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

Kim  0:10  
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  0:17  
Y'all, algorithms are super cool 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.

Kim  0:30  
In this podcast, we help you teach math-ing, building relationships with your students, and grappling with mathematical relationships.

Pam  0:37  
Thanks for joining us to make math more figure-out-able. Kim.

Kim  0:42  
Hello. 

Pam  0:42  
Hi there. What's up today?

Kim  0:44  
Well, I'm super, super happy. I found this super cute review. It's been a little bit, so my apologies for not finding this earlier. But you know Tammy. Tammy McMorrow, so kind.

Pam  0:58  
Oh, what a lovely person.

Kim  1:00  
I know. She left a comment a while back that says, "Dynamic duo. Pam and Kim are a dynamic duo. I'm so grateful for their expertise and willingness to share with the rest of us. They have certainly impacted my classroom practice. I love that I can say Math is... And my first graders respond Figure-Out-Able! I hope they believe this to be true for the rest of their lives. Thanks, Pam and Kim."

Pam  1:24  
Oh, what a super setup for those kids!

Kim  1:27  
I know, I know. Tammy is the best. It's super cute that she said, "I hope they believe this to be true for the rest of their lives," right? That's like... Isn't that what you want for the students that you have? You send them forward, and they still take all the stuff that you've poured into them. Man, Tammy is currently using first grade Problem String book, and she will post in the, you know, the free Teacher Facebook group that we have. She'll post pictures of like her board after she does a string, and she's just like. She is so great because she'll comment like she's wowed by her students. And she does a really nice board. Like, her sketches are like primo. And I'm like. Every time I look at her picture, I'm like, "Man, I really got to get better at like making straight lines." She's a classic first grade. Anyway. Thank you, Tammy. So good.

Pam  2:23  
I really appreciate the fact that I was on her podcast not too long ago.

Kim  2:26  
I was going to say yeah, she's got a podcast.

Pam  2:28  
Yeah, she was a great interviewer, moderator of the podcast. We had a delightful chat. What a wonderful... What's the name of her podcast?

Kim  2:37  
Little Minds, Big Thinkers.

Pam  2:39  
Yeah, yeah, yeah. Yeah. Check that out. Tammy, thanks. Thanks. And a fellow Idahoan. She lives in Idaho, and I'm from Idaho. So, yeah, totally cool. I think I'm going to see her when I do the Idaho State conference this summer. I've been invited to do keynote, and a couple of breakout sessions, and book signing. And it's going to be great. I'll get to hang out with Tammy a little bit. What could be better?

Kim  3:01  
Not much.

Pam  3:03  
Being in Idaho. Super cool. Alright, Kim.

Kim  3:05  
Yeah.

Pam  3:05  
A couple of podcast episodes ago, we talked a little bit about a cool thing that happened while I went to South Korea. Had the opportunity to go to the Chadwick International. It's an independent school near Seoul, South Korea. I had a wonderful time. That episode, we talked all about fractions. Oh, my goodness. If you have not listened to that episode, you should go check it out because, whoa, they not only say, but they write the denominator first. It's so interesting. Super cool link from social knowledge to... Knowledge! That was the word I was looking for a minute ago. Social knowledge to logical mathematical knowledge. Yeah, and just really interesting. Kim, can I tell you about... In fact, funny. When I was on my way home. That's a 16 hour plane ride. Oh, 15 home. 15 hours on the way home. Of course, then I have to, like land, and then come. You know, then I have a 4 hour plane ride from there. But anyway, you don't care. On the plane ride home, I sent you a message, and I was like, "Kim!" and I bulleted these things. It was like, "We have got to talk about..." And so, I am so excited to just like share some things with you today about things that happened that really got me thinking about just math and the math content for teaching. And yeah, I'm just kind of on fire about a few things. So, are you ready?

Kim  4:20  
Yep.

