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

Kim  0:09  
And I'm Kim Montague, 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  0:18  
And we're glad you're here with us because we know that algorithms are amazing human achievements, but they're not good teaching tools because mimicking step-by-step procedures actually traps students into using less sophisticated reasoning than the problems could be developing.
I like it. I like it. 

Kim  0:32  
There you go. Good job. In this podcast, we help you teach mathing, building relationships with your students, and grappling with mathematical relationships.

Pam  0:41  
We invite you to join us to make math more figure-out-able.  Yay! Yeah, so I just tweaked that line a little bit. I kind of like it. 

Kim  0:49  
I love that. I love that. 

Pam  0:50  
Okay, cool.

Kim  0:50  
So, I want to share a review. Hi. 

Pam  0:53  
Okay. Alright, bam. Let's hear a review. 

Kim  0:54  
So, the title for this one is "A Must for Any Educator." 

Pam  0:59  
Aww.

Kim  0:59  
Super fun. I know, and it's McAlpin22.

Pam  1:02  
Maybe a math educator. I don't know that any other educators need to. Do you think? 

Kim  1:06  
Yeah, that's probably true. 

Pam  1:08  
History, art educators. I mean, as delightful as we are, I'm not sure that we are experts. I'm not an expert in anything but math ed, but that's... Math ed. Here we go.

Kim  1:19  
Alright, let's get to it. "This podcast helps bring awareness to the problems students face in math today and how we can better prepare them for not just tomorrow, but their future as thinkers."

Pam  1:31  
Aww.

Kim  1:32  
I love that because, you know...

Pam  1:33  
Five star. Nice. 

Kim  1:33  
Yeah, it's not just about solving problems, right? Like we're not just here to say...

Pam  1:38  
Get answers.

Kim  1:38  
...solve these multiplication problems more efficiently. It's broader than that. It's bigger than that. So, thank you for that. I'm glad you see that in the work that we do.

Pam  1:48  
"Not just for tomorrow, but their future as thinkers." Thanks. McAlpin22

Kim  1:52  
Yeah, great. 

Pam  1:53  
Nice. Appreciate that. And, y'all, we appreciate your reviews and your ratings. It helps the algorithms send out the podcast to more people who would find it helpful. So, yeah, thanks. Thanks for helping us get the word out.

Kim  2:04  
It is January. January 2026. Very exciting times. And we know that a lot of teachers are going back, second semester. Some teachers are starting their year, depending on where you are in the world. And so, as we thought about like starting fresh, starting anew, it's always a good time to think back and reflect on your previous semester or your previous year and to look forward. And part of that sometimes is a refocus on beliefs and what you want your classroom to be like. And we reminded ourselves that we have an episode that we did about like knowing your beliefs, knowing what you bring into the classroom and how you make your decisions. Like, what's in your head when you weigh things out. And so, we thought we would do a quick recap of what we think about, and then send you off to an episode that we did quite some time ago. Pam, it was episode 12, 250 episodes ago. Can you believe that?

Pam  3:10  
Wow! Nice.

Kim  3:11  
I know, I know. So, it's been a minute.

Pam  3:13  
Thanks for keeping us recording episodes, Kim. 250 episodes ago. Cool. 

Kim  3:18  
Yeah.

Pam  3:18  
Cool. Yeah, and I think in that episode, we talked about, a little bit about, my background and kind of how we got here, and what are the things that sort of that we build, that we base the decisions on. What's sort of in our hearts, our psyches, our heads? And based on that, being grounded in that, and sort of acknowledging what we're building it on, then it makes sense. Our decisions can then flow from there, and we have integrity with what we really believe, and about math, and about learning, and about kids, and potential. And we can kind of connect all those things. Yeah, and so today we thought we would talk about maybe three that we didn't mention in that episode.

Kim  4:02  
Yeah, or at least mention very much. Yeah.

Pam  4:05  
Yeah. 

Kim  4:05  
And, Pam, can I interrupt you for just a second? Because...

Pam  4:07  
Of course, of course. 

Kim  4:08  
...the math is not mathing. It has been more than 250 episodes. This is episode 291, so I'm going to call that 279 episodes ago.

Pam  4:18  
Oh, that's good math.

Kim  4:19  
You know, I was just waiting. Like, somebody's going to be like, "What are you talking about, you math people?"

Pam  4:24  
Oh, I thought you were saying you were waiting for me to catch it, and I didn't.

Kim  4:27  
No. No. No. 

Pam  4:27  
I wasn't looking at the number, the episode.

