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  0:09  
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  0:17  
Y'all, algorithms are amazing human achievements, and they are also terrible teaching tools, because mimicking step-by-step procedures has actually trapped students into using less sophisticated reasoning than the problems are intended to develop and use.

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

Pam  0:37  
Y'all thanks for joining us to make math more figure-out-able. Kim.

Kim  0:42  
Hi. Did

Kim  0:43  
I ever tell you once, or ever, that I'm not a massive podcast listener, and so when I go looking for podcast reviews, I'm always so grateful that people leave them because I think I should do better.

Pam  0:58  
Are you saying you don't leave reviews often?

Kim  1:01  
I

Kim  1:03  
don't listen to as many podcasts as I should. And there's some good ones out there. But yeah, I feel like a little bit of a hypocrite saying, "Hey, listen, and leave a review. But also I'm not going to listen to very many."

Kim  1:16  
Well...

Pam  1:17  
So, we're extra grateful for those of you who do listen...

Pam Harris  1:19  
Yes. 

Pam  1:19  
...and leave a review and....

Kim  1:20  
And the reason I was thinking about this is because this review is from Podcast Addict, which means they do better than me, so thanks for listening. So, I guess this is where they listen. This is Sharon652 listening on Podcast Addict. And Sharon says, "I can't tell teachers enough about this podcast. Pam and Kim deliver a message of how to change the world of maths forever. Gone are the rules and memorization that create fear and trauma in many students. It is problem solving through reasoning, using what you know. In the last 18 months, I have worked through all the episodes, and it has truly changed my thinking and teaching. Thank you ladies for your dedication and gift to the world of education."

Pam  2:07  
Aww, Sharon, thanks. Thanks for listening. And we honor the fact that you have given your time to improve your craft. That's amazing. Y'all, teachers, let's improve our craft all together, 

Kim  2:19  
Yeah.

Pam  2:20  
constantly. Cool, nice. So, Kim?

Kim  2:23  
Yeah. 

Pam  2:23  
I have mentioned... And I think you've met, maybe. It's okay if we name him, right? Dr, Brad Belinger? 

Pam  2:28  
I think so. 

Pam and Kim  2:29  
Yeah.

Pam  2:30  
He's amazing.

Kim  2:30  
Delightful.

Pam  2:31  
Brad is... Yeah, delightful is a good word. He has contacted me over time. I think the first couple times... Well, several. I don't know. For quite a while we interacted on Twitter. Am I supposed to call that X? Whatever. And back and forth. And he had, you know, insightful comments and whatever. And at one point he started kind of... I noticed he was like, "What's this algorithm stuff? Why are you dogging algorithms? They're brilliant." And he actually invited me to hop on a Zoom. He's like, "I can convince you algorithms are great." I smiled, and I was like, "Absolutely." And, Kim, I had a delightful conversation with him. Now, this is a while ago. 

Kim  3:07  
Yeah.

Pam  3:07  
He played. He was like, "Pam, look at this algorithm, and how it's connected to that one." And the overarching.... You and I were talking about this the other day, and we decided to do a podcast episode on it because as we were talking about, I gained some clarity around the fact that, some words at least around the fact, that he really came at that meeting... Which I totally loved. Like, I loved what he showed and everything. I think we came away with good understanding of why I'm pushing against algorithms. Not for what he's doing, but... What he was doing was playing. He would say, "See how this algorithm is connected to that algorithm?" And I would say, "Yeah, but do you want kids to mimic those steps to get answers?" And he would look at me almost with like, "Why are you even asking that? Of course not." And I would say, "Okay, so then, you know, the reason you're bringing it up is because it's cool that it's connected to this other ones. He's like, "Yeah, and look how it's connected to this one."

Kim  3:55  
Yeah, yeah.

Pam  3:56  
It was the super atmosphere of playfulness and of connections, and relationships, and number, and how you can reason through stuff. And so in that vein, algorithms are amazing human achievements, and we can play with them, if it's all about connecting and relating, and it's not about a series of steps to mimic.

