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

Kim  0:09  
And I'm Kim, 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  0:16  
Ya'll,

Pam  0:16  
we know that algorithms are amazing human achievements, but they are terrible teaching tools because mimicking step-by-step procedures actually traps students into using less sophisticated reasoning than the problems are intended to develop, and then we get what we've got.

Kim  0:33  
But in this podcast, we help you teach mathing, building relationships with your students, and grappling with mathematical relationships.

Pam  0:40  
We invite you to join us to make math more figure-out-able. Hey, Kimberly.

Kim  0:46  
Hi. How are you?

Pam  0:48  
Hot actually, at the moment. Kind of warm here in the state.

Kim  0:51  
Texas is warm.

Kim  0:52  
Listen, I grabbed this review. It's been a little while, but I grabbed it because it just makes me... A, it's a great review. But also it makes me laugh when I think about... I'll tell you afterwards. This person said, "I'm so grateful. I have done many math workshops and online trainings over my 24 years as a classroom teacher." That's a great

Pam  1:14  
That's awesome. What a good legacy.

Pam  1:15  
Yeah.

Kim  1:17  
"But in January of 2024, I was at a math leadership conference when someone said the words that would have the most impact on me as a math teacher. 'Have you heard of Pam Harris?' 'No,' I replied. And they said, 'You should check out her podcast Math is Figure-Out-Able." This is LNB13, by the way. "And I did check it out," they said. "On the four hour drive home, I listened to Pam and Kim, and my mind was blown. Succinct, engaging, sense making. I was hooked! That bit of advice has since led to my most transformative year of teaching math. Finally, I know how to help my students reason and make sense of math. Now, a bit over a year..." I know right! "Now, a bit over a year later, I'm so grateful to the person who recommended I check out this podcast, and I do my best to pay that gratitude forward recommending Math is Figure-Out-Able to colleagues and acquaintances, hoping that they take the same advice that I fortuitously took. Check it out!"

Kim  2:16  
Check it out. Golly, Kim.

Kim  2:19  
I know. So sweet.

Pam  2:20  
You're not even making these up. (unclear). 

Kim  2:22  
I'm not.

Kim  2:23  
So, the reason that I started to say like I was laughing is it's really sweet because sometimes I'm in other Facebook groups, you know, and I see people recommend the podcast, and it just like makes me smile. I just...

Pam  2:36  
Yeah. 

Kim  2:36  
You know, you can't pay for the kind of people sharing that like I got something out of it. And teachers like just have the best generosity towards each other. They just want to share what has worked for them and what they love. And so, thank you to everyone who's ever shared. But I did snicker a little bit because this is the second review that I've shared where somebody said, like on a four or three hour drive home, they listen. I mean, I don't even like to listen to the radio for four hours at a time. I just like I need change, so

Kim  3:08  
I...

Pam  3:08  
You and I have talked for four hours on a drive on the way home before.

Kim  3:10  
I mean that's because we have so much to do. But I think I picture some of these people who are listening to us, and eventually they go, "I have to turn it off. I'm so sick of their voices." I wonder. You know, and we hear this a lot because some people say. You know, we'll see somebody in person, and they'll say... 

Kim  3:31  
We hear this a lot that people are sick of our voices?

Kim  3:33  
No! We'll hear this a lot. I'm finishing.

Pam  3:35  
Oh, sorry. 

Kim  3:35  
We'll see people in person, and they say, "Oh, my gosh! I just binge listened for like a month and a half. And I'm like, "How many hours is that?" I wonder. Somebody do some math for us. 

Pam  3:45  
Quality hours.

Kim  3:46  
How many hours... 

Pam  3:47  
Quality hours.

Kim  3:48  
...of podcasts would that be? 

Pam  3:49  
I mean,

Pam  3:50  
I feel like we've subjected Sue to that. 

Kim  3:52  
(unclear). 

Pam  3:53  
How many hours has poor Sue been subjected to listening to us grapple on. Hey, ya'll, we appreciate the reviews and thank you for rating. It helps other people find the podcast. Which is the whole point. Thanks LNB13 for spreading the word. Nice. 