Kim  4:28  
You were totally just... Yeah. 

Pam  4:28  
Which episode are we recording? Anyway. Whatever. Okay, so 279. Is that what you said? 79? Yeah. Okay.

Kim  4:29  
Alright, what do we believe? 

Pam  4:36  
So, one of the things, teachers, that we would invite you to consider is that if you understand the framework that we've put out here on this podcast for Developing Mathematical Reasoning that really mathematics is hierarchical. And at least many of the domains are hierarchical. That means they're built on and based on each other. So, once kids learn to count, we need to help them move to additive reasoning. And we need to help build on that to multiplicative reasoning. And we need to help build on that, so they're reasoning proportionally. And then build on that, so the reasoning functionally. And yes, I'm doing the thing with my hands where I'm sort of got a small oval and then a bigger oval. And that functional reasoning is encompassing all those. And, of course, we have spatial reasoning, and statistical reasoning, and algebraic reasoning that are more longitudinal. And if you understand that framework of how we really can develop more and more sophisticated mathematical reasoning, then everything you do aligns with that. Everything you do is, "Ooh, I see what you are doing. Fantastic. Let me represent that," and how do I help you develop to more sophisticated thinking?

Kim  5:48  
Yeah.

Pam  5:49  
Let's celebrate where we are and always moving forward. It's not about getting answers. It's about recognizing the way students are reasoning, and help build more complex, more sophisticated reasoning wherever we are. So, that's a helpful thing to keep in mind that sort of everything can be based on. Kim, what's another one that we didn't mention as much in Episode 12 that we thought we'd say today?

Kim  6:09  
Yeah, so you mentioned the framework for math. Our framework, or what we think about for working with students, we've mentioned several times since this episode is know your content, know your kids. The idea that the more that you understand the content in your grade level, what comes before, what comes after, how deeply you know your content is really in service of when you listen to your students, you're able to know where to help them move. And so, it's not just, you know, know your kids, like what sports they're in. Although, that's part of it is knowing them deeply. It's really so that you understand where they are on their mathematical journey and can help them move forward. 

Pam  6:55  
Yeah, nice, nice. It's the "what" and the "how." 

Kim  6:59  
Yeah. 

Pam  7:00  
Cool. And then a third thing that we would mention that I think we've sort of developed since then. We had been working on it, but we've really kind of codified it. Is our Success Map for teaching.

Kim  7:12  
Mmhm.

Pam  7:12  
And that's a framework that we use as we work with teachers.

Kim  7:17  
Mmhm.

Pam  7:17  
And we help teachers, really their development of mathematical reasoning and their development of mathematical teaching.

Kim  7:25  
Yeah. 

Pam  7:25  
And so, that Success Map framework. We have other episodes on that one. But we really lean on that as we plan podcast episodes, and workshops, and PD sessions. And everything that we do is built on that  framework, which is built on know your content, know your teachers, which is built on developing mathematical reasoning framework. It all sort of ties together, an integral set of frameworks. Yeah.

Kim  7:52  
And I think what's important to note is that the reason why we're mentioning that those are our three is because we, over time, have gotten to the point where we know so deeply what we believe about those three frameworks that it is the lens with which we view everything.

Pam  8:08  
Mmhm. Yeah. So, as you listen to episode 12, which we're going to play in just a second here, be thinking about those three frameworks we just talked about and how does it fit with you and your teaching framework? How does it ping for you and how does it help you begin this 2026 year being grounded in what you know about teaching and learning mathematics? Here's episode 12.

Kim  8:33  
It's going to be so great. So, listeners, welcome to the third part of the series, "The Top Three Things to Start the Year." During the first week, we talked about helping students feel seen, acknowledged, and valued by learning and using their names.

Pam  8:53  
So important. 

Kim  8:54  
Yeah. And then we shared about how we can use lesson types, even if we're teaching remotely to build a community of learners. This week, we're going to talk about the importance of having your vision about teaching and learning mathematics solidified, so that everything that you do and say fits together. Pam, in an earlier episode, you shared some of your beliefs about teaching and learning, and you said that teaching was about relationships, that everyone can learn more real math than fake math, and that math is not about memorizing algorithms, but about thinking and reasoning. Let me ask you this. How were you able to get to a point where you knew and could talk about who you wanted to be as a math teacher?

