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  0:18  
Because we know that algorithms, while they are amazing historic achievements, are terrible teaching tools because mimicking step-by-step procedures actually traps students into using less sophisticated reasoning than the problems are intended to use and develop.

Kim  0:32  
In this podcast, we help you teach mathing, building relationships with your students and grappling with mathematical relationships.

Pam  0:39  
We invite you to join us to make math more figure-out-able. I feel like that was boring, Kim. We should

Pam  0:45  
do... 

Kim  0:45  
Are we flat? We're flat. We needed more energy. 

Pam  0:47  
Wake

Pam  0:48  
up! Poke, poke, poke. Alright, how are we starting today off?

Kim  0:52  
Well, I have a review for us. This has been a

Kim  0:56  
little bit, but...

Pam  0:57  
Thanks for reviews everybody! 

Kim  0:58  
Yeah, I

Kim  0:59  
love it. This one was on Audible. I finally went to other sources.

Pam  1:04  
Ah. Okay.

Kim  1:06  
I don't have a lot of them, but...

Pam  1:07  
Oh, Audible.

Kim  1:07  
Jennifer, I think it's Cuccini. Sorry, if I butchered that. Says "It's a must for math teachers." And she said, "I love Pam's podcast. Such rich discussions and great insight into helping your students grow as math thinkers."

Pam  1:22  
Aww, Jennifer.

Kim  1:23  
Thank you so much.

Pam  1:24  
Thanks, yeah. Pam and Kim do a good job. 

Kim  1:27  
We try. 

Pam  1:28  
We like rich discussions that's for sure. Yeah, if you define rich as sometimes content-- I mean spirited. Spirited.

Kim  1:38  
Spirited, yeah.

Pam  1:39  
Spirited, yeah.

Kim  1:40  
You know what? We say that. I don't know that we have that many on the podcast, but they happen.

Pam  1:46  
Maybe come hang out with us at the conference. I don't know. Today we're going to get you to shoot a little straight. We're going to have this a little bit unscripted, unplanned. 

Kim  1:55  
Yeah, okay.

Pam  1:55  
Today's episode, I'm going to propose, Kim. We've done this in the past where you have rapid fire questions to me.

Kim  2:03  
Yeah.

Pam  2:03  
Today I have this idea. So, first I want to start with this story, true story, that we actually talk about in the K-2 Developing Mathematical Reasoning. Oh, golly, I don't have the whole title. Hold on a second (unclear).

Kim  2:20  
It's a long title.

Pam  2:22  
Hang on, I'm coming.

Kim  2:24  
You're walking away.

Pam  2:24  
I just took it out of the box because it just came the other day. Developing Mathematical Reasoning - The Strategies, Models, and Lessons to Teach the Big Ideas in Grades K-2. 

Kim  2:25  
I like that title. 

Pam  2:25  
It's a good title. 

Kim  2:29  
It is a good title. It's helpful.

Pam  2:31  
It's long. It's very, very long. 

Kim  2:33  
Very long.

Pam  2:34  
So, I haven't memorized it yet. But it's yeah, strategies, models, and lessons.

Kim  2:40  
We just call it the K-2 book. 

Pam  2:40  
That's exactly, or sometimes DMR K-2. 

Kim  2:41  
Yeah, yeah.

Pam  2:41  
Yeah. DMR, Developing Mathematical Reasoning. Anyway, so in that book, one of the stories that we told, true story, is that we were early days, we were working with teachers trying to get them to help kids develop mathematical reasoning, and had a second grade teacher, super well meaning, was, you know, doing her best to implement and had a parent, two sets of parents very upset and very in her business. And this teacher was kind of emotional and was like, "I don't know what to do. I don't know what to say. They're like mad. They're very..." And so, I kind of had some conversations about, you know, like, make sure you include the parent in your conversation. Make sure you are grateful that they're interested in their kid. You know, you don't try to separate the parent from the kid and say, "Don't worry. We'll take care of math here. You don't need to help at home." Don't do any of that. 

