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

Kim  0:06  
And I'm Kim. 

Pam  0:07  
And you found a place where math is not about memorizing and mimicking, where you're waiting to be told or shown what 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  0:34  
So, we're super excited over here at Math is Figure-Out-Able land because we currently have registration open for all of Pam's workshops. 

Pam  0:43  
Woah!

Kim  0:43  
Lots of people from all over the world, which is really cool, are jumping in and reaching out about how much they love the work around subtraction that we did in the challenge, and they want to know more about the newest workshop we have available, which is Building Powerful Subtraction.

Pam  0:58  
Ya'll, I'm so excited about this workshop. Super excited. It's been a fantastic week where we did the challenge, and subtraction, and all the people from around the world. And the new subtraction workshop is amazing. Subtraction is the operation that kind of gets shoved to the side. But we all know students need support, and the workshop is finally here to support you as you teach subtraction. And this is one of the times of the year where I get to interact in the message boards or the workshops, and that is so cool. I was just answering some of the comments just last night actually, Kim. It's one of my favorite things that I do.

Kim  1:36  
I know, yeah.

Pam  1:37  
I'll tell you. The team keeps trying to say, "You don't have time to do that." And I'm like, "But it's so much fun!" And I don't know. It really keeps me in touch with kind of the things that you're thinking about, and it energizes me as I watch people over the course of a workshop just go "Whoa!" Like, "I thought this was good in the beginning, but my brain is changing." And just last night, somebody said, "I am now looking at problems in a completely different way." Yeah, I'll just maybe leave it there. It's so much fun. So, if you want to join us, you can check out what we have to offer at mathisfigureoutable.com/workshops is a place to go. mathisfigureoutable.com.

Kim  2:13  
Yeah, I love when you check the message boards too because you send me some super fun screenshots of quotes, and we get to chat about it, so I'm looking forward to that. So, today, we're going to chat about something that's actually come up a couple of times in the in the past. But it's really been on my mind lately, and in our chat. So, not too terribly long ago, you were doing a virtual event that I was just a part of, and a participant told you what they were thinking about how to solve a problem. And you asked a question back to nudge them, and their response was, "I don't know why. That's just what my brain did." And I have to tell you, in that moment when it happened, I kind of winced a little bit. And I sat back, and I was kind of participating, but mostly I was thinking about why that response. "I don't know why. That's just what my brain did," felt a little bit like crunchy to me. So, afterwards, I mentioned it to you. Do you remember when I called you, and I was like, "Hey, I have a thought..."

Pam  3:09  
Yeah, I do. Because I think you were really wrestling with why did that resonate? It didn't resonate with you, right? It wasn't like you were like, "Yeah!" You were like, "Mmm, how do I feel about that?" Like, "What?" 

Kim  3:20  
Yep. 

Pam  3:20  
And you were trying to figure out kind of how that bothered you. And I was like, "Yeah." Like, when I travel, work with teachers all over the place, do virtual events, I will often get statements like that. See if these resonate for you. Like, sometimes I'll say, "Did you use the problem before?" And they'll say, "No." And I'll say, "Could you?" And they'll say, "My brain just doesn't go there." Or they'll say, "My brain just starts doing steps." Or they might say, "The first thing I think about is not using..." You know like, I'm kind of, like you said, sort of trying to nudge something, and they're kind of like, "That's not where my brain... My brain doesn't do that. It's not going there." Yeah.

Kim  3:57  
Yeah, I

think those all sound related. So, after after I called you, and I kind of chatted for a few minutes, I took some time to think about that.

Pam  4:08  
Yeah, to be clear, neither of us are irritated, right? We're not irritated.

Kim  4:11  
No, no, no, no!

Pam  4:12  
It's noteworthy. It's noteworthy. 

Kim  4:13  
Yes!

Pam  4:14  
Like, "Hmm..." Like, "Let's make some sense of why that pinging for us." Yeah, yeah.

Kim  4:19  
Yeah. And I did take some time because I wondered why I had that reaction like something didn't sit right. So, I think that we all have habits that we formed about lots of things. And that's not new. It's not earth shattering to say we have, you know, tons of habits, and they're based on experiences. But I think that it's true in mathematics as well. You and I grew up creating habits about our mathematical behavior, the way we that we approach problems or math in general, and as we did more and more and more and more, we cemented our habits. And your habits were a little bit different than mine because my experiences were different than yours.