Kim  4:07  
Yeah.

Pam  4:08  
Alright, so today, Kim.

Kim  4:10  
Yeah.

Pam  4:10  
One of the things that came up in the debate that I was in not too long ago...which we could put that link in the show notes if anybody hasn't listened to it yet...is that some words we are throwing around as math education community, and I don't think we know what what we mean anymore. (unclear).

Kim  4:30  
Right.

Pam  4:30  
It always starts out with a good intent, I think. But, yeah. But, like, ready? Ready for the word of the day?

Kim  4:36  
Mmhm.

Pam  4:37  
Could we have a conversation today please about the word... Ready? I was trying to drum roll. That didn't work very well. 

Kim  4:46  
Yeah.

Pam  4:47  
There we go. Can you hear that? 

Kim  4:48  
Kind of. 

Pam  4:46  
No? Oh, kind of. Okay, Craig, give us a drum roll.

Kim  4:48  
Good drum roll. 

Pam  4:48  
There we go. (unclear).

Kim  4:50  
There you go. 

Pam  4:50  
Fluency,

Kim  4:55  
Yes.

Pam  4:55  
Yeah.

Kim  4:56  
Yes. 

Pam  4:56  
Do we hear that

Pam  4:57  
ever? 

Kim  4:58  
On occasion, fluency is a word. 

Pam  5:01  
Lots

Pam  5:01  
of, lots of. Yeah, so interesting. I was just at a couple conferences. And it was interesting push back. They said our standards have just changed, and we are not going to put one of them on our report card. And I said, "Say more about that?" And they're like, "Well, we are a standards based report card system, and the new standard says something about automaticity, and we feel like if we put that on the report card, that then teachers will grade kids. They'll give them timed tests, and the only way they'll get a grade on that is if they have everything, every fact. And we don't want to send the message that every fact has to be rote memorized. And we kind of fear that's going to be the outcome." And it just sort of raised this... Yeah. Kim, what do you think about the word "fluency"?

Kim  5:47  
Well, the first thing I think is that everyone has a different definition. And that is tricky for teachers because when you listen to a bunch of different education leaders, and they all have a different definition, using often very other buzz words that would need to be defined, it's hard to know what fluency really means. I think we can sit down with students and we maybe can see if we know if a kid's fluent or not. But what's the goal? What's the aim? I think it's all about the intent. I think it's important to decide what is our goal here for fluency? And what am I doing to help kids meet the goal that I have? And it's less about the definition or the words. I think the words always get in the way. And I don't know that I have a great definition that I would share with people. I think... Yeah, words are hard.

Pam  6:43  
Yeah, so I think there's been some people out there that have done a pretty good job of trying to define fluency. I think the Figuring out Fluency series by Jon SanGiovanni and Jenny Bay-Williams.

Kim  6:44  
Yeah.

Pam  6:45  
Christina Tondevold has done a good job getting us to think about some good definitions. I think Cathy Fosnot has done a good job. Today, rather than give one more definition of fluency...

Kim  7:06  
Right

Pam  7:06  
...I think what we'd like to talk about is how do we describe what you just said that matters? Like, what do we want with fluency? And why?

Kim  7:18  
Yeah, yeah. And I think you said it well when you said why does it matter? When I was growing up, my teachers probably wanted me to be fluent at facts because I was taught to do algorithms for everything. And so, if I'm going to write an algorithm for everything, then I need to know... Like, let's talk about multiplication facts. If I'm going to write an algorithm for every problem that I solve, then I'm going solve that I'm going to encounter possibly every single fact pretty quickly if I'm given a page of 30 problems. And so, a

Kim  7:52  
goal... 

Pam  7:52  
Single-digit multiplication fact, yeah. Over and over, mmhm. 

Kim  7:53  
So, if the

Kim  7:53  
goal, you know, in third, fourth, fifth grade was to be able to complete a page of thirty multiplication problems, then they might have said the first step is to get you fluent very quick, automatic, know them without thinking for all the facts because then you can use that to help you do these thirty larger multiplication

Kim  7:53  
problems. 