Kim  4:21  
Yeah. 

Pam  4:21  
A little while ago, we did one of our Challenges. You guys, if you haven't joined into our Challenges yet, they're super fun. We'll announce them on the podcast, so just keep listening to the podcast. We'll tell you when they're coming up. He came. He was on my screen. I can see the top 48 on my screen, and I interact with them. And he must have gotten on early, because you got to get on early to get in top 48 or whatever. And he was right in the middle of my screen. And oh, it was just brilliant, because he was smiling and playing. And he sent me some wonderful emails during the Challenge, continuing to play with the math we had done that night. He was like, "Oh, what you just did. Like, I Have, You Need..." Ready, guys? Guess what he was playing with? I Have, You Need with solving equations. 

Kim  5:01  
Yeah.

Pam  5:01  
Super fun. Awesome stuff. Would I ever teach kids to solve equations using I Have, You Need as a series of steps? Everyone say, "No." But would I play with kids with relationships? Once we get kids mathing, and they're not all about, "Ooh, let me just do this series of steps, so I get an answer, and now I'm done, and I can walk away." Oh, what's mathing? Mathing is playing with relationships. 

Kim  5:24  
Mmhm.

Pam  5:24  
Then absolutely, I think it'd be a fun thing to dive into to sort of examine. So, Kim, when I kind of brought that up to you, you and I were both on that email. We've kind of chatted about it. We decided, or at least we started talking abou, playing with math.

Kim  5:38  
Mmhm.

Pam  5:39  
We wanted to beat out in this episode a little bit that maybe we play with math a little differently.

Kim  5:45  
Yeah.

Pam  5:46  
Yeah, so... 

Kim  5:47  
Yeah, and... 

Pam  5:48  
We're going to wonder about

Pam  5:49  
that.

Kim  5:49  
Yeah, listeners, we have no notes. So, this is just a fresh conversation. And I think the first thing you said to me was, "Kim, I wonder if you and I play with math differently." And I was like, "I don't know what you mean. What do you mean play with it differently?

Pam  6:08  
Can

Pam  6:08  
I do a little bit of history real quick? 

Kim  6:10  
Yeah, yeah. 

Pam  6:10  
So, when we first met, I didn't play with math at all because...

Kim  6:15  
You and I?

Pam  6:15  
Yeah, yes. When you and I first met. The math, to me, was repeating series of steps to get answers.

Kim  6:21  
Mmhm.

Pam  6:22  
And there was nothing to play with, right.

Kim  6:25  
Right.

Pam  6:25  
In any way. And if people talked about being creative or flexible, I was like, "Mmm, that has no meaning to me." Like, it literally had no meaning to me. So, listeners, if you relate to that, hang in there. We'll keep talking. What were you going to say? 

Kim  6:41  
I think people probably don't buy that, because you are so strong with relationships and connections, and you can verbalize all the things that you know now. I'm here to say true. And so, I guess, in the vein of like helping people understand that you cannot see connections or relationships right now. If you're listening and you're like, "I'm

Kim  7:11  
listening, but I don't see it."

Pam  7:12  
You're with me. You're with Pam. You're like, "There's nothing to play with. There's no..." Yeah. Hang in there because we can help with that.

Kim  7:17  
Yeah. 

Pam  7:17  
Yeah, we can help with that. Yeah. Because I was an adult, right, when we met. I had children that were in your classes. And you said something to me once. "You know like when you're running down the road, and you you see a house number, and you start to wonder is it prime and can I factor it?" And I don't even know what else. In fact, I think we have an episode where we talked about that.

Kim  7:39  
Mmhm. 

