dumb. Like, okay, I'll memorize your squiggles. But wow, this isn't related to my life. And when are we going to use this? Alright, math is completely irrelevant, but here we go. Step, step, step. Does McDonald's sell cheeseburger? Blah, blah, blah, blah, blah, blah." And math, to them, becomes about squiggles, and wavy things, and dots, and they never actually see the shark. They don't ever do the mental actions that mathematicians actually do. They just buy into the myth that math is memorizing a set of disconnected facts and mimicking procedures. Alright, I think there's another. So, these are the distortions, right? The first... Well, I'm going to get distortions in just a second. So, the last group of students, could you be a student in the class that goes, "There's a shark there? Cool! I want to see the shark." And the teacher goes, "Alright, so here's the first squiggle and the second squiggle..." What are you doing in the background? 

Kim  23:53  
I'm sorry. I'm sorry. 

Pam  23:54  
I'm like, are you walking around? 

Kim  23:57  
No! No,

Kim  23:58  
no. I... Well, I just hit my glass of water. And also I...

Pam  24:04  
So, in that 30 minute, the first thing I would do is say take a couple of minutes, turn to a partner, and just let it all out. What are you thinking about? You know like, just like vomit your your thoughts. And so, we did that a little bit. And then I said, "Alright, now come back together. What do you want to talk about?" And almost to a T in each of those eight different sessions, the first thing that teacher said was, "You wait a long time." That was (unclear).

Kim  24:32  
Yep.

Pam  24:32  
And then they all kind of pause. They're like, "Like, wow. Like, you really wait before you..." And I was like, "Say more about that." And they said, "We just found it sound it so interesting that how long you waited." Now, Kim, I'm going to be really clear. There were a couple times that I maybe would kind of categorize it as I waited long. But most of the time I just don't think it was all that long. I just think it was longer than many of us are used to waiting.

Kim  25:00  
Right. 

Pam  25:00  
Especially because I wasn't allowing students to just call out. I was asking for a private signal. Now, did kids call out a couple of times? A few times kids would, you know like, pop out an answer, and I would say, "Ah when you've got an answer..." Most of the time they didn't because I very clearly said before, "I'm about to ask you a question. Before you give me an answer, give me a thumbs up when you have an answer. And I very clearly demonstrate. If you can see me right now, my thumbs in front of my chest.

Kim  25:30  
Of course it is. I picture it. I knew you were. 

Pam  25:30  
And then the kids would put their hand up, and I would just look at them, and I would put my hand on my chest. And if they didn't get the message, I would put my hand up and move it to a thumb on my chest. And I just... In fact, then teachers would remark, "Yeah, and then you didn't let it go. Like, as the lesson moved on, 15 minutes later, when you ask another question, the hands went back up. You would  remind them again, just quietly." Teachers would often note that I didn't make a big deal about the thumbs up. In fact, I would say, "Oh yeah. And I got that going by having this five minute discussion at the beginning and having all the kids practice putting their thumb up, and having this big discussion about why and how and when." And they would look at me like, "No, you didn't do that at all." I'm like, "Yes, you don't need to do that." You just over and over. You just keep. You're steady that you're not letting kids call out. When they would ask, "Yeah, how did you make it happen?" I think, Kim, an important teacher move is the idea of a private signal. Now, it doesn't have to be a thumb up. We often use thumbs up. I don't know why. Why did? I don't know why we chose thumbs up.

Kim  25:30  
I don't know, but it works for us. 

Pam  25:30  
We saw it somewhere. Somebody the other day, I think in our teacher Facebook group, said something about an index finger up. Whatever. I don't care. As long as it's private, right? It's all about not interrupting other kids thinking. What else can you? Help me? What? Private signal.

Kim  25:30  
Well,

Kim  25:30  
I appreciate that you said that it wasn't a big like lesson ahead of time, right?

Pam  25:30  
Mmhm, mmhm.

Kim  25:58  
It's a simple move, but the biggest issue that we run into that people are saying, my kids won't do it is because the teacher lacks consistency using it over time, over the first day or two that they introduce it, in the first chunk of time. And so, there's no reason for students to alter their behavior over the way that they've been giving answers in the past if they kind of can do whatever and they get called on anyway.

Pam  27:22  
Yeah.

Kim  27:23  
So.

Pam  27:23  
Or if they can shout out and the teacher runs with it.

Pam  27:26  
Mmhm, mmhm.

Kim  27:26  
Yeah. 

Pam  27:27  
Yeah. Whoo! Kim, that was fantastic! Alright, listeners, we really hope that you enjoyed listening to the important messages and the maybe less important. But ya'll, thanks so much for joining us. Kim and I are really thinking hard about what to do next on the podcast. Where  should we take it next? 

Kim  27:50  
Yeah, in

Kim  27:50  
true Pam fashion, lots of ideas.

Pam  27:53  
All the ideas.

Kim  27:54  
You know, yeah, weighing out all kinds of good stuff. So, we're excited to do some maybe new things, and we hope you'll come along with

Kim  28:02  
us. 

Pam  28:02  
Yeah, 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. Kim, do you know somebody the other day told me that when I say "figure-out-able", they don't understand and that it sounds more like... Well, now, I can't remember what they said. 

Kim  28:17  
Math is forgettable. 

Pam  28:14  
Forgettable! And I'm like, "What?" 

Kim  28:17  
Definitely not. 

Pam  28:19  
Okay, visit mathisfigureoutable.com and keep spreading the word that Math is Figure-Out-Able. Da dum, dun, psh.