Pam  7:54  
Kim, I think that's really important. Did you want to keep going? 

Kim  8:14  
No, go ahead.

Pam  8:17  
I think you bring a really, really pertinent point that many, if not all of us, have this visceral memory of 1-39, Odd. I don't know, 40 multiplication problems. Where, like you said, in those 40, two by three multiplication problems, two by two multiplication problems, we're going to end up doing so many of those single-digit facts, and if we are refiguring them all the time, especially additively, or trying to from rote memory, that that will bog us down in that work, that we would have a visceral memory of, like, "Wow, if I just had these, you know, retrieve. If I could just retrieve them." Because, to be clear, when you're doing all those single-digit multiplications, and then all those single-digit additions when you add the rows together, you're not reasoning. 

Kim  9:07  
Mmhm.

Pam  9:08  
You're mimicking a bunch of steps. 

Kim  9:10  
Mmhm.

Pam  9:11  
If those are the mental actions that you're... In that moment, that's your interpretation of what what is supposed to happen is for the next hour, I'm going to do these problems over, and over, and over, and over again, then yeah, we would have a visceral memory of like let's just get those facts down because then you're more successful with that. Then throughout long division, the same thing. I got to be able to do all these single-digit multiplication facts. And when I do this subtraction. Either the addition in multiplication algorithm or the subtraction in the division algorithm. Again, I'm going to have this visceral memory of man these thirty problems would sure go faster if I knew them all, if I wasn't trying to, "What was that one again?" And then having to figure it out, getting bogged down in that. So, I think that's one reason why "fluency" can be a tricky word for us. 

Kim  9:59  
Mmhm.

Pam  10:00  
Because we have this sort of experiential gut feeling of like what it felt like to be, quote, unquote "fluent" in those algorithms. And so, yeah, then we better be fluent in those single-digit facts.

Kim  10:14  
Mmhm. I think another tricky word that goes along with this is "automatic" or "automaticity". And maybe...

Pam  10:21  
It started out good.

Kim  10:22  
Yeah. I think it's not that we are saying we don't want students to be fluent or automatic. It's just that... For me anyway. Yeah. It's just that we are in such a rush job for kids to get there because we feel like they're stuck without them. And if your goal is algorithm based, then I can understand why that would be so. If you are a classroom teacher who lives and dies by algorithms, then I understand the need for fact fluency in third grade. And I do think that there is a need for students to develop fluency over time. It just doesn't have to happen by October of third grade. I think kids work with facts. And as they continue to work with facts, more facts get wrapped in, and then more facts get wrapped in. And all the while they're building relationships with those facts.

Kim  11:17  
And so when there...

Pam  11:18  
As long as we define "work with those facts". Can I do that really fast? 

Kim  11:22  
Yeah,

Kim  11:23  
let me finish one more thing real fast.

Pam  11:28  
Yeah, go ahead, go ahead.

Kim  11:29  
Because I do think that when you're factoring in middle school, it is helpful for students to quote, unquote "know their facts".

Pam  11:31  
Mmm, mmhm. Agreed. 

Kim  11:31  
It's not that we're saying we don't want kids to know them. It's just that we don't say rote memorize them right away. And we've seen what happens there.

Pam  11:40  
Yeah. So, when you said... And I would add, when we want kids factoring quadratics. When we want kids using binomial theorem. Like, there's lots of times where we need to... Modular arithmetic. That's even higher math. I didn't get modular arithmetic. And I remember the day when I had mathematized enough that I was reasoning multiplicatively, that all of a sudden I was like, "That's what modular arithmetic is!" All of a sudden I had a sense of, "Oh, like, you have to be reasoning multiplicatively for that to make any sense. 

Kim  12:07  
Oh, memorizing

Kim  12:09  
your facts didn't help

Kim  12:12  
you?

