Pam  0:00  
Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam, a former mimicker turned mather.

Kim  0:08  
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  0:15  
Because 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

Pam  0:29  
develop. 

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

Pam  0:36  
Thanks for joining us to make math more figure-out-able. 

Kim  0:41  
Hi.

Pam  0:41  
Hey. How's it going? 

Kim  0:44  
It's good, how are you?

Pam  0:45  
I'm good. I'm good. How do you like the new mic that we're using?

Kim  0:48  
Well, I hope that our podcast person likes it, and we're not too loud. 

Pam  0:52  
Hope our

Pam  0:52  
editor is okay, yeah. 

Kim  0:53  
Yeah.

Pam  0:54  
Yeah, Listeners, you have to tell us if you can tell if there's a difference,

Pam  0:56  
Yeah. Or not. 

Kim  0:57  
Maybe it's super clean. Maybe it makes our words better

Kim  1:01  
too, maybe. 

Pam  1:02  
Oh, not just crisper, but actually better. Hmm, okay. 

Kim  1:05  
We sound smarter.

Pam  1:07  
We'll go with that. That works. 

Kim  1:08  
Okay, hey, I... We got this great review, and it actually said, "Long overdue review". 

Pam  1:17  
It's never too late, never too late. 

Kim  1:18  
So... 

Pam  1:19  
Thank you. 

Kim  1:19  
jstingerbenton said, "I love podcasts! For over a decade, I've been listening to education related podcasts on my commute to school. When I started a new position as a math interventionist, I searched for a podcast that could help. Finding Pam and Kim has changed my life. I began listening three years ago to become a better teacher, but in the process, I have gained so much awareness about my own mathematical thinking."

Pam  1:42  
Oh, I love that. 

Kim  1:43  
"I'm now able to take my newly found knowledge and confidence into the classroom and share with students and among colleagues. With so many fixed mindsets and the fake mathing that exists in schools, it feels like an insurmountable task that I'm convinced that the Math is Figure-Out-Able movement will prevail. Spread the word!

Pam  2:01  
That's awesome. Thanks, jstingerbenton. I feel like... 

Pam  2:05  
Oh, I love

Pam  2:05  
that.

Kim  2:06  
...a lot of comments like that. Either from the podcast or maybe in the teacher Facebook group that we have. Where people say, "I intended to listen or to do something with you guys as a way to help my students, but what I realized was that it was changing me, my mindset, my understanding. And, you know, then I get excited, and I wanted to help my students and my colleagues." So, that's... I mean, I think that's a huge goal of ours, (unclear).

Pam  2:34  
Absolutely. And it's never too late, Long Overdue Review. I like it. Yeah, (unclear). 

Kim  2:39  
Never too late. 

Pam  2:39  
Give us a review. Give us a rating. Helps more people find the podcast, and then more people can have that Journey, just like jstingerbenton did. Hey, and Jay Stinger Benton, we'd love to invite you to check out our Math is Figure-Out-Able Solution to work with your school in your district. We do that, listener, so check it out. Hit the website. Get on my... Let's chat. 

Kim  3:00  
Alright.

Pam  3:01  
Alright. 

Kim  3:02  
We, one of the things we do, as you know, are create fantastic workshops. And recently, we were at a workshop filming. And when I go, one of my jobs is to notice things that are happening. You know, I pay attention to the words that Pam's saying and...

Pam  3:21  
Make sure, like in case I have to correct

Pam  3:22  
them. Mmhm, yep.

Kim  3:24  
And we're like staying on track for what we want to accomplish. We always way over pack these workshops. 

Pam  3:30  
It's the worst.

Kim  3:30  
And I'll say to Pam at a break, "Yeah,

Kim  3:35  
we're going to have to..."

Pam  3:38  
"What are you going to fit in? What are you going to speed up? What are you going to cut?" I'll just say, "No, no. We can get it all in." You're like, "Pam, you have to make a choice."

Kim  3:45  
Lunch time, sometimes I have really hard conversations. It's just, you know, there's so much to do. It's so much to do. And anyway.