Pam  4:20  
Okay, so I did several things while I was there. I did like a one hour PD session for anybody who had never heard me before, new teachers, and some things. I did a one hour PD session. So, I was there last year, so I did a one hour PD session for everybody, the teachers who had heard me last year, and also then the new people that had heard the new version. So, I did a little bit of that. We also did some classroom observations. And then I did nine lab lessons where we met before and we talked about what was going to happen, made sure everybody was ready, and then we did the lab lessons. Pre-K through grade 8. Bam. Had such a good time. And then we had sort of a debrief afterwards where teachers got a chance to ask questions and, you know like, why did I do what I did? And what would you do next? And, yeah. It was super. The only thing better. We really like it when you can actually co-plan and co-teach, but that doesn't... We can't really facilitate that when they're in South Korea, because it's a 15 hour time change, and so it's like the opposite end of the day. It's kind of difficult to get on with them. Anyway, one of the things that happened that I just, I want to talk to you about. I think you're going to find this super interesting. So, I'm doing these lab lessons. So, picture me in front of a grade 2 class. Picture me in front of grade 5 class, grade 6, grade 8. Like, I even did pre-K. And by the way, I had terrible time management. I don't know if I told you that. You're not surprised. Kim is so not surprised. That was a Kim. Like, Kim are you surprised? Kim was like, "Pam, of course you did." But here's the deal. Here's the deal. I knew going into the pre-K... No, sorry. The kinder through grade 5, I knew that I was going to have 45 minutes to teach and had actually planned it out, knowing I had 45 minutes to teach. But it took me three lab lessons of not getting everything done by like a lot to be self introspective and say, "What is happening? Why am I not getting done what I planned?" And, Kim, I had subconsciously believed I had 60 minutes. Like, I knew I had 45 minutes. I had planned for 45 minutes. But my body, like my psyche, was...

Kim  6:30  
Yeah.

Pam  6:31  
...in 60 minutes, so I was always 15 minutes short. Like,

Kim  6:35  
Oh, no.

Pam  6:35  
all the sudden you know, it would be time to just...

Kim  6:37  
Did you just like stop? You're like, "Oh, oops."

Pam  6:39  
Well, because like Therese, who's wonderful, would like, "Pam, you need to be done." And I'll be like, "What? No, I got 15 minutes more." 

Kim  6:46  
Oh, no. 

Pam  6:46  
I'm in the middle of a sentence. It was so lame. I just... Yeah. So, after, you know, the three times of kind of looking like a ding dong because I was not doing it well. I was like, "Okay, let's go actually plan for 45 minutes, not 60." Yeah, isn't that wild?

Kim  7:01  
That's amazing, yeah. I mean, yeah.

Pam  7:04  
I did the same kind of thing when I went from a 50 minute class period in the one school I taught at to a 90 minute class period in the other school I taught at. That one wasn't hard. That one I knew I had to plan more for. But then going from a 90 minute back to 50 minute? That was like... I just shoved it all in. We're getting it done because we're going to get 90 minutes of stuff done because I just had this... I know. You would have laughed through the whole thing. What were you going to say?

Kim  7:31  
It reminds me that you and I did a presentation like last summer together, and we were like, "Oh, we have 75 minutes." And then at the beginning they were like, "Oh, no. We need 15 minutes to do some introductions," and then some technical stuff happened. And we were like off kilter the whole time.

Pam  7:50  
Because we had planned to the minute, right, for 75 minutes. And now we have, what, 48? it was terrible. Good heavens. And the band came in at the wrong time.

Kim  7:59  
Oh, gosh.

Pam  8:00  
It was great. Okay, cool.

Kim  8:01  
Cute.