Pam  7:39  
Or you said, "You know, when you walk into H-E-B..." That's our grocery store in Texas. "...and you see the oranges or this many pounds for this much, and you start to wonder how many oranges and how it compares to the apples." And I looked at you, and I was like, "No." Like, flat out. You were like, "You know when you..." And I was like, "No." And it took me a while. And one day I was on the elliptical, and I was counting down. Because I do time. I think we talked about that on a recent episode. And so, I needed, you know, whatever, say it was 20 minutes, and it was 18:52. And I was like, "Okay, a minute and eight seconds," you know, or whatever. And I do this thing where it changes every minute, and so I'm always looking at the seconds, and I'm always... I do a lot of partners to 60 because of that because it's going to changed on the minute. I began to realize that I was now playing more, because I owned more relationships and connections. And math now was look at a problem, use what you know to solve it. What do I know? What's pinging for me today? I had things to ping. First of all, I had strategy and relationships, and I knew that that was mathing, and I had built my brain to own enough of those relationships and connections that now I began to play. But the other day... Okay, so that's kind of in the past.

Kim  8:57  
Right. 

Pam  8:57  
So, I think for a while now I have been much more playful for math for years, but I still... The other day, I thought, "I wonder if we play differently." Because now I play.

Kim  9:07  
Yeah, yeah. 

Pam  9:08  
Before it was you played, and I didn't play. Now, I think we both play, but maybe differently?

Kim  9:14  
Yeah. I think you're right. Well, and so at the time, I think what you said was, "I think you play with numbers for fun, maybe just to tinker, just see what happens, and to see what new relationships you can come up with, and see how it's connected to different things." But am I right that you said that you play for the purpose of how to

Kim  9:37  
teach? 

Pam Harris  9:38  
So, it's almost like I could repeat everything you just said. I play to see what relationships are happening, to see if it's consistent, to see if I can predict what's going to happen next. But almost always with an eye toward is this something major that I would then want to teach someone? Is this just fun, but I don't think it's like an important one of the things that I would purposely try to develop in kids. Is this like a tangential, interesting thing? Or would this be something that I'm like, "Ooh, I think that actually might be a major thing that would really influence me to be able to continue on thought in this vein." Does that make sense?

Kim  10:19  
Yeah. And I wonder... So, this this different purpose for playing. I wonder if it's like math feels more like a hobby and interest fun for me, because maybe it always has been. Like, I'm constantly bombarded in my brain with like random mathy things. And I wonder if because of the work that you do to create workshops and to speak and to write, I wonder if because you want to change the way math is viewed in the world, if that's why your purpose is different.

Pam  11:01  
Well, let me add to that. Because I create frameworks.

Kim  11:04  
Mmhm. 

Pam  11:05  
So, it's not just let me create a lesson. Let me tinker with a game. But I create developing mathematical reasoning frameworks. Like, what does it mean to have counting strategies to additive thinking to multiplicative reasoning to proportional reasoning to functional reasoning? So, when I run into mathy things, I am constantly asking myself, "Do I need to refine my framework? Does that influence the framework that I've created?" One of the things that you and I have talked about before is I don't publish, and then stand by it. I'm going to die on that.

Kim  11:37  
Right.

Pam  11:38  
What's that phrase? I'm going to die on that... Line? Whatever the metaphor is.

Kim  11:43  
Die on the hill. I don't know. 

Pam  11:44  
Die on the hill, yeah.

Kim  11:45  
No dying, no dying. 

Pam  11:46  
No. Let's just stop dying. But I am not only willing to write something new, even if I've published something different in the past. I feel obligated to update, to always take new information in and make sure that it fits. And if it doesn't, then we've got to figure out a way to say it more clearly. 

Kim  12:06  
Yeah.

Pam  12:07  
I'm very willing to say, "Oh, yeah. I did say that in the past, but I'm tweaking it now." 

Kim  12:13  
That's growth.

Kim  12:15  
I mean that is a sign of constant learning. That's a sign that you're willing to take in more information, and grow, and mold. And I mean, I look at some of the stuff that we did a while back, and there are things that are more clear. There are things that are more articulated well.

Pam  12:40  
We realized how people heard it in the past, so we can now say it differently.