Pam  12:12  
No! And to be clear, I had all of them rote memorized. There  wasn't one that I... Well, okay, there were some twelves I had to kind of figure quickly. But other than that, like bam. So, when you say, "If we work with facts over time, then students interact with them, and they encounter them, and they get better at them." We're not going to do it in this episode, but we would invite listeners to go check out our episodes that we have on facts for all of the different what we mean by "work with facts". Because what we don't mean is rote memorization of single points of light in a dark cave. We mean building relationships and strategies to have your brain travel the mental path of figuring those facts using strategies so often that those mental paths become well traveled mental paths, so that then those mental paths, those strategies, grow up, and we can use those same strategies with multi-digit numbers.

Kim  13:14  
Mmhm. 

Pam  13:14  
And as we do that, we not only get the single-digit facts because we've been using them so often, but we also get those strategies that just grew up and now we're reasoning about multi-digit numbers. Those strategies build on each other. I think, Cameron, who works with us, said it so well when he said, "Strategies are synergistic. You learn one, and that helps you learn the next one. An algorithm is a point in time. It's like learn this one."

Kim  13:38  
Yeah, that's great. 

Pam  13:39  
"And then another algorithm is completely unrelated, and you do completely different things. They're not related to each other, and  learning one algorithm doesn't necessarily help you learn another algorithm." And it's so, so... That's a really good point. 

Kim  13:42  
Yeah. 

Pam  13:44  
Anyway, so the work of... I couldn't agree with you more. But we need to be clear on what that work is. So, we'll put some episodes in the show notes that you guys can go check out that would give you some examples of the kinds of things. Oh, let me say one thing. The kinds of things that would help build all those relationships and connections, so that then we can compress that knowledge into when you need 7 times 8 inside of something else. Bam, that 56 pops out. But if needed, when needed, you could also uncompress that knowledge, and you have all of those relationships and connections you've built in there that could lend you to do other things with them. What you don't just have that rote memorized, disconnected set of facts.

Kim  14:38  
Yeah. Can we talk about the kinds of things that we think we should aim for fluency with? We just mentioned multiplication facts. I think that's standard on the list. Most people would say multiplication facts. I think it's pretty common to hear people younger grades, say, "We want our kids to be fluent with addition facts." 

Pam  14:55  
Yep, yep. 

Kim  14:56  
If you're not new to the Math is Figure-Out-Able, you've heard us say a bunch that I Have, You Need is a routine that we love that helps students become fluent with partners of 10, and 100, and 1,000. We think those relationships are incredibly important.

Pam  15:12  
Mmhm.

Kim  15:14  
I also just raised this to you recently. I also think that it's really important to help students gain fluency with decomposing numbers in a few different ways.

Pam  15:26  
Mmhm. 

Kim  15:26  
Not necessarily a few specific ways every time. But when I look at a number, one of the things... Like, if I look at 132, I might think 100, and 30 and 2. So, by place value. But I also might think about how far away is it from 125. Like there's this solid like landmarky number within it. Yeah.

Pam  15:49  
You said landmarky. And I said, benchmarky. Haha.

Kim  15:52  
Yeah, probably not landmark (unclear).

Pam  15:54  
No, no, no! Both! Both! I was laughing because the e on the end. E.

Kim  15:57  
Oh, at the end of benchmarky and...

Pam and Kim  15:58  
Landmarky. 

Kim  15:59  
Yeah. So, I think if kids look at a number like 16, and they can only picture that amount in one way, I think it's tragic. I think the more that we can get kids to say, "Okay, this number feels like this other equivalent thing," for at least a few for each number, that builds like connections within them that they can draw on. When I see 76, I go, that's 3 quarters and a penny.

Pam  16:27  
And it's also even. Like, both of the numbers that you just said are even. I think that's worth. Not a vocabulary word that I'm spitting out.

Kim  16:35  
Right.

Pam  16:35  
But like having a feel for the fact that it's divisible by 2, and so it might be divisible by 4, or 8. Or like now I start to think multiplicatively. In fact, when you said 132, I started to ask myself can I think about that multiplicatively? And because of a video that we watched Jordan do all the time, I know that's 11 times 12.

