Pam  0:00  
Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able! I'm Pam. 

Kim  0:07  
And I'm Kim. 

Pam  0:08  
And you found a place where math is not about memorizing and mimicking, waiting to be told or shown or to do. But it's about making sense of problems, noticing patterns, and reasoning using mathematical relationships. We can mentor students to think and reason like mathematicians. Not only are algorithms not particularly helpful in teaching mathematics, but, ya'll, rotely repeating steps actually keeps students from being the mathematicians they can be.

Kim  0:37  
So, there are some times where we learned some hard lessons as teachers, right? And so, today... We've learned some lessons. So, today, we wanted to share about something that we learned a while back that we think might be especially helpful to you, listeners.

Pam  0:55  
Yeah, so we want to make sure that we are clear that we're learning all the time, and when you know better, you do better. So we thought we'd share something with you today. We had... Kim and I work together. She was a teacher and my kids school. My kids were... You know, I was working with teachers, doing some professional learning. My kids were at the school. And at one point, I realized that one of the teachers had videoed her students in second grade. And then, I went back, and I grabbed some students to video solving some problems in fourth grade. And at some point, I realized I had some of the same students in that teacher's second grade video who had grown up, and then I had videoed in fourth grade. And I said, "Oh, cool! I'm going to go grab some of those kids, and I'm going to video them in fifth grade." Because they were doing such good math, and I was so excited about what was happening. I wanted to kind of show that longitudinal growth, you know how excited I was. And it was fabulous when you could see what these kids had done in second, and then when you can see what they were doing in fourth. And so, I was so excited to get them in fifth grade. And at that time, I went. I grabbed some of the students. I went into a place. I had a camera. And I sat down with Jordan. So, Jordan's one of these students that we'd videoed in second. We videoed in fourth. And so, I said, "Hey, can I video you? I have permission from mom." "Yeah, yeah, yeah." So, he sits down, and I gave him a fifth grade-ish division problem. And I was super curious to see. In fourth grade, I had him doing multiplication. In second grade, I had him doing addition and subtraction. So, in fifth grade, I'm like, "Division. This is great." So, I said, "Okay, Jordan, solve this problem." And as I watched him solve the problem, he... Well, first of all, he wasn't doing a lot of solving. He was doing a lot of sweating. (unclear) And he sort of drew this up arrow and this down arrow on the paper. And, you know, I had this video from second and fourth grade where he was calm and confident and really, you know he just would start explaining his thinking. I should say, he would always pause because he's a real thoughtful kid. He would pause and think. But very confidently, you know? In second and fourth grade. In fifth grade, it was like instant, almost panic, like nervous. And I kind of looked at him, and I knew that he'd had you for third and fourth grade. So, that was a little weird for me that I kind of saw him. Like, it looked like he was kind of reaching in rote memory, and that wasn't what I was used to. 

Kim  3:27  
Yeah. Oh, I remember this

so well. And I think, Pam, that's so real, right? We get asked questions all the time about like if I'm doing kind of this thing, if I'm building numeracy in my classroom, like what happens when my kids go on, right? So, teachers will say like, "Will my kids be prepared? Did I do a good enough job?" It's a super real concern. And I also think there's something to this about how we often hear that people will say that their job in their year is to get kids ready for the next year. So, as a fourth grade teacher we'll hear teachers say like, "My job is to prepare you for fifth grade." Or like, "My job is to get you ready for the future." And that wasn't ever really a concern for me. Like, I feel like if I'm a fourth grade teacher, my job is to get you ready for fourth grade, right? Like, we're in this year to get you prepared (unclear).

Pam  4:19  
Do the fourth grade stuff. 

Kim  4:20  
Absolutely.

Pam  4:21  
Yeah.

Kim  4:21  
I wasn't like, "My job this year is to get you ready for next year." Like, that just seems crazy to me. But I wasn't worried about that. I cared about this job, and it wasn't about prepping, but I did care about the kids.