Kim  3:27  
Yeah.

Pam  3:27  
Invite them in. Be grateful if they're there. But the math part of it, I wasn't quite sure what to think about what they were complaining about because I didn't... I wasn't quite sure what to think about what their daughter was doing. Yeah. So, I called you in. I said, "Hey, Kim..." Well, first I said, "What do you think about this?" And you said, "Well, I

Pam  3:44  
really would like to talk to her." 

Kim  3:45  
That's always my answer. 

Pam  3:47  
I mean,

Pam  3:47  
it was really noteworthy, right? It was like, "I got to know more about this kid." And I was like, "Well, I just told you about the kid." You're like, "I got to know more about this kid." Like, know your content, know your kids.

Kim  3:56  
Yeah. 

Pam  3:56  
And so you said, "Can I just interview her?" And I, at that point, early days, I had no idea what that would look like, sound like, whatever. So, I said, "I don't know. Let me see." So, we kind of worked it out. The teacher's there. The kids there. You're there. I'm kind of in the background. And you basically said, "Hey, before we get started, can you just help me with something? And I don't exactly remember what you did. Is this the one where you took the change out of your pocket? I don't remember.

Kim  4:20  
I

Kim  4:21  
don't think so. I think this is earlier than that.

Pam  4:25  
So, whatever you did, you said something like, "Hey, before we get started will just help me? I was thinking about something." And you threw out a problem. And the kid, this gal, just drew a number line and then started doing these random... not random. She started jumping. So, it was like 29... Maybe the problem was like 29 plus... Or 20... Let's say 28 plus 6. And... 28 plus 7. I'll do that. And she... No, it was 27 plus 7. There that's better. 27 plus 8? It doesn't... It has to start at 27. Has to start at 27, just to make sense, because she drew a number line, mark 27, and then started making the same size jumps without any lands. So, just like, jump, jump, jump, jump. No how big the jumps are. And I said, "What are you doing?" She's like, "I've decided to jump by 2." So, y'all, she started on 27. That's why I just changed the problem because I realized she jumped by twos, and it was a nonsensical jump. And I was like, "Jump by 2?" And you said, "Why?" And she said, "Well, because I'm going to jump. That's what we're supposed to do is jump. And so, today, I'm going to jump by twos." And you said, "Well, hang on. Make that first jump." And you put a 2 above the first jump. "Where would you land?" And she said, "It doesn't matter. I'm going to jump by twos." And I don't know if she was exactly that clear. That was her feeling tone was it doesn't matter. And so, she just kept making all these jumps. And then she went back and wrote, "I jumped by 2," and where she landed. And you said, "Oh, interesting. You just landed on 29. That doesn't seem very friendly to me. Is there something friendly here?" And you were like helping her think about either Make a Friendly Jump or Get to a Friendly Number. Anyway, it was really interesting in that moment, the moves that you decided to make. And so, I don't know. Do you want to say anything more about that story before I...

Kim  6:07  
Well, I

Kim  6:07  
mean, when you first raise it, I'm like, "I can't remember that." But I am right in that room. There was like an empty classroom down the hall. Who has empty classrooms? This is that long ago. And I remember. And yeah, I remember having a conversation with her. And I

Kim  6:23  
was like (unclear).

Pam  6:24  
You're at that round to that half round table. Mmhm, yep.

Kim  6:26  
And it was like, Oh, you're trying to mimic this idea of jumping. You're  doing a number... "Doing." ...a number line. And you're jumping some jumps, but they don't... There's no purpose behind them. You don't know why you're jumping. It's like, the idea is to jump. Yeah, I remember

Kim  6:27  
that.

Pam  6:29  
Yeah. So, today, I'm going to rapid fire some pedagogical situations at you, things that could happen. And I'm just going to time you. You can only have... Where'd my phone

Pam  6:53  
go? I got to find my timer.

Kim  6:55  
Oh. This is like your serious rapid fire.