Kim  16:53  
Mmhm. 

Pam  16:54  
So, like, it would be nice if we had some multiplicative relationships. What was the other one you said? 76? Is that double 28? 38? So, like...

Kim  17:03  
No, 70... Yeah, 76.

Pam  17:05  
76, 38. So, like, that would be another way that we would want kids not just thinking additively. So, I think we want multiple additive. You know, we almost want the frame of mind that there are other things to look for than just the place value sort of (unclear).

Kim  17:21  
Yeah, and we're not saying memorize, you know, six relationships or six ways to think about a number for every number you're going to come across. It's the idea that numbers are made up in different ways, and that the fluency that you've developed is that when I look at a number, I look for relationships. Like, I examine number based on like odd and even. Or examine numbers related to other benchmark numbers. 

Pam  17:47  
You

Pam  17:47  
know, I was playing around with Stick N Split the other day. So, there's that app out there, Stick N Split. And this is pinging for me right now because I was showing somebody. I think I showed just a couple people the other day. I pulled it up on my phone, and I chose a level where you're trying to make 20, but the level I chose, you make it out of twos, threes, fours and fives. And so, the first thing both of the people that I showed, they clicked on 5. Five 4s or four 5s, and they stuck them together, but now they're left with threes, and there's not enough twos. So, once you put the twos together, there's not enough, there's not 10 of them. And so, they're like, "Uh..." And I'm like, "What are you going to do?" And there's this idea of like how can you put threes together to make something that then you can split to then make 20 out of it. So, it's like what makes up 20? It's kind of what you're saying. What are some ways to think? If the goal of this Stick N Split level is 20, how do you make 20? Whoa, you don't make it with threes. That's a thing to know! And so, then what can you make with threes that you could split? Anyway, it just sort of reminds me of that robuster... Is that a word? More robust set of connections that we want for kids?

Kim  17:48  
Yeah.

Pam  17:48  
(unclear) a good look at it. Yeah.

Kim  17:48  
I think that you would say that in high school, we want students to be fluent with the look of some specific graphs. 

Pam  17:48  
Yeah, absolutely. 

Kim  18:15  
That they don't have to... We've given them a lot of experience, so that they don't have to like rethink about it every time. That's kind of the goal of fluency, right? That you've compressed this knowledge and that you can draw on it. You can use it in a moment's notice. But in a different way than most people want facts. Like, their outcome for multiplication facts is so that you can do algorithms.

Pam  19:30  
Yeah. 

Kim  19:30  
Ours

Kim  19:31  
is... 

Pam  19:31  
Or maybe find common denominators

Pam  19:33  
for fractions.

Kim  19:34  
Yeah, yeah, 

Pam  19:34  
Yeah. 

Kim  19:34  
So...

Pam  19:35  
Yeah, sorry for interrupting (unclear).

Kim  19:36  
Parent function. The look of parent functions (unclear).

Kim  19:38  
Absolutely.

Pam  19:39  
So, that's a really good example of the compressed knowledge that you just said because I want to be able to look at a linear function like the the y equals whatever, and I want to be able to go, ooh, that's a line. But then if I need to, I can dive into that, and I can talk about the rate, or I could talk about the Y intercept, or I could talk about where it's been shifted. Like, I have more in there. But like that's a cubic function. Or that's an exponential function. Like, have some sense then of what it looks like, and so therefore if I know what it looks like, I have this end behavior, and I know something about it's short run behavior. And now, again, I can have just a, "This is what it looks like." But I can also unpack that. I can dive into how I've compressed that. I can't tell you the number of times I've seen high school teachers treat parent functions the same way we were just saying don't treat multiplication facts. They're like, "Here is a picture of all the parent functions. Go rote, memorize this." Ah!

Kim  20:36  
Wow.

