Intro

Kyle Pearce 0:02

We came in as these like, math geeks, both wanted to be math teachers. And it was sort of like, one day we were in the classroom and finally realized that other people don't like math, and that's a real shocker, especially when you've gone through schooling and you have this excitement, you want to share it with students. And very quickly we recognize that, Oh my gosh, the majority of the students that we've been entrusted to actually educate are not on the same train as us.

Vanessa Vakharia 0:32

Hi, I'm Vanessa Vakharia, aka The Math Guru, and you're listening to Math Therapy, a podcast that explores the root causes of math trauma, and the empowering ways we can heal from it. Whether you think you're a math person or not, you're about to find out that math people don't actually exist. But the scars that math class left on many of us definitely do. Oh, and don't worry, no calculators or actual math were involved in the making of this podcast. Guys, big news. This is the first time I've had two guests on the podcast at the same time. Editing was a nightmare, David wants to kill me, yet here we are and it was totally worth it. Today you're going to meet Kyle Pearce and Jon Orr, hosts of the podcast Make Math Moments. I tried to start beef with them, but it didn't work because they're like both actually so nice and Canadian. So, and instead we ended up having the best chat about how to authentically fuel curiosity, the roots of math trauma, and why some people just hate math. Most shocking of all, we actually did math on the podcast, which I know goes against my little disclaimer in the show intro, but whatever, it all worked out. I think. Anyways, let's dive in.

Turns out some folks hate math

Vanessa Vakharia 1:40

Okay, Kyle and Jon, welcome to the podcast. I'm so excited to have you here.

Kyle Pearce 1:45

Hello!

Jon Orr 1:46

We're excited!

Vanessa Vakharia 1:47

This is the first time I've ever interviewed two people. And I actually, like, do people know your names? Or do they just know you as, like, the Make Math Moments bros?

Jon Orr 1:54

I don't know. I don't know. You know, I've never really asked anyone if we were the math people or like, do you know who we are?

Kyle Pearce 2:01

But Jon, you gotta, the people who do know one or both of our names always get it backwards.

Jon Orr 2:07

That's true. That's true.

Kyle Pearce 2:08

So at conferences, people call me Jon all the time, and they call Jon Kyle,

Vanessa Vakharia 2:15

all the time. Which is fine. Well, I didn't know who was who until literally this moment.

Kyle Pearce 2:20

I don't think

Jon Orr 2:20

We're one person. That's, that's, what everyone thinks. You know, we're one person, talking to ourselves every day.

Vanessa Vakharia 2:26

Okay, can you, I, I rarely do this, but I'm so confused about what you two actually do. can you tell me what you do?

Kyle Pearce 2:34

I wish we prepared for this, Jon, cause I'm not sure either.

Vanessa Vakharia 2:37

What is your role? Like, why are you here? I know that you have the Make Math Moments podcast, which I've been a guest on. I know you have the Make Math Moments Teacher's Conference, which I can't wait to talk about because it's one of my favorites. But like, what's your nine to five? What's your morning routine? Like, what's your mission?

Jon Orr 2:52

Well, up till the last, you know, year, uh, we have been, practicing classroom teachers. So, you know, our mission is to help change math instruction for a million students, in terms of trying to get more engagement, but also create that, uh, you know, positive and productive disposition towards mathematics that most people, you know, don't have, you know, knowing you this podcast, Math Therapy, you know that, like the people have this like need to go through math therapy. We're trying to change it from the classroom level.

Vanessa Vakharia 3:23

Kyle, it's your turn.

Kyle Pearce 3:24

I think for both of us, early in our careers, we came in as these like, math geeks, you know, like we both got math degrees, uh, separately, different universities, never knew each other, both wanted to be math teachers. And it was sort of like, one day we were in the classroom and finally realized that like other people don't like math, you know, and that's a real shocker, especially when you've gone through schooling and you have this, you know, this excitement, you want to share it with students. And then you go in, and very quickly we recognize that, Oh my gosh, the majority of the students that we have to interact with each day, that, that we've been entrusted to actually educate are not on the same train as us. And we could do one of two things. We could just do it and say, we put it up on the board we did what we had to do, we checked off the curriculum expectation and moved on, or we could start going down the rabbit hole and try to figure out like, how do we actually do this better? And, you know, for both of us, we took that path and I will argue that without making that choice, I don't know how long I would have lasted as a math teacher, because that would have been really tough to do for 30 years straight if we were just trying to do the same thing over and over again, expecting a different result.

Vanessa Vakharia 4:47

Were you surprised? Like, were you surprised in the classroom that like, people weren't into math instruction the way you were? Like, were you like in there being like, Oh fuck yeah, I'm going to spread this, I'm going to like be teaching math and you're factoring quadratics and you're like, why does everyone hate this? Like, was,

Jon Orr 5:02

I don't think so. I don't, I don't remember. Like, I remember that was the gig, the gig is that you're, you're in a math class and you know, like Kyle, like I think when you said you'd like, you were surprised that other kids just didn't like math, like, I don't think I was surprised the kids and like my peers didn't like math. Everyone says it, you know, everyone says like, Oh, you're a math person or, you know, like, Like, you're, you're the math geek, I'm not the math, like, it's, it's, it's just common, common phrasing.