Pam  5:03  
Yeah, absolutely. I think you had an experience of a dad and a brother that were often talking about playing with numbers and the relationships they were using. It's funny now that my dad and I are talking more about numbers. He was doing stuff like that in his head. He just never talk about it. So, I did not have somebody around me... Well, same with my mom. She was doing... Her excuse is that her native language was German. Swiss, German, and so, we spoke English together. And I was getting good grades in math, and so we just didn't. I didn't have anybody that was kind of lobbing any relationships at me. I was sort of figuring it out on my own. But what I was figuring out was how to make sense of the procedures that teachers were giving me. 

Kim  5:45  
Yeah.

Pam  5:46  
I knew that math meant, "Wait for the teacher to tell you what to do. Mimic what the teacher was doing. If you couldn't figure out why to do the next step, then, you know, do four more of them and check your answer. And Nope." You know like, "And go back and forth. Oh, that got me the right answer, so it's got to be this thing. And then, just try to memorize which ones kind of came when." And that was my experience. When I saw a subtraction problem, those numbers lined up in my head, and I saw a little crossy-outies, and 9's, and 0's and that's where my brain naturally went.

Kim  6:20  
Yeah, yeah. So, when this participant said, "That's just what my brain did," they had a habit, right. I don't doubt that that happened for them. They had a natural inclination towards whatever their thinking was. But I think what's really important to note here is that just like any habit that we have, any natural inclination, it can be changed, once you're aware and you're willing to think differently. And I don't think it's sufficient to just leave with "That's just what I do." I think once people are aware that there is something else.

Pam  6:54  
That they have an urge.

Kim  6:55  
Yeah.

Pam  6:56  
Yeah.

Kim  6:56  
There's something else that they can do, and if they're willing to think differently, it's no longer sufficient to just say, "Well, my brain does that."

Pam  7:10  
Yeah, so it's almost like... I'm thinking kind of a two part thing. Once you can acknowledge the way, what your perspective is, what your inclination is, and you can acknowledge there is something else that seems to be... What's a good word? Desirable. It seems to be more efficient, or sophisticated, or any of those sort of positive things, that we can then have that growth mindset to say, "I want that." Yeah, go ahead.

Kim  7:40  
Well, and I think that what I settled on was that what struck me is that it felt very like, "Because that's what my brain did, I'm stuck here."

Pam  7:51  
Yeah, sometimes I feel like people will do that when they go, "Oh, I'm a visual learner. Or I'm an auditory learner. So, that's not going to work for me." To which I want to go, "A, learning style things has kind of been debunked." We should do an episode on that sometime. Do we all have natural talents that make some things easier than other things? Sure. But that doesn't mean that we can't then dive into and make ourselves stronger in different areas. Ya'll, I was terrible at doing layups. I can't even tell you how long it took me to learn how to do a layup. But I can tell you the day my coach went, "Whoa, was that Pam?" I heard him. I heard you coach. Because I had finally got it. I had finally gotten the (unclear) of a layup. I'm talking basketball for those of you don't know what a layup is. It took me years of practicing the steps of a layup before it became kind of a natural thing that I could kind of do. It might take some of us longer for us to build those connections than others, but once we know that there is a thing. Once I saw Cameron, my oldest son, once I saw heard, experienced what he was doing, I was like, "What?" Like, I was so intrigued. What I didn't do is go, "Well, I don't know why your brain does that, but this is what my brain did." I didn't stop there. I was like, "Wait, I want to be you when I grow up." My little kid. Like, "I have access to what you're doing. I can see the relationships you're using." I mean, it took some doing because I had to help him verbalize what he was doing. He's doing a lot to sort of natural. We've all talked about how we can do more than we can say. And so, he was doing a bunch of stuff. And me trying to get him to say it was a little like pulling teeth. You know, it was like, "I don't get it. Say it again." You know, "Okay, I'll give you another example." But I was not willing to say, "That's just what my brain does." And I guess that's what his does. No, I want to learn how to do a layup. Like, I believe I have access to that. I can do that layup. And I can think mathematically the way that you are. So much so. Kim, I have this. Such a strong memory. It's visceral, body memory that I was in a grocery store. I don't know which one, but I can picture like the aisles, you know where stuff is like on the shelves. And for some reason, I don't even remember why, I had to do subtraction. And I don't know. I can't even tell you why. Why would I do subtraction in a grocery store? But I remember thinking to myself, "I now have different strategies to do the subtraction problem." But watching my mind's eye line those numbers up and start to do digit subtraction, start to do the traditional algorithm. And I remember going, "No, don't do that." And I literally like had to take my hands physically. I had to embody this. I had to grab those two numbers. Now, they weren't like in the air, but I kind of put my hands in the air, and I moved them to the side, so they weren't stacked on top of each other. And I thought to myself, "Okay, if I can think about how far apart those numbers are, and then I shift them just a little bit." If you could see me right now, my hands are kind of like up in the air like in karate chopping both hands. And like ones representing the one number. The other ones representing the other number. And I thought to myself, "If I can represent this subtraction problem as how far apart these numbers are, and then shift both of them up a little bit." And I moved both hands to the right a little bit. And I was like, "Then, it would be..." And all of a sudden, I could see both numbers I'd shifted to, and I could see them. And then, clearly the difference was so obvious. It became something like 203 minus 100. Bam! I mean, it was. Or 247 minus 100. I could just see the difference of 147. It's just like. But I had to almost physically take my body and go, "Don't do that brain." 