Pam  3:49  
Well, and

Pam  3:49  
you help me realize that if we don't decide what to cut, then what we were going to do at the end, gets cut, and so let's make a decision. But yeah, you used to made me so mad when you would say that. I was like, "Shut up, I'm just going to get it all done." And you're like, "So, we've tried that how many times? Better together. We're better together.

Kim  4:05  
Yeah, we are. At this particular workshop, the more recent one, I started to notice when you were talking to the participants and record these noticings that you were naming mathematical behaviors for participants as they were happening. And I've heard you do this kind of, you know, here and there on occasion, but in this workshop, it felt like something must have been on your mind because you were saying it more often. And I think our participants really appreciated. They sat up taller, and they felt like, you know, what they were doing mattered. So, when I say "mathematical behaviors", I don't mean just necessarily the Standards for Mathematical Practice and and what (unclear). 

Pam  4:50  
Those are fine. Those are good. 

Kim  4:52  
For sure.

Pam  4:53  
Yep, mmhm.

Kim  4:53  
But those weren't what you're naming. You weren't saying, "This is practice standard number two," but you were named things that people were doing when they were cognitively involved in the work they were doing, when they were mathing. And so, I made a list of these things, and I want to share those with you. I don't know if you've seen them all, but I want to share the ones that I jotted down. And I'd like for you to give an example of what you mean when you say this to somebody. 

Pam  5:19  
Okay.

Kim  5:19  
Okay, so one of them you named was, "That is fantastic mathematical behavior, where you look back, and you recognize what I could have done."

Pam  5:29  
Right, so that happens when somebody has done their best job. When you solve a problem, you usually use your best instinct. You know, you don't say to yourself, "I'm going to solve this with the least inefficient, unsophisticated..." You know, you do your best to solve it. But then, it's a mathematical behavior to not be done at that point. "Oh, I got the right answer. I'm done. Or I got the wrong. Well, I'm done," and so then you just walk away. But somebody in the workshop had solved the problem, and then had said, "Oh, now that I'm... I've kind of got the relationships in my head. Now I'm looking up. I'm sort of from a bird's eye view, and I'm realizing that I could have done something more sophisticated, or more slick, or more clever." That's a mathematical thing to do. Mathematicians don't just stop when they get an answer. They look at it from a different perspective. They're interested in... Yeah, that. There you go.

Kim  6:17  
Yeah, I think this happens in workshops or in classrooms when people have the freedom to. A teacher's not moving on right away. They're not like, "Okay, cool. You got an answer. Move on." And I think this particular behavior helps people become more efficient over time. So...

Pam  6:33  
Well, and if I can also say. And it's not just that the teacher is not going too fast. It's also that the conversation isn't about the answer. It's about the way you got there, and so then... And we're targeted. Often, we're trying to develop a particular relationship that leads to a particular strategy, and so it gives people an opportunity to go, "Well, oh, for this problem, it didn't incur to me I could have... It didn't occur to me that I could have done that. But now it does. Now. Oh, okay. Alright, now that I'm listening, ah. I'm looking. Now, I can see. 

Pam  7:04  
Yeah. 

Kim  7:04  
Yeah.

Kim  7:05  
Okay, another behavior you named was to be curious, and you often say seeking for the "aha" moments.

Pam  7:12  
Yeah, nice. You know, I was just in Virginia with an amazing crowd. Man, they were so responsive and just super engaged. And one of the things that happened several times, but a particular time was one of the participants was sharing their strategy. And, ya'll, this was in a big room. I think there's 200 people in the room. And somebody was sharing their strategy. And across the room. Big, big ballroom. Across the room, a participant said, "Ooh!" And I was like, "Oh, yeah. Like, how many of you right now are like I want that. I want to come with a strategy that where I get the 'Ooh'." And so now we're kind of building this community where it's not about, "I was fastest. I was first done. I got the right answer. I'm cool." It's not that. Now, it's, "Ooh, I did something clever enough that I got the 'Ooh' factor." So, now we're seeking for the "Ooh" factor. We're trying to be... Not stupid clever. Not like... I don't know. What's a good word for that? Not like...

Kim  8:09  
Complicated. Convoluted for no good reason. 

Pam  8:11  
Thank you, that. But, like, actually slick.

Kim  8:13  
Stupid clever. 