Pam  6:57  
This

Pam  6:57  
is rapid fire. Yeah, you can't go over, so you got to like have your stuff together. So, I'm going to give you a scenario. So, you can do it. You can do it. I have faith in you. I'm going to give you a scenario. And you're going to do your best to give us... Why can't I find the timer on my... Okay, I found it. What do I really want to do? Countdown or time up? Do I want to count

Pam  7:18  
down? I don't know. 

Kim  7:19  
Is it going to be like [timer sounds].

Pam  7:19  
Yeah, yeah.

Kim  7:19  
Great. 

Pam  7:19  
That's what it should be, right? Okay, you get a minute and a half. 

Kim  7:19  
Oh.

Pam  7:19  
No. No more. 

Kim  7:19  
Oh, wow. Talk fast. 

Pam  7:19  
Minute and a half. 

Kim  7:25  
Okay.

Pam  7:26  
So, I'm going to give you a scenario, and then you just give us your pedagogical response. Like, what would you do in the moment? Kind of like you did with this gal. You know, "I got to talk to her," and then what would be the... Yeah. Got it?

Kim  7:40  
Uh, sure. 

Pam  7:40  
It's going to be fun. I'm looking forward to it. I have to remember now to ask the question and push the start. I can do it. Okay, here's the first one. You notice as a student's doing work that the student always solves addition problems from left to right. Meaning, not like lining them up and from left to right. But meaning, if they saw 8 plus 9 or 2 plus 9 or 8 plus 7, they would start with the first number, and then add on a second number. They never think about which number is bigger. Maybe is that a good way to say that?

Kim  8:17  
Mmhm.

Pam  8:18  
Okay, go. 

Kim  8:18  
Okay.

Kim  8:20  
This actually happened once, so I'm glad you gave me an easy to start. So, first I would wonder if they have an idea like what is their general idea of adding? Do they think it means to start with the first number? Have they had an exposure to the idea of the commutative property? In this scenario, where this happened before, I was working with a student, and they did this. He always started with the first number. And when he in his classroom was kind of exposed to the idea of starting with the second number when it was the larger addend, he would hear it in the classroom, but never did it on his own. So, I pulled him in the hallway, and we started having some conversation, and what I discovered was that he did not trust the commutative property. He didn't buy that 8 plus 9 and 9 plus 8 was going to have the same result. And so, I pulled out a number rack, and we did some work where we modeled 8 plus

Kim  9:21  
9. Got the (unclear). 

Pam  9:23  
8 on the top, 9 on the bottom.

Pam  9:25  
Uhhu. And then we modeled. And I actually flipped the the number rack, flip the rekenrek over to represent 9 plus 8. And so, the idea was that he could solve addition problems. It was that he didn't trust that he could reverse the order and use the commutative property, and so he was doing exactly that. Adding things like two plus 9, starting with the 2.

Kim  9:50  
Okay, it's buzzing. And I have a terrible timer sound. Oh, I can't hear

Kim  9:54  
it.

Pam  9:54  
You can't hear it, can you?

Kim  9:55  
Thank goodness. No. No, no, no.

Pam  9:57  
Time's up. 

Kim  9:57  
Okay.

Pam  9:58  
I got to fix my sound. Oh, okay. Hold on. It's better. [timer sounds].

Pam  10:08  
Can you hear that? No, that's dumb. [timer sounds].

Kim  10:11  
I can hear that barely.

Pam  10:12  
You can hear that one? Barely though.

Kim  10:14  
Mmhm. 

Pam  10:14  
Maybe I'll turn my phone up. [timer sounds] That's dumb. [timer sounds] All these are dumb.

Kim  10:19  
You're like my kids right now.

Pam  10:21  
You can tell how often that I have... Wait, "Classic". What's "Classic"? Wait, what? [timer sounds].

Pam  10:27  
There we go. 

Kim  10:28  
Oh, awful. 

Pam  10:29  
Okay, okay.

Kim  10:29  
It's like my morning alarm.