Pam  8:02  
Alright, so one of the things that happened that I just kind of wanted to talk to you about. So, I'm doing this lab lesson. I don't even remember what grades. So, it happened three separate times where there was a moment in the lesson where I'm like, "Do you think? Like, why would that happen?" Or, "How are you making sense of that?" Or it's a moment where I'm pausing. It might be a moment where I'm... Well, for sure, it's a moment where I'm pausing, and I have that look, that neutral or interested response on my face. I'm looking back at the kids. I'm like, "Wait. That? How does... How do you jive that with this?" Or. "Hmm, is everybody making sense of that?" Or, "Ooh, did everybody hear what Damian just said?" You know like, pick a kid. Or, wow, you know, half the kids are Korean nationals, so Chung Hu. And I'm like, I could not.... I probably just... That's probably not even a name. But I could not. Like, for the most part, they wrote their names on their name tags, and I would go around and try to pronounce their names. And I just sometimes if the spelling looked so not like what I thought that sound would, I couldn't. But I tried, valiantly. If I messed up their name, I would say, "Say it again," and they would say it, and I tried again. And they would laugh. And I was like, "Nope, say it again. I would try it again." Anyway, it's that moment where I'm like, "Wait, did everybody hear? How are you making sense of that?" That pause moment. Three separate times, I would hear a "Ooh". Or a "Oh!" Like a gasp. Like, "What?!" Or, "Ah." And I would be like, "Ooh, who was that? And I look. I look, I'm like, "Who said that?" Because I want to pull out that "aha" moment. I want to get that person who just had that kid who just had the "Oh!" moment. You know like, it's that they're realizing something. Like it's I want to be able to go, "Oh, what are you realizing now in that moment?" So, then I said, "Oh, who?" And I'm looking across the room. And the kids look at me, and they're like, "It was that adult back there." Kim, I was like, "Wait, what?" When I'm  teaching those kids, Kim, I don't even recognize the adults in the room. Like they are just dead to me. Like it's... And so, I was like, "Oh. Okay." I'm like, "Well, why do you think?" So, I smile at the kids. Why do you think that teacher just had this "aha" moment? And then the kids smile. They're like, "Well, because we just realized..." And it didn't hurt the moment at all.

Kim  10:26  
Yeah.

Pam  10:26  
But it was just so, I don't know, precious almost, that there was these adults that were just like, "Ah!" Like, "Oh!" Or like, "Ooh!" So cool.

Kim  10:38  
I love that so much. You know, sometimes I think teachers get nervous. In fact, I I recently was talking to a teacher who said something about how nervous she was because she wasn't sure that she had learned all that she needed to know in order to start talking with her students about what they know. And, you know, I get that. I get the nervousness. But, man, how real is it that you can be learning with your students? And I think I just want to encourage. Like this teacher, how great was it that she was learning something? Sorry.

Pam  11:18  
She/he. Yeah, it was both. It was both.

Kim  11:20  
(unclear)

Pam  11:21  
Yeah, it was good. I mean, because it was a different person all three times, right? It was a different adult.

Kim  11:25  
Oh, it was?

Pam  11:26  
Oh, totally. Totally different. I mean, it was a different grade level, different set of teachers.

Kim  11:31  
Okay, okay.

Pam  11:32  
Yeah, it was really only like the main leader at the school who heard all three of them. You know, because it was different groups of teachers each time. Yeah, yeah, yeah. Totally different.

Kim  11:41  
I love that. I love the idea that they're learning alongside their students. And so, yeah. And listen, you might not even hear a sound, right? Like, those people kind of made an outward sound. But in those moments, those kind of like those pivotal "aha" moments, there might be somebody who's not making a sound, but those are great moments for turn and talks. Like, when you plan for that moment, those might be really nice opportunities for turn and talk, so that they can talk to each other and get out the thinking that they're having, the learning that just occurred because some people are having them internally. They're just not verbalizing it.

Pam  12:20  
Yeah, those moments, capitalize on. Those are... We seek for those. And, you know, we hope they happen. And we set things up. And we try to have the opportunity for students to realize new things. And, I mean, that's learning occurring. And I just thought it was so amazing that those adults were willing to be engaged. And in it. And, you know like, like really thinking. You know what I mean? Like, they weren't just there because they had to be. That's a sign of an educator who's improving their craft, of an educator who's like, "I'm in this to learn. I'm in this to grow." And right? Because if they were just like, "I have to be here, and I'm watching some lady from the United States teach these kids." You know, wonderful people. They had just had this attitude of, "What can I get out of this?" And, "Oh!" And, "I just had this moment." And, yeah, it was brilliant. It was.