Pam  8:16  
Thanks for defining stupid clever for me. But you're curious to see like how can I understand the relationships even better? To now come at it like I'm seeking for that, "Ooh" factor. That "aha" moment.

Pam  8:29  
Yeah.

Kim  8:31  
Yeah. Another thing I jotted down was, "It's a mathematical behavior to compare strategies." 

Pam  8:37  
Yeah.

Pam  8:38  
So, in the workshop, you're talking about, one of the participants had said, "Well, my partner did this, but I did that, and I'm noticing these connections." And so, yeah, that's a mathematical behavior that we're not done with the answer. Really, we're trying to build our brains to math, and so we're curious to compare. Yep.

Kim  8:57  
And when you can find things to compare, the similarities and the differences, I think that really strengthens when you would want to use one particular strategy over another. Like, why did these strategies work really well for this problem and would that be true for other problems? 

Pam  9:12  
What

Pam  9:13  
was it about the number and the structure that... Yeah, nice.

Kim  9:16  
Yeah.

Kim  9:16  
Another time you said something about, "It's a great mathematical behavior to have choice."

Pam  9:22  
Yeah, like recognizing that you have choice and that you're making a choice because of something. Kind of like what we just said. Depending on the numbers or the structure, I'm going to choose this strategy. It's not a mathematical behavior to go, "Okay, where have I seen this problem before? How have I seen someone else do it? Can I mimic those steps?" Like, mathematicians don't do that. They don't mimic steps. They might say, "Where have I seen this kind of problem before? And does that bring other relationships to mind?" But not in a "Retrieve from rote memory, so that I can mimic" kind of way. It would be in a, "How can I connect this to what I'm currently doing?" And that is all all based on the fact that you have choice. That you can... Yeah, it's not one and only one right way.

Kim  10:05  
This reminds me a little bit of what you said when you first realized that when I look at numbers, I don't automatically know the best thing. Like, I'm considering what do I want to do? What do I want... Yeah, how do I want to solve this? And then, because I had choices. I could choose what I wanted to do in the moment.

Pam  10:23  
Boy, that freed me up when you said that that day. You're like, "You know, I don't know the right thing to do instantly, I try this. No. That? No. Yeah. Oh, ooh, that way." I was like, "What?!" Because I was feeling less than that I was having to try a few things to decide what I thought the best one was. When in reality, that was a mathematical behavior.

Pam  10:42  
Bam.

Kim  10:43  
Yeah, yeah.

Pam  10:44  
Cool. 

Kim  10:44  
You might have mentioned this one enough, but another thing you said was, "Mathematicians seek to be clever." I don't know if you have anything to add to that one. I think you mentioned

Kim  10:51  
a little bit. 

Pam  10:52  
Yeah, maybe I'll just say seek... Not stupid, clever, but seek to be efficient, but also seek to represent the relationships generally. Seek to be able to say, "Well, you know like, make generalizations. That's part of being clever. They don't seek to just brute force something. They're seeking to be, yeah, clever.

Kim  11:13  
You know, when I see this happen is in MathStratChat that you put out every Wednesday night. I sometimes see if the problem is, quote, unquote, "not challenging" for somebody, they own some strategies. And, you know, maybe it's a two-digit addition problem or something. Then, they might go like, "Okay, I have some strategies, but now I want to play. I want to play. I want to see what other relationships I can call on." I see a lot of people being clever with the way they represent things. Just because they can find the answer pretty simply, then it frees them up to mess around a little bit extra.

Pam  11:50  
Yeah, could we shout out a couple people? I think Mariana often does that. Cathy Campbell. Karen Campt. Those are a couple of names that come to mind that often will put in, "Well, here's my first one, second, third. Ooh, I actually liked this one the most." 

Kim  12:05  
Mmhm, yeah, yeah.

Pam  12:05  
Yeah, we love that playing around. Nice, yeah.

Kim  12:07  
You also named that it was mathematical behavior to say, "What do I know" I think we say that a lot.