Pam  9:35  
Yeah, I appreciate you asking that. So, I want to start off with two brief stories. When I very first got my very first teaching gig, I was hired by a gentleman by the name of Scott Hendrickson. He was the math department chair. He taught calculus in the school, and he ran the math department. And I found him fascinating. And the best word that I have to describe Scott is "integrity". And what I mean by that is everything he did fit. Like, kids could never poke holes in his discipline, in his grading system, in the way that he taught because it all matched up. It all fit together. He wasn't punitive. Everything was more based on like opportunity to learn. It wasn't about, "Ah, I've caught you doing something." No, it was really much more about he cared and kids could feel that in everything he did, and said, and the way that he set things up. And so, there was just really this sense of that he cared about the students. And if they cared, then they would work together, and they would all make it work. I mean, he was kind of like a Mr. Rogers guy. Kind of a nerdy, unassuming, down to earth. But really, ironically or interestingly, everybody respected him. Like, the different cliques in the school all treated him with so much respect. I've never seen it before or since. It was just an amazing thing. But I really felt like it was because he just had so much integrity with everything that he did. I've never seen that number of AP Calculus kids in a school. It was unreal the calculus program that he ran and the scores that he got. Kids were succeeding and feeling really, really good about how well they were mathematizing them. It was cool in that school to be in higher math. And so, from looking at that, I was able to sort of figure out ways to make my system mesh, to make the way that I taught have more integrity. I was able to think through systems and structures in the way that I set up my classroom management, and grading, and just the whole ball of wax to where it fit me. And that I felt like I could have integrity of the way that I taught and that kids really felt like that things were fair. And I really liked the fact that my reputation around the school became one that I was really tough, but that I was fair. And that students would kind of come in with almost a little bit shaken in their boots, and then within a couple months, they would be like, "You know what? You're actually really cool. Like, why do you come off so hard nosed at the beginning?" And I just smiled a little bit. And it was a way for me to kind of make sure that things just like fit together.

Kim  12:17  
How cool to have such an early mentor. And I feel like I've even heard you talk about him when you decided on grading policies for your university classes.

Pam  12:26  
Yeah, absolutely. He still influences the way that I do things today. If I ever have a question, I often can just sort of think about what would Scott do? You know like, how would he handle the situation? Really, really grateful for him. 

Kim  12:38  
That's really cool. 

Pam  12:39  
So another quick story. When I... So, I was a high school math teacher, and then my kids started going to school, and I dove into the world of research about how we could teach elementary math better. And when I did, I read a lot of Marilyn Burns and Investigations in Data, Number, and Space and Young Mathematicians at Work. And I noticed that as I traveled around the country and talked about building powerful numeracy, I would then see things people would do with like Investigations. And I would see them sort of miss. I'd be like, "Wait, what do you do?" Like, they would almost misread the intent of the task. Or I would sort of notice how they would use graphing calculators. And I, "What? Like, how are you...?" I would kind of cock my head and raise my eyebrows. How could these really good teachers be using these really good materials but kind of misunderstanding or misapplying things like that?

Kim  13:46  
Yeah.

Pam  13:35  
And it took me a little while to kind of ferret out what was happening, but I realized two things. I realized that one, I was kind of looking at everything through a particular lens. And in a huge way... I know I've shout out to Cathy Fosnot, Maarten Dolk before. But in a huge way, I caught their stuff early, and I was looking at things through their lens of a landscape of learning and a modeling lens that was pretty unique and a little bit differently. And we're going to talk more about that in the podcast about that unique lens. But because I was looking through that unique lens, I sort of looked at things in wherever it was coming from, and I was kind of able to make... I was able to take from it the really good stuff that fit and kind of ignore the stuff that didn't kind of fit in that system. And then also, I was looking at things from a higher math perspective. I would meet a lot of elementary experts that were inadvertently kind of using rules that expired or were doing sort of things that kind of looked like they work at the elementary but didn't really follow through with the higher math. And so those two underpinnings were really important for me that they were the lens through which I looked at everything and did everything.

Kim  14:21  
Yeah, so why is that important? We see a lot of teachers who sort of sway in the wind a little bit. And what I mean by that is they try whatever new thing comes out. And we're suggesting that you need to have a system of beliefs, and then weigh that new thing that comes up against your system of beliefs. You need to know what you think about how kids learn math and really what math is, so that your decisions are based on that foundation. It's less about, you know, "I need this engaging thing to do today, and what's Pinterest got," and more of "What's the mathematics at hand? And how can we best get students' minds around those ideas?" And I'm not saying that Teacher Pay Teacher or Pinterest is full of garbage. There's some great things out there. But you really need to have a discerning eye based on what you're looking for. Is it the math or the attractiveness of the game or the worksheet? 