Kyle Pearce 5:25

Maybe I was the only clueless one.

Vanessa Vakharia 5:27

Kyle, were you surprised?

Kyle Pearce 5:29

I I guess like I knew that there were some people that didn't enjoy it but I don't know if maybe I just thought that somehow they'd like it better from me. Like maybe, it was like, people would like me more, or I could do this better. And then you go to do it, and then you realize that, wait a second, I haven't brought anything different to the table than what was taught, you know, all these other years to these students. And I think that was the part that hurt.

Jon Orr 5:56

I think you go in right, like you go in going like, I know kids hate math and I'm going to make it better. I'm going to do it better and I'm going to like make sure, and then it hurts when you're you know you're trying different strategies in there and it's like all of a sudden that strategy you thought was going to be like, that's going to be the one that turns that kid into a math believer, and it doesn't, and you're like, Oh man, what's going on here? And that kind of like takes you a step back going like, Oh, I feel deflated now because I put so much effort and thinking and work and emotion into this lesson and it, and it falls flat sometimes.

Vanessa Vakharia 6:30

I think that's probably so relatable to teachers. When you say you're like, our mission is to like, help, you know, a million students become math believers, as you put it, what's your like thing? Like, how do you do that? Like, are you like, ooh, it's like open middle problems, it's, you know, low floor, high ceiling, it's like some whiteboard. It's like, do you have a thing?

Jon Orr 6:49

I think, those are all like structures. Those are all resources. Like those, like, we've got all of that that we grab. And I think where we're like, Oh, I'm gonna, I'm gonna, I'm gonna do the open middle problem. I'm gonna, you know, I'm gonna do a three act math problem. Like, I'm gonna like put all these things that I've been searching on the internet for, for years. And I've got this, database of, things that I think work, but what we like, to do when we Kyle and I, this is actually how Kyle and I kind of partnered up together is, is that we were looking at what is going on in our lessons that makes this one engaging, but that one fall flat? Like what is going on here? And then we ended up doing a presentation at O. A. M. E. You know, years and years and years ago, 10 years ago together on on that. And it was, we realized that there are elements all of these things have in common. You know, if you're doing an open middle problem, what is going on in that that engages the students more than your typical lesson? Or like when you're doing a three act math problem, like, why is that, or how do you structure it so it's the same as the open middle problem? So what we realized, and this is not like rocket science here, but what we realized is that, you know, when you're in teachers college, they're saying you got to have a hook. And really what you're saying is like, I have to draw my students curiosity in somewhere, and I have to create that curious moment. And when you have an open middle problem like that, there is curious moments at the beginning. You've, got this task to do, and then all of a sudden this middle, it makes it very curious. What happens if I change this number? What happened when I changed this number? Like you're creating that. You give those students that opportunity to kind of step into a lesson and start asking questions that they weren't going to ask before when you just like, Hey, I'm just going to teach you how to solve two step equations. No one's wanting to know that answer. But if you create that curiosity moment, you know, to begin your lesson to go, Hey, I'm going to create an environment and an experience where you have to, you have to kind of step in with curiosity, then that allows us to go into in depth and kind of fuel sensemaking. Because for years, Kyle and I started with curiosity and go, how do I create these curious moments? But then it was like, as soon as I got them hooked, it's like, ha ha, I'm going to switch the gears. And now I'm just going to show you how to solve two step equations and not actually get thinking out of this. So it was like, well, now we need to fuel sensemaking once we have that part. And that's actually where our lessons, you know, really came together. It was like, we got their curiosity. We were engaging them, but now we're really focused on the mathematics, the conceptual understanding of mathematics. Part of the engaging part of a lesson is getting that curiosity, but it's actually more engaging to get your students thinking on a regular level instead of just giving them everything. So it's like, how do you structure that part? So when we started structuring our lessons that way, that's where we started to see the change. And that's kind of like morphed into how we try to make sure we craft our lessons, craft the resources that we make, talk about how to engage, help teachers teach that way, because most teachers, they're not sure how to do those things and are scared to do those things, or don't feel equipped to do those things, or don't have the background knowledge to do those things.

Fuelling curiosity

Vanessa Vakharia 9:43

Kyle, so one thing, um, Jon said that I loved, I love that you said you talked about creating mathematical experiences for students. Like this idea of, because when I think of an experience, I don't think about a question, I don't think about a lesson, I actually think about a holistic view of like what their entire experience is, like both emotionally, like mentally, physically in the classroom. You, one of the cool things about interviewing you guys, like because I haven't interviewed like another podcaster, is that you've had like everyone on your podcast, so you've heard about every single like new framework, and new idea and whatever. What to you is like your most favorite like framework or resource or like perspective that's come out of your interviews with guests that you think kind of fuels this idea of creating a positive mathematical experience that's rife with curiosity. Like, do you have anything?