Pam  4:37  
Absolutely. So, it was interesting to me because I knew what you had done. We'd been working together. I knew how you taught your class. And I also was clear that the fifth grade teacher he had would come to the mandatory workshops I was doing with teachers. But what was also not having it. So, at least she was clear on that. She wasn't sort of under the, clandestinely, like "Sure, I'll do your thing," and then not. She was like, "No, I don't believe in what you're saying. I believe in teaching kids algorithms and drilling them on the steps. That's going to hold them in better stead over time." And so, I kind of knew that while I was interviewing Jordan, and so when I looked at him, I said, "Hey, Jordan?" Like, "What are you doing?" And he goes, "Okay, so my teacher said that if it's a big number..." And that's why he drawn the up arrow. "And a small number..." And he drawn the down arrow. And he's like, "Is that when you multiply?" And I was like, "Oh, it's a rote memorize thing. Okay, there's like some trick that she's taught him. Based on the size of the numbers, that's the operation you do." And I said, "Hey, Jordan, can you just think about the problem?" I will never forget this moment. He just took a deep breath, and he was like, "Oh, gosh. Is it okay to just think? My teacher told me I had to memorize this stuff." And I was like, "Umm..." Like, "No." Like, "Absolutely." So, I smile, and I said, "Jordan, just think." And he like, "Yes!" And then, he then did a very fourth grade, excellent strategy to solve that problem. And in that moment, what I realized was, she could have taken him from that great fourth grade place, and her job was to then, you know like, help him do that problem in a fifth grade way. Fifth grade, more sophistication. And so, in that moment, I realized that. Kim, we talked about it, right? Like, what did what did you and I realized, when I came and I talked to you about Jordan. What did we both? We kind of were like, "Oh!"

Kim  6:36  
Yeah. Well, I think we both knew where he was headed. We realized that we needed to spend the time. I needed to spend the time sending the message to my students that no matter what your teacher next year tells you, math is still figure-out-able. Right? Like, we we knew that he wasn't going to get developed further. But he had enough in him that he could still do some thinking. And so, I think the message that we received at that moment was, I could have said, "Done my job in fourth grade. Let me give you a little heads up about fifth grade." Like, "Let me tell you, what you might encounter." And that heads up could have really made a difference for them, right? We could have said like, "You might see more algorithms. You might see less conversation. You experienced math the way that we did it this year, but not all classrooms might look like that. But you can feel good about the experiences that we had this year and think about math this way, even if you're in a place where they don't.

Pam  7:43  
Yeah, that's so important. And it's interesting how we just kind of hadn't. You know, you had prepared the kids so well in their mathematizing, and the way they were thinking and reasoning. But just that one little message of, "No matter what you see next year. No matter what your teacher says. If your teacher says, 'Hey, you need to memorize this.' You could say, 'I bet it's figure-out-able.' Like, you could dive in, and do your best to actually figure it out." Yeah?

Kim  8:09  
Yeah, yeah. 

Pam  8:11  
It's so interesting.

Kim  8:12  
And

sometimes the teacher that they're moving into just doesn't know, right? And it's a really cool opportunity for our students who are moving forward to be confident and to share their thinking and say, "You know, I actually thought about this way." Sometimes, the next year teacher's just not aware of what you know and what you're doing. Sometimes it's that's not true. Sometimes they're, you know, they're steadfast in "I don't believe what you believe." Sometimes those kids can nudge teachers along as well. They just have to know (unclear)...

Pam  8:42  
Absolutely

Kim  8:43  
...that they can do.

Pam  8:45  
Yeah. And so, thank you for saying that because I don't want to give the impression that I would want to send the message at the end of the year, "Hey, your teacher next year is going to suck, and you've got to..." I don't usually use that word. "They're going to be this horrible person that's going to force you not to think." I don't want to do that at all. I'm not suggesting that in anyway. I want, like you said, in a very positive way, "Hey, you can think, and you can use relationships to reason, and you can share that thinking. And even if next year you might be in a situation where they say, 'Hey, memorize this,' you could still figure it out. You know, math is always figure-out-able. And you can do your best to share that message next year with confidence because, ya'll, you're figuring out this year." Yeah, in a very respectful way, we acknowledge that when you said "some and some", I'm like, maybe most teachers haven't yet had the experience to either know that Math is Figure-Out-Able or to know how to teach math that's figure-out-able. That's why we're trying to spread that word, right? I certainly don't know it until I dove into all the research and did all the experimenting and met people like you that helped me figure out I could actually reason about math. And so, yeah. It's not about being ornery towards next year's teacher at all. It's about helping equip students to know that they are thinking mathematically, and they can continue to do so. 

Kim  10:16  
Yeah.

Pam  10:17  
So, two important takeaways that we think that you could listen to this story and go from our listeners today.