Kim  13:16  
Yeah, it's hard to have an "aha" moment if you're not being open to learning.

Pam  13:21  
Mmhm, mmhm.

Kim  13:21  
And how cool that they get to learn even from their students.

Pam  13:25  
Yeah. So, teachers out there, we just really encourage you. You might not feel like you own it all. Problem Strings are such a good way for you to dive in and learn alongside your students. And what a gift you give them when you're like, "Whoa. That, nice." And they're like, "Really?" You're like, "Yeah. Like, that was well said. I'm still thinking about what you said." What a gift for them to realize they can contribute that much. I think if you're vulnerable enough, it doesn't come across as you're less than and that they're going to ridicule you. I really think it comes across as "Huh. I as a student have something to contribute here." Yeah, it was cool. Alright. Well, thanks for let me tell you about that. I got another one.

Kim  14:07  
Okay.

Pam  14:08  
So, I had met this teacher the year before, and I'm going to be very general, so that nobody at Chadwick can pick out who this was because I had met lots of teachers the year before. And this particular time that I went, this teacher, who shall be genderless because I'm not going to point out who it was, pulled me aside. It's a younger grades teacher. But, you know, I did pre-K through grade 8, so that could be lots of grades. Pulled me aside and said, "Hey, don't call on me." And I was like, "Okay. Like, you know, if you have a really good idea, you could share. Or, you know, if you're thinking about something, you know, feel free to put your thumb up. You can put your thumb up with a point. You know, like choose someone else. You know, when you're ready, whatever." But I could tell while this person was asking me not to call on them, there was definitely some anxiety. You know like, there was definitely like, "Like, no, really. Really don't call on me." Like, it was definitely, you know, almost like a pleading of, "Don't put me in that position where I'm going to panic in front of my peers." And I was like, "No problem. You know like, we're good." Here's the fascinating part. Throughout that day, and the next day, and the next day, this person was able to come to several. Not all, of course. You know, had their own class to teach. But was able to come to several of the lab lessons and things and several of the debriefs and stuff. And throughout those three days, every time that person was in the room, I was able to catch that person thinking deeply and having relevant, mathy, helpful things to say. Every bloomin' time! 

Kim  15:42  
Yeah.

Pam  15:43  
I'm still thinking about all the ramifications of that. I feel like you have something to say.

Kim  15:49  
Well, I'm thinking about how they said to you ahead of time, "Don't call on me," and maybe because you agreed that you wouldn't call them out.

Pam  16:00  
Mmhm.

Kim  16:01  
Maybe they were worried. I mean, we all have different PD experiences, professional learning experiences. But maybe they were worried that they'd be put in a position where they were supposed to know something, and then maybe be embarrassed. Maybe like be put on the spot a little bit. But with that pressure off, maybe. Maybe they were like able to contribute a lot in a content area that they don't teach because of the way that you were facilitating. It wasn't just about how did you get the answer? And like was it the way that you, you know, go back and remember what you did then. Maybe they were able to approach the work with thinking and using things they knew. And what's cool is that because they didn't feel the pressure, and because of the way that you facilitated and what you were asking...

Pam  16:48  
The Kinds of math-ing we were doing, mmhm.

Kim  16:50  
Yeah, yeah. I mean, like it's cool that I hope, that at the end, they were able to like learn a lot. But also realize that maybe, you know, they can take some pressure off themselves to not worry about doing it a particular way. Yeah.

Pam  17:08  
Absolutely. Yeah.

Kim  17:10  
And you said it was a younger grade teacher, right?