Kim  11:39  
Yes. 

Pam  11:40  
"Brain, I'm going to do something different." And, Kim, it probably took me longer to stop walking in the store, to put my hands in the air, stop the numbers from lining up. You know, tell myself I find the difference, make my hands move to the side. And then bam! There it was. It probably took me longer than I could have just done that digit, traditional algorithm. 

Kim  12:04  
Maybe, yeah. 

Pam  12:05  
But I was developing a mental pattern that was worth it to me. I wanted to mathematize. I wanted to have it be about my thinking. I wanted to think more sophisticatedly. I knew it was possible. But I had to do it. I had to make that choice to embody that.

Kim  12:24  
Yeah.

Pam  12:24  
Yeah.

Kim  12:24  
And I think it was last episode that we talked about how when young kids are learning strategies, at some point it's okay to say to them, "We're done counting. You've demonstrated to me. We've talked about. You've given the experiences. I know you know the strategies, so we're going to use those. You said to yourself, 'I have access to something else.' And you said to yourself, 'Don't do what your brain wants to do, has a tendency or a habit towards doing, and made a different a different choice.'"

Pam  12:56  
Yeah, absolutely.

Kim  12:57  
And you've mentioned before about how I said to you once that I don't always know right away how I want to tackle a problem. 

Pam  13:04  
Yeah.

Kim  13:04  
Or that maybe I don't know like what the most efficient way to solve a problem is.

Pam  13:08  
I'm so glad you said that. I'm so glad. That was such a watershed moment for me to realize that you didn't just know.

Both Pam and Kim  13:15  
Yeah. 

Kim  13:16  
Yeah.

Pam  13:16  
Yeah. 

Kim  13:16  
So, we are aware that we both kind of see a problem, we dig in, and start working and sometimes we change our minds midstream. And that's perfectly okay.

Pam  13:25  
Absolutely. That is the real work of a mathematician. And when you do that, more and more of that real work, the stronger you become, the more those connections in your brain becomes stronger, and the inclination that you have to use them, the more likely you are to use those connections the next time. Especially just the inclination to think, to not just revert, to summarize steps. Like, that inclination becomes stronger. Yeah, sorry.

Kim  13:54  
Yeah. And when you're doing that, it probably also means that you're likely to be forming new habits, right? We have these old habits that we naturally gravitate towards. But when you do what you did and say, "Stop, I have access to other things," you're doing the work that then helps you form new habits. It's not really a problem that your brain has an inclination or a tendency. That's true for all of us, right?

Pam  14:19  
Sure.

Kim  14:20  
But when we want the number to influence the way that we think about problems, we need to acknowledge that we have power over that. 

Pam  14:26  
Yeah, absolutely. Yep.

Kim  14:27  
So, one other note is that sometimes, maybe often, we have teachers say to us that they have students who don't think and reason. Or maybe they themselves say like, "I recognize that I have not been thinking and reasoning for quite some time." And you and I talked about how there's almost this expectation for strong numeracy to grow overnight, right? Like, "I know that's the thing, now I'm going to be good at it."