Pam  20:35  
I don't want that. That's not what I meant. You know, it's not like flash carding the parent functions. I really want kids to get into... I was about to use the word "investigate". That's a tricky word, right? That's one of those that's like. I want them to really dive in and feel the relation. What does it mean to have a constant rate of change? What does it mean to have a changing rate of change? What does it... Do you know the number of high school teachers I've worked with lately that  will be looking at a quadratic function? It's that... Kim, it's that... We've done it on the podcast. I think. I know we've done it in Journey before. Where we graph a parabola, and then we graph a line, and then the next one is sketch a graph of that parabola plus that line.

Kim  20:59  
Mmhm.

Pam  21:03  
And the number of people as we're talking about the end behavior of that parabola plus the line will say, "Well, it's growing exponentially." And I have to go, "It's growing... It's growing quadratically." But there's a difference between growing exponentially and quadratically. And I know we have this colloquial, you know, people just say it's growing exponentially. Well, we ought to be kind of like that's a thing. That's an actual mathematical behavior, exponential, and we can't just throw that... Anyway. So, it's not just rote memorizing parent functions. It's  having... I do want to recognize it. You know. I want it there at my fingertips. But I also want to be able to uncompress how we got there, all of the ways that we were messing with those.

Kim  21:54  
And I think...

Pam  21:55  
Which also... Yeah, go ahead. 

Kim  21:56  
Go ahead. 

Pam  21:57  
I also leads to transformations. It's not about memorizing. If you put the number out here, it gets skinnier. Ah, the number of Algebra 1 teachers that are like only deal with transformations on a quadratic. Which then sort of makes the y values get bigger faster, and so the quadratic looks like, if you just look at appearances, look like it's skinnier. That's not the behavior at all when you scale a function by a number greater than 1. The y values are getting bigger faster. And that will look dramatically different. An assigned function are dramatically different to the y-intercept on an exponential function. Like, so it's not about rote... Do I want parent functions and transformations at kids fingertips? Absolutely. But I want them there because we've traveled those mental paths often as we've figured out all the relationships and has become compressed knowledge. 

Kim  22:42  
Yeah, what I

Kim  22:43  
was going to say was related to transformations. That the reason that you want students, at least in part, to become fluent with parent function is so that something pings for them when it's been transformed, when there's something that has a different look from the parent function. They're like, "Ah, something's happening here. I'm noticing that." And if the parent functions aren't... They're not fluent with parent functions. If they're like, "I don't even know what that means, or what it looks like, or what's happening, then it's not drawing for them. The transformation doesn't like ping for them. I think another... Go ahead.

Pam  23:06  
Can I make one other?

Kim  23:17  
Yeah. 

Pam  23:17  
So, now I want to be able... I learned this so... I totally just hit the microphone. Sorry, Craig. In Functions Modeling Change, one of the things they did... Gah, I did this several years ago. Is they would give data, and they would say for this data, what is the parent function? And I had to say, as an expert high school math teacher, "I don't know."

Kim  23:39  
Mmhm. 

Pam  23:40  
"Like, what am I looking for?" And, oh my gosh, realizing that I could look for differences, and then second differences, and that would tell me something about polynomial behavior. Or I could look for ratios and equivalent ratios, and that would tell me about exponential or logarithmic behavior. Like, I could look for cyclical behavior. Like, none of that was rote memorizing parent functions and transformations. All of that's part of that compressed knowledge.

Kim  24:04  
Mmhm. 

Pam  24:04  
Like, what does it mean? Yeah. Anyway, that was... Yes. Yeah.

Pam  24:08  
Yes. 

Kim  24:09  
I think another thing that when we think about things we want kids to be fluent in. Not early on maybe, but the more fluent you are with what numbers are prime and what numbers are square numbers. You can use those ideas. You can use the fact that something is prime to aid you in solving problems, and that something is a square number to aid you in solving problems. And so, if I don't have a repertoire of like  prime and square numbers in my head, then I'm kind of starting a little bit further back. That I have to like work on figuring that out. So, as kids get older, it's one of those things I know that teachers aim to have kids become fluent. But rather than do it in such a way that you give them a list and you say, "Memorize these prime numbers and memorize these square numbers," we aim to give kids experiences, so that they become fluent and they could draw on those experiences (unclear).