Pam  17:12  
Yeah, yeah. Yeah, younger grade teacher. You know, I think you're right. It was clearly like, "Look, I don't remember that older grade stuff. Don't call me in front of people. Don't." Like, I don't know if math, little T trauma is too strong. But I don't think so. I think there was definitely some panic, definitely some, you know like. Until. And I was like, "Don't worry." Okay, alright. We got a deal." And then I could go up, and, you know, sort of listen in on partner conversations. Or several times, that person then chose to just contribute without me. I didn't call because I promised I wouldn't. But that person felt. Yeah, like, "Oh, well, here. Here, it's okay. Here, it's okay that..." In fact, in one of the debrief sessions, this person offered something that the middle school teachers went, "Huh." Kim, I was just... You know, at that moment, I kind of wanted to go, "Ha!" Of course, I didn't, you know. But I really wanted to like... Like, and so I did kind of... The conversation went on, and I kind of looked back. And I kind of like not winked, but kind of gave that look. And that person kind of sat up a little taller. Kind of looked like, "I did that." Like, that was, you know, so cool. 

Kim  18:19  
Yeah. I have poked you in the past a little bit about the...

Pam  18:24  
Which is good. I like it when you poke me.

Kim  18:26  
Sometimes.

Pam  18:27  
Kind of, kind of.

Kim  18:28  
Because here's the deal. A lot of times we give younger grade teachers experience with math outside the content they teach because they're adults. So, we sometimes put them in a position to do something that maybe they... That like middle school work. Or maybe even high school work. Or, you know like, if they are a really young grade teacher with some multiplication/division, and they haven't experienced in a while. And so, it could almost sometimes sound like you're saying, you know, "Younger grade teachers. And look at them, they can even do upper math," But I think the same is true the opposite.

Pam  19:04  
It could come across negative, yeah. And I don't mean it that way,

Kim  19:07  
But I think the opposite would be true. If we had a middle school or high school teacher who could deeply think about the really complicated stuff that happens in first grade, we'd be equally impressed. Not because the math is necessarily, quote, unquote "harder". It's just work that they don't do on a regular basis. Like, I would be shocked if a high school teacher really could analyze counting strategies and what would come next on a landscape of learning for a kindergartner because that's not the work they do on a regular basis. It's just that we often ask younger grade teachers to do more older math, older grades math, then the vice versa. Like, I think we should do some the other way. I think we should give some older grade teachers the experience that our K-2 teachers handle. There's a lot.

Pam  19:54  
Yeah, and maybe I'll also add that just because you did the content when you were a student, that's math content. That's not math content for teaching.

Kim  20:03  
Sure. 

Pam  20:04  
So, just like we don't expect younger grade teachers to have the math content for teaching for older subjects. We also don't expect older grade teachers to have the math content for teaching for like. You got to learn that stuff. Like, you got to experience it and have... Yeah, it's a body of knowledge that we are trying to help share with everybody. There is math content knowledge for teaching, and it is important. And, yeah, it is important. Let's just say that.

Kim  20:31  
Yeah. I think the bigger point is that when you open up what you're asking about, and... 

Pam  20:39  
When you're real math-ing. When we're doing real math. Because real math is open. I know there's got to be a better way to say that. When we're actually math-ing. When we're not rote memorizing and mimicking. We're actually math-ing. Is that better? Did I say it better?

Kim  20:53  
When we're math-ing. Yeah, when we're using what we know.

Pam  20:56  
It's more open.

Kim  20:57  
It's more open for everybody. Everybody can participate. Yeah.