Pam  10:31  
See if we can... Oh, wait. I don't even know if it's set that. Anyway, okay. We'll see what... Moving on. Hey, when you say "trust the communitive property" just to be clear, you don't mean that you've used the word commutative property, and the kid never learned the definition of it. You literally mean that...

Kim  10:46  
He didn't trust that it would provide the same sum. Yeah.

Pam  10:51  
Yeah, nice. Okay cool.

Kim  10:52  
He probably heard it, but didn't have an experience of it for himself. 

Pam  10:55  
Yeah.

Pam  10:56  
Nice. Alright, that was excellent. Yeah, let's move on to our next one. 

Kim  11:03  
Okay.

Pam  11:05  
Let's say that you are facilitating Problem Strings in a classroom. 

Kim  11:08  
Okay.

Pam  11:08  
And when you say, "Alright, everybody, give me a thumbs up when you have an answer that this particular student either never puts their thumb up or always gives you a signal, I want to pass today. Don't call on me yet.

Kim  11:15  
Always? Always? 

Pam  11:15  
That's always. "I've got an answer, but I'm never..." And you keep waiting. You wait. You're looking. And every time, it's like the kid doesn't even know the other signal for "You can call me." It's like the pass signal.

Kim  11:27  
Is this my class?

Pam  11:29  
Um...

Kim  11:30  
I need more. My class? Or am I going in one time? 

Pam  11:33  
Am I starting the timer? 

Kim  11:34  
No, not when I have clarification questions.

Pam  11:39  
It's your class. 

Kim  11:40  
It's my class. Okay.

Pam  11:41  
Yeah.

Kim  11:42  
So, ooh, always passes. That is a kid, I'm going to suggest, that has some fear, that has some nervousness, that has some probably trauma in their past. And so, I think this is relationship building conversation. This is me sitting down outside of the string and saying like, "Hey, I noticed that you pass. Can you tell me about that?" And then I think it's a conversation about why do they pass? And let's work together to find a space where their voice can be brought in, where they feel secure. You know, maybe it's the first problem. Maybe it's me circling around and noticing something that they're doing well and saying "Just that." I'm not...

Pam  12:26  
"Share just that."

Kim  12:27  
"Share just that. That's all I'm going to do. I promise you. You can trust me. It's just that. I'm not going to put you in a position where you have to say anymore." Because sometimes that first hurdle, that first share, especially if you've passed for a really long time, that first opening into your voice being in the classroom is the scariest, so if you can find one or two small instances where they're willing, then it can potentially open a floodgate. And it might not. You know, it might not be a floodgate. But their voice needs to be brought in. And so, I think that's just a private conversation to learn more about them and why they are passing.

Pam  13:07  
Nice. And that might not be a one time conversation.

Kim  13:10  
Right, right. 

Pam  13:10  
Yeah,

Pam  13:11  
nice. [timer sounds].

Kim  13:12  
Look at that.

Pam  13:13  
Can you hear it?

Kim  13:13  
I'm awake. I'm awake now.

Pam  13:16  
Alright, cool. Nice. 

Kim  13:17  
Yeah. 

Pam  13:18  
Next. 

Kim  13:18  
Yeah.

Pam  13:19  
Let's say that you have... Okay, I can't read my writing here. Hang on. Oh, yeah. You have students that participate in Problem Strings, and they're using the strategies. You're super clear they've got them down. They can even discuss them. You're not like, "Ooh, I wonder..." No, they are owning a particular strategy. But you notice that when they're doing like a test prep item or maybe a homework, some kind of individual work, they revert to some memorized set of steps and procedures. 

Kim  13:47  
Mmhm, yeah.

Pam  13:48  
What would you

Pam  13:48  
do? 