Kim  10:27  
The first one, I think, is it's okay to take the mindset that I took, and that some of my colleagues took, that you don't need to worry so much about next year. Your job is to do this year well. Get your kids super involved in rich mathematics, and give them the experiences. If you are overly worried about next year and getting them prepared all the time, take a deep breath and focus on knocking this year out of the park because that's your mandate.

Pam  11:01  
Nice. And number two, take your experience from this year into next year. Tell your students, "Take what you've learned here. Take the relationships, and connections, and conversations, and the way that you are mathing. Take that experience into next year. You can still ask questions. You can still think. You can still use strategies. Math is still figure-out-able." Alright, So, Kim, what do you want next year's teacher to know? If you're thinking like, "If I could sit down with next year's teacher..." What would you want them to know?

Kim  11:42  
Oh, my. That's a big question. So, if I could talk to next year's teacher, I would say, "This year in this class, we worked on developing relationships, so that the strategies that you'll see my students doing become natural outcomes," right? I want to give them a picture of what these kids had this year, so that they have an understanding of what kids are coming with. We want them to like hold stuff longer, right? This idea that you dump stuff in, and then they hang onto to it for a little while, and then it comes out of their brains is not acceptable. So, we want them to hold stuff longer. We want them to have more stamina, so they're more productive. Like, those are the kinds of mathematical behaviors that we worked on this year. And I think it's fair for the next year teacher to know. But also it's an opportunity to say like, "Maybe adopt a little bit of that because these kids were super successful at thinking and reasoning this year."

Pam  12:40  
Kim, say a little bit more about "hold stuff longer". What do you mean by that?

Kim  12:44  
Well, I mean, I think that a lot of teachers will experience that you can do some tricks, and you can do some quick fixes, and kids can memorize some things for a bit. But then, when time goes on that stuff typically falls out of their heads, right? And so, that's part of the dilemma where year, after year, after year, we're saying the same things about what kids have difficulty with. So, we want to interrupt that. We want to give them richness, and deepness, and understanding, so that they can move forward mathematically and not just repeat these same things over and over again.

Pam  13:28  
Nice. Nice. Yeah, that makes a lot of sense. 

Kim  13:30  
Yeah. 

Pam  13:30  
So, does that look somewhat? When you're talking to that next year's teacher, does that? If I'm trying to imagine. Clarify for me. That you might say, as a fourth grade teacher, you might say, "Hey, this is what we did with division this year. We really approached it very multiplicatively. When a student is looking at a division problem, they might say, 'Oh, I'm thinking about how many of the divisors in the dividend.' And so, they might multiply up in some ways. And you might see many students make great choices about the numbers they start with. Like, they going to take out big chunks all at once, or they might even go a little Over, and then have to compensate Under. And that's fantastic. But some of the students are still working on smaller chunks, and they're working towards that idea of making better choices. And so, know that when you give students a division problem, here's what you're not going to see, next year's teacher. You're not going to see them draw the hous top and start just robotically doing a bunch of steps. So, in that moment, when you don't see that, what you can do is say, 'What are you thinking about? Tell me how you're approaching this problem?' And help those students tell you what they're thinking about. In other words, next year's teacher...if I'm wrong, let me know...but I'm anticipating you're going to expect that when a student see a division problem, that they're going to instantly start doing the long division algorithm. Or maybe what you've learned in school is that you might be inclined to then go, 'Oh, you don't know to divide. Divide.' And when the kid doesn't immediately draw the house top, you're going to say, 'Oh, well here. Let me show you.' And you're going to draw a house top. But when the kid goes, 'What?' And then, you're like, 'Oh my gosh. Didn't the teacher last year teach you anything?' Then, may I just respectfully, next year's teacher, suggest to you, oh they know a lot. But let me give you some ways that they are thinking about division. They might be thinking like this. So, ask them, and then it would be wonderful if you could help them make better choices, bigger choices about the way that they're dividing." Does that make sense, Kim? Is that? 