Kim  12:44  
Right. 

Pam  12:44  
And there's also new information that we've gotten that I've had to think about. Where does that fit? And...

Kim  12:51  
Yeah.

Pam  12:51  
...does it fit? 

Pam  12:52  
I'll give you an example. When I ran into Les Steffe and his work. He did a lot of work with younger learners and sort of younger math. And it highly influenced what I was doing. Then I didn't really follow his graduate students as much for a while, for a period of time, and I did a lot of my framework building and working with teachers. And then I stepped back into like the work of Anderson Norton, and Amy Hackenberg, and Katie Ulrich, and the Units Coordination. When I ran into that work, I had to do and still doing some thinking to make sure about how that has impacted my framework and the work of realistic, mathematics education, and the Freudenthal Institute. Like, as I run into different people's work... Well, you and I looked at Jenny Bay Williams and John San Giovanni and their numeracy work. And we weighed it up. You know like, their strategies are a little bit different than our strategies, and how do we feel about that? We wanted to like how does their work influence and inform the work that we're doing? So, I don't know. Maybe that's why when I play. I definitely play for fun.

Kim  14:00  
Mmhm. 

Pam  14:00  
But then there's always this little bit of, "Where does this fit? And do I need to now adjust? Do I need to clarify something in the model that I'm creating, the framework that I'm creating?"

Pam  14:12  
Does that make sense? 

Kim  14:13  
Yeah, absolutely. I'm also wondering.... So, like we might have a different purpose for playing. I'm also wondering about like when each of us plays. Like, are there times that you feel like you play more than other times? I mean like when you're super busy and head down writing.

Pam  14:31  
So, I wonder. I don't know the answer to this. I wonder if you play more by yourself, and I enjoy playing more with someone else.

Kim  14:40  
Well, I think that really depends. If it's something that... I think here's what happens for me. I've got kids, a kid who has taken higher math classes than I took in high school. So, what I have found... I said something to him recently. And I was like, "You have to stop talking." Because he's not a teacher, right? And he gets excited that I'm interested in what he's doing, and so he'll try to tell, and I'll be like, "Shush. That's not what we do." 

Pam  15:09  
You want to think about it.

Kim  15:09  
I want to think about it. So, in those moments like I want to be around people who want to play, but I want to feel free to say, "Now, stop."

Pam  15:18  
Give me a chance to think.

Kim  15:19  
Because I like to think alone. Like, I like to wrestle until I feel solid because I know I can. Like, I know if I have just enough of relationship, that there's lots of things that I see now that I didn't maybe see in high school or didn't have the experience with. But I have more experiences now. And so, I think it's kind of like a mutual thing. I do enjoy wrestling with other people, but only to a point.

Pam  15:49  
And I really wish... I love it when I have a more knowledgeable other next to me that gives me just enough.

Kim  15:55  
Right.

Pam  15:55  
You know, that listens to me think out loud and sort of gives me just that next, or not even, just reflects what I'm saying or maybe represents my thinking. I don't have it very often at all, right? 

Kim  16:07  
Yeah, I was going to say that's

Kim  16:08  
super tricky because you would need somebody who knows higher math but also has like the pedagogy work, right? That.

Kim  16:15  
So, yeah. So, the next best for me is someone who will just listen to me.

Pam  16:19  
Yeah. 

Kim  16:19  
And kind of reflect back and kind of learn with me.

Pam  16:22  
Yeah.

Kim  16:22  
What I think maybe what I was saying is that I think in my spare time, you might spend more time playing with things, and I might spend more time reading a novel. I don't know.

Kim  16:34  
Oh, for sure.

Kim  16:35  
Yeah, I...

Pam  16:37  
I tend

Pam  16:37  
to play more with like if somebody hands me something, if it shows up on social media, I'll engage in play. But I won't play as much if A, if I don't think it's going to impact my framework, or B, if I don't have somebody to play with.

Kim  16:52  
Yeah.