Kim  13:48  
Again, I'm going to have a conversation. This feels to me like my gut response is that these students probably feel like they were going to do this fun, cool, mathy thing during Problem Strings, but when there's a piece of paper in front of them, then they're like, "This is the right way to do it." So, I think the first conversation is, "Oh, no what we're doing in Problem Strings is math. That is." So, an awareness to what we're building here, I want you to be using on your paper, right? So, as I'm circulating, if I see them reverting to something that they've done in the past, you know, I might kneel down next to them and say, "Oh, I see this problem. This feels like a great opportunity to use the blank strategy." And I think it's okay to name a strategy that I might use in the beginning. I'm not demanding that they do it, but I'm bringing to mind strategies that we've built. I might point to an anchor chart that we've used and say, "Oh, there's two really good strategies here. Do either one of those strategies feel like something that you would want to use here?" So, we're bringing awareness to remind them of what we've done in strings and connecting it for them, like very intentionally connecting. I also might say aloud. You know, we might put a test prep question up, and I might model for them strategies that I would choose to use, so that they're making the connection between the work that we're doing in strings and how it is applicable to this paper, pencil. [timer sounds] A minute and a half is so

Kim  15:23  
fast.

Pam  15:24  
It is very fast. You did a great job. Yeah. No, I like it. I like it. I like it. So, it's our job to help them realize they can...

Kim  15:30  
Yeah.

Pam  15:31  
...transfer that. It is real math. Yeah, nice. Okay, cool. Next, you are doing work, and a student yells out answers, and you're not allowing that because you're like, "Give me a thumbs up." But that student is  getting discouraged, frustrated, because they have forever, probably before your class, they've been allowed to yell out. And that's their, what? M.O. Their modus operandi. That's the way that they've just been used to education.

Pam  15:56  
Go.

Kim  15:57  
Wow. I think there's a couple of different reasons kids do that. So, it might be an impulse thing. And so, it could also be a like, "I get my self- esteem from being really good at math, and so I just want to show you that I know." 

Pam  16:10  
Mmhm.

Kim  16:11  
I think there's a couple things you can do. So, for either one of those circumstances, I think having a notebook, a dry erase board, some way for them to record that they... I just wrote. I said that really, really fast. They could record. They can record an answer. They can have a private signal to let you know that they're ready to share.

Kim  16:32  
I also think it's really...

Pam  16:34  
That gives them that instant feedback.

Kim  16:36  
Yeah.

Pam  16:36  
It's like, ooh, okay. I got my ping. I got my acknowledgment.

Kim  16:39  
Right.

Pam  16:39  
Okay.

Kim  16:39  
And I'm making eye contact, and I'm smiling, and I'm winking, and I'm like, "Yeah, good for you," because there are kids who just want to be acknowledged, and they've been told that speed matters for so long. And in the process of helping them understand that it's not about speed, I think you have to acknowledge that that's where they are, that that's what they've been told, that's what they've been told they're good at. And I don't think overnight you can say, "That doesn't matter," because then if they have felt like that mattered, and that's what they've been acknowledged for, then you're ripping away part of what they have felt mattered. You know, I have a kid who has some impulse. He's got some drive to just get things done. So, giving that kid a dry erase board to get it out of his head, so he doesn't lose it is super helpful. [timer sounds].

Pam  17:26  
Sorry. 

Kim  17:27  
I'm sad. 

Pam  17:27  
Do you want to say more?

Kim  17:29  
 It's okay. You probably have more.

Pam  17:31  
No, I think that was great. I think we all have students who, for whatever reason, that that's... And I think recognizing which of those might be helpful.

Kim  17:41  
Yeah, for sure. It's so important to understand why this particular situation is happening. And I think I've said for every one of these questions, "I'm having a conversation with the

Kim  17:51  
student."

Pam  17:52  
Yeah, it's almost like you're suggesting we should be human with them.

Kim  17:55  
Mmhm. And get to know them.

Pam  17:56  
Relationship, yeah.

Kim  17:56  
Know your kids. 