Pam  15:39  
Yeah. And here's another way to clarify what we're talking about. Kim, you and I have some similarities. When we facilitate workshops together, sometimes people like would look at us and kind of go, "Oh, there's like the Pam and Kim show." And sometimes people might get the mistaken impression that what we're advocating, what we're suggesting is that they adopt our personality type. 

Kim  16:00  
Yeah, so we're not the same, and we have some differences, but we look similar. We have the same personalities. We're kind of outgoing and loud. But it's more that we have the same philosophy on teaching. 

Pam  16:12  
Yeah, so here's another way to exemplify that. You have a teaching partner that you taught with for years. Her name is Monica. My personal kids had you two. It was wonderful. So, tell us a little bit about you and Monica in that teaching partnership.

Kim  16:28  
Oh, so Monica and I are nothing alike, personality wise. She's quiet. She's very relaxed and calm. And she has different interests than I do. But we made a great partnership in co-teaching because we share the same vision and philosophy about students, and the way they learn, and the way we taught. We didn't really struggle with each other's practice because, more often than not, we believed the same things and wanted the same things for our classrooms.

Pam  16:53  
Like, when you guys planned together, you were totally able to plan together. You're on the same page as far as math and math teaching and what it meant or how kids learn. And so, because you had those things in common, you really worked well together.

Kim  17:05  
Yeah.

Pam  17:06  
And then similarly, but different, Kim had my kids in her class, and so I would see stuff that you sent home, right? And sometimes I would look at the stuff you sent home, and I like, "Kim!" 

Kim  17:15  
And I'd smile and say, "You can read the directions, Pam." 

Pam  17:21  
Because I had just like glanced at it, and I had kind of had a knee jerk reaction to... Like, I would see it, and I would go, "What in the... Oh. Oh." And then when I actually read the directions, you had rewritten the directions, so that they were good directions. And you took what would normally be kind of a lame, dumb worksheet, but you made it into something really mathy, really where kids were using relationships and connections. And I kind of all too often would have this kind of quick reaction. So, I learned to look at what you sent home and really weigh out why would... And sort of trust you a little bit. What did Kim have in mind? "Oh, that really is good work for kids to do." Because you have this cohesive vision about what it means to learn math and what real math is. And because of that, Kim, I can hand you any resource, and you can find a really cool way to use it.

Kim  18:14  
Yeah, sometimes we're not given choices, right? There's things that you're told you have to use, but I could choose how I was going to use that resource.

Pam  18:22  
Yeah, and you did it really well. In fact, there's still times today where I'll look at something, or I'll be sent something, or someone will ask a question, and I'll call you up. I'm like, "Kim, what's your gut instinct on this?" because you'll have a way of helping me maintain my integrity about like how does this sort of sit in our system of beliefs. Just yesterday, I hollered at you, and I said, "Hey, somebody just..." And I'm not going to get a little picky because I don't want anybody to know who I'm talking about. But somebody proposed something on social media and I had this gut instinct of like. "Eh. Like, no." Like, it worked against what I... But I couldn't quite ferret it out why, and so I gave you a call, and I was like, "Mm I right on this?" And you kind of laughed, and you're like, "Yes." And then the more we talked about it, the more we were able to kind of go, "Oh, because it doesn't fit in our system. This is where it works against what we think about how kids really learn." So, y'all, if you're wondering what you get by listening to a Pam Harris podcast, or taking a Pam Harris workshop, or joining our brand new membership site called Journey. What is that thing that you get? What you don't get is a bunch of tips and tricks. If that didn't gimmick work, then try this one. If kids are disengaged, here's a song or a dance to try. You won't even get a bunch of advice from a lot of different educators unless that advice fits, unless it makes sense in our cohesive vision of math and math teaching.

Kim  19:48  
So, we want to challenge you, listeners, to take some time to think about and record. What do you believe about teaching and learning? Does everything that you do fit inside your beliefs?

Pam  20:00  
And make some decisions. Like, instead of picking something up just because it's flashy or it will make Tuesday more fun. Like, how does it help your students mathematize more? How does it help them gain a growth mindset about what it means for them to learn, and think, and use what they know, and build themselves as developing mathematicians? Alright, cool. So, if you want to learn more, check out the blog on the website, mathisfigureoutable.com. We love for you to join us on Wednesdays on your favorite social media at hashtag MathStratChat. And if you don't mind, and if you like our podcast and would give us a review, that would be fantastic and help more people find the podcast. So, if you're interested to learn more math and you want to help students develop as mathematicians, then the Math is Figure-Out-Able podcast is for you because Math is Figure-Out-Able!