Pam  14:52  
Yeah, absolutely. And we recognize that sometimes we hear that there's this inclination where it's not that kids are too stubborn or too unwilling. It's that they have these habits formed just like I had. I had habits formed. And so, in order to create a new habit, there needs to be a reason. 

Kim  15:11  
Yeah.

Pam  15:11  
It's why so many of our students who haven't been successful, dive in and they're often more interested than those students who have done fairly well with traditional methods. To a certain point. Like, we get students who haven't been successful, they're like, "Ah." Like, "I can just think? I can just use what I know?" And so, they might be the ones that we actually see dive a little faster into real math. Versus the students who have been successful just mimicking. They might be the ones that hold back a little bit. They might be the ones of like, "Hey, I could get an answer this way. I don't know what you're doing over there. I've got a method." So, if we can help them recognize that the goal isn't about getting answers, the goal is to build their brains to be able to think and reason more sophisticatedly. "Ah." Like, that's the conversations about coming up with a slicker, the clever strategy that can help those students who might be a little bit less inclined. But also, it's important to recognize it doesn't happen overnight. But we can shift that perspective overnight. It's why we do the strings that we do. It's why we do the math. When we work with a group, the first thing that we do with them is we dive in and have a mathematizing experience because it's not. I don't just start talking at them. I don't just pretend. "Hey, let's..." It doesn't work. Like, let's dive in. Give them an experience, so that they get a chance to go, "Ooh, What are my mathematical habits?" Yeah.

Kim  16:40  
Yeah, yeah. And, you know, it makes me really grateful because I did do, you know, kind of some mathy things, but it didn't have a lot of... You know, I know we talked about, you know I had family members who kind of did stuff. They were probably more silent about it, then. You know, we definitely talked more than you did. But growing up and doing more math at school, I didn't have a ton of experiences talking about or modeling my thinking. So, it just makes me really, really grateful and feel so lucky to be a part of people, a group of people that enjoy having regular conversations, right? And we talk a lot with teachers and leaders who are working hard to grow themselves, and how humble, and like just being willing to say, "I want to grow more, and I want to do more, and I want to change my current practice," is just... I don't even have words for it. I'm just so honored to be a part of a group of people who do that because they're working to grow themselves, and their students, and change those habits through experiences.

Pam  17:47  
Yeah, and it's why I do the work I do. I honestly want to change the way we view and teach mathematics, and I want to help teachers and students not to have to do it on their own, and frankly take the longer path that I did. You might see me now and go, "Woah, I want to be like Pam." But yeah, it's been a journey. And part of that journey was because I was diving into the research, and I had to sift through all the less helpful stuff and figure out what worked, and experiment, and to try new things. And so in a huge way, I've paved the way for you by outlining what are the major strategies. And then, we can put those up in front, and I can say, "Ooh, not this, but that." And then, you get a chance to sort of learn from all that experience. It's now my work to help you and your students become the mathematicians you can be. It's one of the reasons why it's so much fun for me to read the comments in our message boards because it is amazing. I'll see often comments in the first module where people are like, "Oh, yeah. Let me..." We'll ask people to put the message board, "What was your experience learning math?" And often they'll say, "Well, I rote memorized, I mimicked, but I want to learn."

Kim  18:55  
Yeah, yeah.

Pam  18:55  
And then, as it goes, by the end of the workshop, I've got people, "Bam! Pam, I can't tell you. I'm seeing numbers differently. I'm looking at problems with a whole new perspective. My brain is now doing things differently." But you know, it took the course of them diving in and actually doing the work. And like you said, having the experience to make those changes. Ya'll, I would love it if you would help me help us change the world. If you want to give yourself an experience to create new habits, I'd invite you to check out the podcast and my workshops. They are so good, jam packed for all that stuff. And let me just for a second talk to those of you, teachers, who for whatever reason would maybe be paying for some of that stuff on your own. You are welcome to send me an email at pam@mathisfigureoutable.com. Tell me your story, and I bet we can find a way to make it possible for you to dive into more and more Math is Figure-Out-Able stuff. 

Kim  19:58  
Yep. 

Pam  19:59  
Alright, ya'll, thanks for tuning in and teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. Let's keep spreading the word that Math is Figure-Out-Able!

Transcribed by https://otter.ai