Pam  16:52  
Where I think you're a little different there.

Kim  16:54  
Yeah, I almost try to avoid seeing things because, you know like...

Pam  16:59  
What do you mean seeing things? Seeing mathy things?

Kim  17:01  
Seeing math puzzles. Seeing, you know. Because Sue will put something in our communication for work, and I just, like can't not. Like, it's so dumb, because I'll be working...

Pam  17:11  
You have no self control.

Kim  17:12  
Like, I can't do it right now. Or, you know, I'll... 

Pam  17:15  
Which

Pam  17:15  
means you want to, right? 

Kim  17:16  
I do, yeah.

Pam  17:16  
You want to dive and play. And, mmhm, mmhm.

Kim  17:19  
Yeah, I really enjoy engaging in puzzles.

Pam  17:22  
You know, the story that I'm remembering is when you and I went and did... Golly, were we in Longview, Texas? "Kim." 

Kim  17:27  
Oh, yeah.

Pam  17:29  
We had the night. It was a two day thing or something, and so we were in the hotel room at night. It was one of those that has like the common living area and whatever.

Kim  17:38  
Mmhm, mmhm. 

Pam  17:38  
And you sat down and you said, "Teach me something." And I was like, "What?" "Do some higher math,." 

Kim  17:39  
Yeah.

Pam  17:39  
Yeah. And you wanted to play, right? You didn't want me to tell you.

Kim  17:41  
I do, yeah.

Pam  17:43  
You wanted to actually like give you an experience where you got to play, yeah.

Kim  17:51  
Always interested. Yeah, so you play more when there are other people around.

Pam  18:01  
I think so. Or when I have somebody who will play with me. It's not just random people. Somebody who'll play with me.

Kim  18:05  
I think that's probably why when there's something mathy, you and I like enjoy the conversation. You know, we beat out like what numbers would you choose for this? Or why? And I think for me it's fun to play with the numbers, and at the same time you're thinking about what you would do with that.

Pam  18:28  
The structure, and how does it impact the framework, and how am I going to teach teachers about it? And, yeah, absolutely,

Pam  18:33  
 Make a good team.

Kim  18:36  
Yeah. We do other things besides play with math.

Pam  18:39  
But it sure is fun. Yeah.

Pam  18:41  
Hey, so one of the things that you talked about earlier was, you know, you might be the person that's like, "I don't play with math at all." I feel like you had a suggestion for people of where they could go to...  

Kim  18:52  
Oh, I don't remember.

Pam  18:56  
Well, I'll remind you. I think you were going to point them to MathStratChat.

Kim  18:59  
Oh! Yeah, yeah! So, I think there's plenty of people who are probably listening, and they're like, "I don't...  It sounds like it will be a lot of fun to play with numbers. Sounds like it would be a lot of fun." We have... You know, we put out MathStratChat problems every single week, and there are plenty of people who see those problems, and they just kind of lurk. They just... That sounds awful. They just kind of watch. "Lurks" sounds horrible. They just kind of watch. And they just are like, "How do other people respond?" And it might be that the first time you see a problem, you're like, "I don't even understand what these people are saying or how they solved it." But I would encourage you to read. Read the suggestions. Read how people are talking about it. And then, if you have noticed, there are problems in a string. So, we'll put out 3, 4, 5 problems of the same type maybe.

Pam  19:52  
It's like one Wednesday, the first problem. The next Wednesday kind of a follow up problem. The next Wednesday. Mmhm.

Kim  19:58  
And if you stick with it, and you've read some ideas, some strategies that people have have used, the more that you engage, you'll notice that you start to understand some of the relationships. You might pause, think about how you would solve it, and then read what other people are doing. But it's a great way, on a regular basis, to say, "I'm committing to playing with numbers once a week. I'm committed to looking for some relationships." And it's consistent. There every single week.

Pam  20:31  
Nice. Great way for you to learn to make math more figure-out-able. And when it is, play more. 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!