Pam  17:57  
Know your content, know your kids. Yeah, know your kids seems like it's becoming an important theme. Alright, next. You are circulating during a Problem String or a Rich Task, or whatever they're working on. You're conferring with students. Oh, sorry. It is a particular task. I should read down. They are flash carding each other. The flash cards have hints on them. And so, we have some podcasts that talk about hint cards. We'll put that reference in the show notes, where they have a fact, but it has a hint for them to think about, so that they're traveling the path of using that hint to find that multiplication fact, that addition fact. And so, the kids are now flash carding each other with those hint cards. 

Kim  18:40  
Mmhm.

Pam  18:40  
And you notice that a student is getting bogged down with one of those cards. What would you do?

Pam  18:42  
Go.

Kim  18:43  
Bogged down. So, I would wonder why they chose the particular hint that they chose. Sometimes when we create hint cards, students have a particular strategy in their mind because maybe it's a fresher strategy. And in that moment when they write the hints, they're like, "Oh, this makes sense for this problem." But then as they walk further away from having created those hint cards, it's not quite as cemented. That particular strategy might not be as cemented anymore. So, maybe at the time, it was a great strategy. But, you know, it hasn't been. They're not fluent with it. They haven't done some work with it. So, I would want to know why. And then I would want to know, you know, what else do they know about that problem? It is perfectly fine for students to have created a hint, and then change their mind. It's perfectly fine. In fact, I think it's desirable that we have lots of different ways to attack a problem. So, I think, you know, it's a conversation. Again, sitting down and saying, "Tell me why you chose this one. Oh, you don't remember? Cool. Well, we can change a different one. What are you thinking about right now?" Or it might be the same strategy, but they need a little bit more language around the hint.

Pam  19:52  
Maybe they haven't written enough on the card.

Kim  19:54  
Right, right.

Pam  19:55  
Okay.

Kim  19:55  
Yeah.

Kim  19:57  
And then, you know, in the idea that the point is to practice these hints. I think I have added more than one card with the same problem on it, so that it comes up more often. So, there's a sneaky thing I don't think we've said before. But sometimes I'll add some problems that are

Kim  20:15  
repeats.

Pam  20:16  
Did you hear the buzzer just hit? 

Kim  20:18  
Oh

Kim  20:18  
no.

Pam  20:18  
No? 

Kim  20:19  
That's rude.

Pam  20:20  
Oh, weird. Okay.

Kim  20:21  
Okay.

Pam  20:22  
I don't know what's wrong with my phone. The buzzer just hit, but... 

Kim  20:24  
Hints can change. 

Pam  20:25  
I think that might be the first time I've ever heard you say that you might put in a double of a card. Would you have the same hint on that card? 

Kim  20:33  
I

Kim  20:33  
think it depends if... Yeah, I mean some kids yes, and some kids, if I...  Yeah. Depends. I've done both. But I haven't done it with a ton of kids. I think just some where I noticed that they keep getting stuck on a couple. I mean, there's some facts that are funky, so... 

Pam  20:53  
Sure.

Kim  20:55  
Yeah.

Pam  20:55  
Just gives them more of a chance to travel that mental path of figuring out that hint more often. Nice. Alright, last one. Deep breath. Here we go. You have two students that have IEPs. They have some accommodations given to them for whatever reason. They have some sort of... Yeah, they have accommodations.

Kim  21:12  
Mmhm. 

Pam  21:12  
And for both of these students, they get more time on assignments. So, that's a common thing, right?

Kim  21:18  
Okay.

Pam  21:19  
You feel that it might be that one of them never finishes because he'll get started, but he doesn't finish because there's no deadline. Because  he has this extra time, it doesn't actually encourage him to get going and like do it. He doesn't... There's no sense of urgency because of that extra time.

Kim  21:37  
Mmhm, mmhm. 

Pam  21:37  
The other one you feel like needs the extra time, but struggles to get going.

Kim  21:43  
Mmhm.

Pam  21:43  
Go. 

Kim  21:43  
So, the one that struggles to get started, those students, I think are the ones that you help them create a plan. What's the step one? What's the step two? Or like what are you going to attack first? I have a kid who once he knows exactly what to do, then he's off. He's on his own. But making a list or knowing what the plan of attack is is a bit of a challenge. I have a different kid

Kim  22:12  
who...