Pam  21:01  
And an example of that that I'll just tell really quickly is the lesson I was the most worried about was the grade 8 lesson because... See if I can say this shortly. These half of the kids, Korean nationals, go to these after school academies a lot, and they've done it their whole lives, and so they have a lot of experience. And so, there's this gap of experience between some of the kids that have just a lot of experience and some kids who are just kind of more typical kids that just have grade level appropriate experience. And so, one of the things they asked me to do, specifically. The middle school teacher said, "Help us figure out how to differentiate for these kids." You know, can we do it in one lesson? Do we have to create four separate lessons for these kids? And, you know, do we have to separate them out and segment them? And I was like, "Uh, no." Like, yeah, so I was highly aware. I don't know. I felt a lot of pressure to get this right, and so I planned a lesson. And I think we've actually done this on the podcast. If we have, we'll put in the show notes which episode it was. But it's a Problem String, where it had everything to do with geometry. And I gave kids this sort of turned square. So, you have a dot paper, and the square, the length of the square, is kind of a diagonal, and so you can't count that the unit between dots is not the side length. It's this weird diagonal length. And it really often throws kids off. They're like, "Well, how do I do that?" I'm like, "Well, can you find the area of the square?" And a lot of the kids were counting triangles. And they could tell that the triangle was half of a square, and so the area's half. And they could add up the area of the triangles. Or there was a couple of other ways. They could find the area of the encompassing square, the big one that was around, and then they could cut out little triangles. And most of the kids were sort of playing with that to find the area of the square because if they know the area of the square, then they could find the square root of it to find the side length. Well, bless his heart. One student in the front who had been very thoughtfully participating throughout the lesson. I walked up and said, "How are you thinking about that?" And he said, "Well, I know that this is a 45/45/90 triangle." This is above where these kids are right now. They haven't done that yet this year. "It's a 45/45/90 triangle, and so I know that this hypotenuse is a square root of 2, and therefore it is the side length of the square. So, square root of 2 times the square root of 2 is 2. So, I know the area is 2." So, he kind of went the other direction, right? Like, I'm... Well, why? Because... So, later... Well, let me finish. So, one of the students kept contributing, and then I asked this kid how he was doing it. I didn't share that strategy because none of the other students in the room knew anything about 45/45/90 triangles yet. They were just starting the Pythagorean Theorem. A couple kids were dabbling with that Pythagorean Theorem because they were just starting it. So, at the end of the lesson, I had a couple of other kids share. I had this one gal share who was right in the middle, who was just sharing the whole lesson. I said in my head, "Man, I'm going to have to be careful not to call on her the whole time because I'm pretty sure she's just so..." What's the word? She just gave me this feeling like, "Oh, I know that. Oh, you could call on me. Ooh, I want to share." And I was like, "Okay, obviously she shares a lot. I want to make sure that I elevate other kids' voices in the room." Kim, when I got done with the lesson, those teachers came up to me and they said, "You did it." And I was like, "What do you mean?" And they said, "That kid?" So, the kid that found the square to 2. "We can't keep him thinking. We can't. He was listening to those other kids find the area using the triangles. He was so interested in how they did that." They're like, "You kept him thinking. He's the kid that we cannot. He just knows so much. He's so quick, and he does so much in the academies. We can't believe you kept him thinking." Wow. Then they said, "The gal? They're like, "She never contributes." I was like, "Wait, the one that I was like, oh no. I better not call her too much?" They're like, "She never has her hand up. She never says anything. We never hear from her." I was like. "Oh, wow." When you open it up to real math... Oh, gosh. To real thinking, to math-ing.  To math-ing, the way mathy people math. Like, really like let's math. Let's use what we know to reason. Was just amazing how we can naturally differentiate for kids.

Kim  25:17  
Yeah.

Pam  25:18  
It also signals a good problem. 

Kim  25:19  
Yeah,

Pam  25:19  
It's a good problem when you can come at it from different angles, and then we can share, and we all grow, and we all get better. 

Pam and Kim  25:26  
Yeah. 

Pam  25:27  
Alright. Thanks for letting me share a little bit about some amazing things that happened in South Korea. I hope that was helpful for anybody to kind of... for some takeaways. We'll keep trying to help on the podcast to be able to think more and more of ways that you can naturally differentiate for your kids to get that math-ing happen.

Kim  25:42  
Yeah.

Pam  25:43  
Alright. Y'all, thanks for tuning in and teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. Keep spreading the word that Math is Figure-Out-Able!