Pam  25:04  
They have at their fingertips. 

Kim  25:05  
Yeah. 

Pam  25:06  
But they can also uncompress that and say something about square numbers and say something about prime number. Like, they have some sense of why they're prime and square because they've dealt with them. Yeah, that's really nice. 

Kim  25:16  
Yeah.

Pam  25:16  
That's really nice. Hey, Kim, one other thing that I want to talk about. We've talked a lot today about specific areas of math that we want kids to be fluent in and, for us, what that looks like. But there's a different take on that that I just want to briefly mention. I think one of the ways that I recognize fluency... Oh, that's not even the right way to say it. One of the connotations of fluency for me is the idea that when you when you hit a mathematical situation, or a situation at all, that you can dive in and use what you know to solve the problem. That  fluency looks to me like, "Alright, I'm going to see if I can figure out what this problem is even asking." And I'm confidently like, "That's the first step. I got to figure out what it's asking. Now, what do I know? And how can I use what I know to solve that problem?" And I just want to put that in contrast to my former self when, in a huge way, I wasn't. I was so quote unquote "fluent" with all the algorithms. But what I wasn't fluent at was solving problems that I hadn't seen before. In fact, if you would have told me that was a goal, I would say, "No, no. You got to wait. You got to wait until the teacher shows you how to do it." So, a story that I told I think couple weeks ago on the podcast. Oh, go ahead. Do you want to

Pam  26:27  
say something?

Kim  26:30  
Yeah, I was just going to say so what you're saying is the fluency that you want is students... You want students to be fluent in solving problems that they haven't seen before. That's the fluency that you want.

Pam  26:43  
Yes. Not because I'm mean and I'm trying to make guess something that I could just tell them. Not that.

Kim  26:49  
Yeah.

Pam  26:50  
But it's... So, I told the story about my son that said, "Mom can help me with the physics problem?" And I was like, "I haven't done angular velocity momentum since I was in high school." I was hoping he would forget. He said, "No, no, help." And he convinced me to sit down with him and just like figure out what the problem was even asking. And as we kind of went back and forth, "I think it's asking this. Well, then that," then we like answered the question. And I was like, "Oh, my gosh! Physics is figure out able!" One other... I don't know if anybody recognizes this. This was me as a young student. I went in seventh grade. I didn't have any friends. I wanted friends. I was like, "There's a math club. Maybe I can find friends there." I went to the math club. I sat down. Nice coach walked over, handed me a half sheet. I'll never forget. It was half sheet of paper. Had like maybe six word problems on it. I read the first word problem. I read the second. I read them all. And I was like, "Oh, I've never seen these before." Not troubled at all. Not panicked. You know, I was just, "Okay." I raised my hand. Guy came over, coach came over. I said, "I've never seen these before. Will you teach me how to do these, and then I'll join right in with everybody here." And that math coach goes, "Oh, that's not what we do here. Like, we just dive in and we solve stuff." And so let me tell you how I was not fluent in mathing in that moment. I stood up, and I walked out, and I never went back because that was so foreign to me. What do you do in math? You wait until they show you how to do it, and then now you can mimic. And I had no... And that continued, Kim, until I had... Now, maybe people are like, "Really, you were that..." Uh, yes. And so are many people. Don't... And be nice to us. Be nice to us because we just believed you when that was the impression that was given in math classes. The good news is we can have kids fluent in the math and in the mathematical behavior of diving in, figuring out what the questions even asking, and using what they know to solve the problem.

Kim  28:36  
Yeah. So, I think at Math is Figure-Out-Able, we would say that the reason that we want kids to be fluent in anything is that we want them to be able to call on that knowledge in the midst of the work that they're doing. And it's not just facts. There are also mathematical relationships, and like you said, behaviors that we want kids to be fluent in.

Pam  28:53  
Oh, quote, that somebody! Nicely said. Ya'll, thank you 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. Ya'll, let's keep spreading the word that Math is Figure-Out-Able!