Pam  22:13  
Can I pause you on that? I'm going to pause the timer.

Kim  22:15  
Yeah. 

Pam  22:16  
Am I right that you don't mean a series of steps to solve the problem? 

Kim  22:21  
Correct!

Kim  22:21  
Oh, thank you. It means like first I need to complete this portion of the assignment. Then, I need... Like, you know, sometimes in classes, you know, especially if you have a longer class period, a teacher might say, "These are the things that you need to accomplish today in class," and so it can feel overwhelming. And they might say, "Okay, there's a lot for you to do, so we're going to give you more time. So, I have two drastically different kids. One of them, if he can organize what needs to be done in his mind, and he knows what he needs to accomplish, like a checklist, then he's off and running. You don't even have to have any more conversation. Other kid can organize what needs to be done, but needs frequent check-ins because he has no sense of urgency. He's like, "Oh, I've got all the time in the world." So, what I found was that additional time actually was a negative thing for him. What he needs is frequent check-ins to say, "What have you accomplished? What have you gotten done? Okay, I'm going to come back in ten minutes. Let's try to get this much done." So, we've talked about this modification or this accommodation of additional time. And this is so particular to actually what is holding the kid back.

Pam  23:32  
What does the kid need? And I feel like... Did the kids that you just talked about, did they come with that instruction manual that said... Or did you have to actually like get to know the kid with trial and error?

Kim  23:43  
Trial and error. And like why you have additional time. And why, you know, it's still (unclear).

Pam  23:48  
What do you do with it?

Kim  23:49  
Mmhm. 

Pam  23:50  
Sure, yeah. 

Kim  23:50  
And observation. I mean, I think in all of these situations... I'm glad that you have a bunch of kid situations. So much of it is about observing and conversations with the students. And they don't always have the words to describe what's going on, but if you are really carefully observing and paying attention to the hiccups along the way, and conferring with teammates or parents, I think more often than not, you can figure out what is going to make a positive impact for the students. And, you know, I certainly don't get it right all the time. But I think part of the great thing is because I have developed an understanding of the content that I teach, that I'm freed up a bit to really pay attention to the students that I'm working with and spend my mental energy like understanding what they need.

Pam  24:44  
Nice. Which is maybe this whole episode was kind of focused on know your content, know your kids, the know your kids part of that and ways that you can actually use that, implement that. How does it actually impact? When we say, know your content, know your kids, here were some super ways that knowing your kids can impact the teaching that you're doing. Thanks, Kim. That was kind of fun. 

Kim  25:05  
Yeah. 

Pam  25:05  
I was a mess with the timer on that last one, so I just let it go. Alright, thanks. That was awesome. Hey, listeners, we are toying with the possibility of a video component to the podcast. So, if you're an audio podcast listener, don't worry. We would keep the audio part of it. But what would you think if... Kim just said, "Oh, heavens." And if...

Kim  25:26  
You want to watch me look out my window for 25 minutes.

Pam  25:30  
When Kim's thinking, like she looks off to the... I guess it's your left, right? 

Pam and Kim  25:33  
Yeah. 

Pam  25:34  
I don't know what I do. Yeah, I guess we'll learn right? So, we'll always keep the audio, but we are wondering what would happen... Would you be interested in a video component? So, let us know because if no one says yes, we'll probably keep it just audio. 

Kim  25:45  
Yeah.

Pam  25:45  
But if we have an influx of a lot of people saying, "No, video would be awesome." I will say if we do video, the chances are high that we would actually show you what we're thinking more, which we have definitely heard people say, "Oh, you know, it's really hard to see what you guys are talking about when you're describing."

Kim  26:03  
Picture everything. 

Pam  26:03  
Yeah. So, anyway, let us know. Alright, ya'll, 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. Thanks for spreading the word that Math is Figure-Out-Able.