Pam  12:15  
Yeah, that really reminds me of my own personal kid who was like, "Come help me with this physics problem." And I said, "Go get your textbook." And he's like, "What? I don't even know where it is." And I was like, "Dude, I haven't done this for a while. I don't even know." And he's like, "Well, just like dive in and help me understand the problem." And I was like, "Okay." So, we started reading the physics. I think it was angular velocity, momentum problem. And as we read the problem, and was like, "Wait, so this?" "And, "Okay, that's... Wait, no. I think it's like that. And this is connected to that." And by the time we kind of understood the problem, we had solved it. And I learned from him, like I can ask myself, "What do I know here? Let's make sense of what, use what I know." Get started. Dive in. You don't have to wait to be shown, told, demonstrated, steps to mimic. Yeah.

Kim  13:04  
One more I wrote down was that mathematicians ask for more and they want to understand. It's a behavior that they have.

Pam  13:11  
Oh, that's nice, yeah. I mean, so often, the older the student gets, the  more it's like, "Just tell me how to do it. Just give me the steps. Just..." And I think we've ingrained that in kids because we haven't had this wide field of learning where there is... Where they're clear that what mathing is, is making connections. So, when we can make that, that's the sea that we're swimming in, then yeah, then it's just curiosity blooms. And they're realizing wanting to understand and asking for more, that's absolutely a mathematical behavior. 

Kim  13:39  
And

Kim  13:40  
you and I each have a personal kid who may have not always been a favorite in class. But they do ask for more, and they do want to understand, and they don't give up when somebody says, "It's just this." And I wish we could engender that in all kids. That you have a right to understand, and you have a right to ask for more, so that you can understand how to math. Anyway, in this workshop, I was just really excited, and it was nice to hear you name those. I know you've done it, like I said, here and there. But I'd like to encourage teachers to take on this teaching move of naming behaviors when they see them, and encourage students to be thinking about what they can do some of these behaviors. There's more mathematical behaviors. Yeah. Anyway. Props to you.

Pam  14:39  
Nice, thanks. So, Kim, why name the behaviors in class like we're naming them in a workshop, like we're putting them out in front of teachers to say, "Hey, Pam, did this. Let's acknowledge that," so by doing that, we're kind of suggesting that, hey, you could name these mathematical behaviors in class. 

Kim  15:00  
Yeah. 

Pam  14:58  
I want to give some credit to Kristen Frang. I think she might have been the one who really got me. Other people had said some things. You said some things. But she really got me kind of... I don't know. Maybe there's a competitive spirit in me when she's like, "I'm doing it." And I'm like, "Well, I'm going to do it too." But as she was telling me the fact that, you know, she would have these students that felt so beaten down, and, "I'm not good at this." And she would say, "Well, you're good at this part of it. Like, that  thing you just did? That's a mathematical behavior. That if we name those and make the doing of mathematics also to include the behaviors we've talked about today, that's going to bring in... It's going to make mathematics. And we're not blowing smoke here. These are real. This is real mathematical behavior. It invites more kids into what it means to math. That's one of the reason.

Kim  15:01  
One of the things that I loved she did was I got to see her teaching some. And in the beginning of class, there were times where she would say, "What mathematical behavior are you going to take on today?" 

Pam  15:01  
Oh! 

Kim  15:01  
And the students would say to themselves and commit, today, I'm going to ask for more. Today. I'm going to seek to be clever. Today, I'm going to...

Pam  15:01  
Try to be curious. 

Kim  15:09  
Yeah. And I think when you set that as a goal, that is, like we talked about last week, that's the explicit part. We're going to name these behaviors. We're going to say this is a behavior that happens in a math class. You can do this, and we're going to name it for you, we're going to support you. We're going to encourage you when you do it, and it's going to create more behaviors that we want to support.

Pam  16:32  
Which sends the message that these behaviors are figure-out-able.

Kim  16:36  
Mmhm. 

Pam  16:36  
That part of mathing is not whether you're born naturally doing it.

Kim  16:42  
Right, right. 

Pam  16:42  
It's we can all work on these and become better at them. And if there's one that you want to work on today, say you write that one down. Let's work on those.

Kim  16:51  
Absolutely.

Pam  16:52  
Brilliant. Alright, ya'll, thanks for tuning in and helping get more mathematical behaviors in your classrooms 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!