Kim  15:30  
Yeah, 

absolutely. It's all about communication, right? It's about digging into what kids know. And if the this year's teacher can help the next year's teacher have a better understanding of what kids do know, then everybody wins. And I'll add to that. You know, we're kind of at the end of a school year for some of us. Like, I'm at the end of the school year. And I was thinking, that if I were in the classroom today, I think that one of the things that I would try to arrange with next year's teachers is to come in my room, and do some math with my kids like we would, and have them be observers, so that in the safe space that my students are in right now where they're communicating, and they're working, and they're partnering, and they're sharing their thinking and strategies. The next year's teachers can hear it, and they can see it, and it's not... Like, I just think that the next year's teacher would have a different mindset of asset based. Like, "Oh, I see these kids doing these things, and maybe I'm not super familiar with it, and maybe it's not like traditional looking, but I hear them talking about what they know." Yeah, I just think that will be a great way to end the year. Like, "Hey, these are the kids that are coming to you. This is what they do."

Pam  16:46  
That is such an amazing, amazing idea. Because I can't tell you the number of well meaning, wonderful teachers I've talked to who say, "These kids can't do anything." And when I dig into that, I said, "You know, give me an example." They're like, "It's a multiplication problem, and they just start writing down some things off to the side, and I don't even know what they're doing because this is what I'm expecting to see."

Kim  17:09  
Right.

Pam  17:09  
But what they're expecting to see, and no fault of their own, is the traditional algorithm for a problem like that. And when they don't see it, then they immediately assume students don't know anything, I have to reteach that algorithm. And so if they had a chance to see those kids, doing whatever the thing is, in a really sophisticated ways for fourth grade, then they could be like, "Oh, okay. So, I don't..." That might cause a whole other conundrum. You know like, "Well, then what do I do in fifth grade when we have bigger, badder numbers?" And then, ya'll  send them to our Developing Mathematical Reasoning workshop. Get them hooked up with the podcast. You know, lots of ways that then you could say, "Oh, well, if you want to know how you can take these kids and grow them, I'm happy to, you know, give you some resources." Yeah, that's super cool.

Kim  17:57  
I think it boils down to communication, right? You're communicating with your students, "What we do here, you can carry on to the next year." And then, communicating with your partner teachers. "This is what my students have have been doing for a year. I think it's worthwhile for you to know."

Pam  18:20  
Yeah, absolutely. So, Kim? 

Kim  18:23  
Yeah. 

Pam  18:23  
To finish a little part of this Jordan story. So, Jordan was our student that we talked about at the beginning of the podcast too.

Kim  18:29  
Love him.

Pam  18:30  
Was thinking and reasoning in second, third, fourth grade. And then, when I interviewed him in fifth grade was like memorizing, up arrow, and down arrow. "My teacher told me I had to memorize it." And I said, "No, no. Just think about it." He's like, "Can I just think?" And we sent him from then saying, "Math is still figure-out-able. You can still figure out math. You do not have to rote memorize." In sixth grade, I went back, and I wanted to grab some of those kids that we had in second, and fourth, and then fifth grade, and I wanted to see how are they doing in sixth grade. Ya'll, I grabbed Jordan again, and I sat down with Jordan. And before we actually sat down to do the video, I knew his sixth grade teacher a little bit, and I said, "Hey, Mr. Jimenez, how's it going? Could I grab Jordan for just about five minutes out in the hall? We're just going to do a quick video." He knew I was coming, but he didn't know quite the time and everything. So, I was like. And Jordan. And it was near the beginning of the school year. Not the exact beginning, but you know kind of near the beginning. And I wasn't even sure if he, you know, knew a lot about Jordan yet or anything. And he said, "Oh, Jordan? Yeah. Yeah, he's a great kid. Man, that kid mathematizes. This is fantastic." I pulled Jordan out. We have a super video of Jordan doing a fantastic division problem with a slick, very sophisticated strategy, with a big ol' smile on his face, as if math is still figure-out-able. I mean, this kid went on to do great things, including taking calculus his senior year. All because I think he had a fantastic background where he learned to think and reason, and then we sent him on with the message that Math is Figure-Out-Able. So, props to you, Kim, for the fantastic foundation. Also he had Stephanie Lugo for second grade. I'm trying to think. She's the one that videoed him in second grade. So, super props to the teachers that really gave him that foundation that he was then able to build on after that. It was amazing. Yeah. Alright, thanks for tuning in. Oh, say that one more time.

Kim  20:35  
I said, Thank you for teaching us the best.

Pam  20:38  
Oh,

you're welcome. Cool. Hey, ya'll, thanks for... Wow, I can do this. 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. Let's keep spreading the word that Math is Figure-Out-Able!

Transcribed by https://otter.ai