Kyle Pearce 10:32

What I would say is, you know, kind of goes back to what Jon was saying is like, what are those elements? And I would argue that we in education and we, we are guilty of it, like Jon and I were there, we did this for many years. Where it's like you find a resource, or an idea, and then you kind of like, you know, you had mentioned open middle, uh, Jon, you mentioned three act math tasks, like Jon and I kind of went down the three act math task rabbit hole for a really long time. And I'll be honest, was like great at the start, but then it was like the rest of the lesson was still flat. It was a great curiosity sparker, but then it was like, we didn't have the tools to do it well. And I'm going to argue that any other structure or, or any other resource can lead to the same result, if there isn't more there for us to dig into. So what I mean by that is let's say, uh, you know, an open middle problem. If you just sort of go, here's the problem, go do it. And then the kids do it and then that's it. And you move on. It's going to lose its luster, And really what it comes down to for us was like, how do we question students so that they're doing more of the thinking, talk about Peter and, you know, building, thinking classrooms and all of that work, how do we do that? And then how do we bring it back together, and tie it up with a bow? Like how do we consolidate it in a way that students are going to walk out of this classroom and not just think I solved a problem about blank, but actually get a better understanding of the mathematics and the behaviors of the mathematics. And that's something that I think is really easy for us to miss. And here's the sad reality. You can have a fully engaged group of students working on a really amazing task, and they could walk away and the vast majority of the students may not actually understand what it was that they learned or be able to apply it to a different scenario that is similar, that follows the same big idea. And that to me is the part that I think we struggle with the most in mathematics education. And that's what sort of captivated Jon and I around this work is like going down deeper and going, okay, how do we ask students to get them to lean in? How do we give them good problems, but then how do we be intentional about it so it's not just like entertainment, you know, like we're not in there just entertaining kids or giving them something to keep them busy, but rather that there's a very intentional goal, that at the beginning you were like, I knew this was going to happen, there's always surprises too, but you're like, I did it this way so that you hit this part in the journey and now, I'm going to step in and I'm going to do something very specific based on what you've done so far, and I'm going to use all of your thinking and I'm going to help you to make sense of the behaviors of mathematics. That's like a Kathy Fosno line, she talks about the behaviors of the mathematics. And only when you understand those behaviors, can you actually start thinking mathematically. And only when you feel confident to think mathematically, can you truly feel a productive disposition towards the mathematics. Cause that's when you start to trust the mathematics and you trust that you have the tools in place to help you work your way out of any issue or any situation that you might find yourself in.

Bridging the teaching gap

Vanessa Vakharia 13:54

I mean, look, I'm going to be honest here. Everything you said sounded amazing. It sounded so good. I'm listening to it, I'm like, yes, you're bringing trust into it, which I can't wait to talk about. But honestly, at the end of it all, I still, I'm like, I don't know what you mean and I bring this up because I actually think something you guys are really, really good at is, uh, creating ways for teachers to take these philosophies and actualize them in, in their classrooms. And you're talking about that, but I need an example because I'm listening to this and I'm like, I still, like, I still don't know what you mean. So I started with an open middle problem. It was all good. People were curious. And then you keep being like but that's not enough and we have to like, get the, but what, what is everything you just said mean? Can I have like an actual example?

Kyle Pearce 14:44

Absolutely.

Vanessa Vakharia 14:45

Was that mean? I just, like, it sounds like these really good words but I don't know how it like actually works.

Jon Orr 14:50

I'll, before Kyle gives you the example, because he's got a good example, But, Kyle and I actually for the last couple of years have, you know, worked with school districts on a regular basis. So that's also what we do during the day. Is in help them shape the structure of the math PD that they're giving their teachers. And what we're finding, you know, what we're finding is that is, and we used to, we used to travel, you know, across North America and go in and do a, you know, a one hour session or a full day workshop or, those types of things. But we would leave and, you know, there's remnants of what you did, but there's no like real lasting change. And, and the work that we've been doing, we've actually uncovered, I, I think it's not, it's not like we uncovered it, but I think it's kind of like, it just needs to be pointed out that so many of the, the routines, you know, those things that we just said, an open middle problem, you know, Dan's three act tasks or, or any of the other structures that we, you know, we, we've mentioned

Vanessa Vakharia 15:42

I like that you're calling them structures.

Jon Orr 15:44

Yeah, because they are, they're like framework structures, you know, routines that we're doing in our classroom. It's like every, every one of those. So if you think of Peter, uh, Liljedahl's, you know, Building Thinking Classrooms, his 14 practices. Like we're asking teachers, like all of these ask teachers to step away from the, the, you know, the tested I've done this for years. I'm just going to lecture. I'm going to give you the content. And then I'm going to ask you to practice the content. Why, why teachers have relied on that so much, especially, especially middle school and lower teachers is because they're, they're not confident with the, the mathematics. They don't, they're not sure why things work or how to represent them differently than the standard algorithms that, that we, we've been, you know, we've learned. So what we're asking teachers to do and why there's pushback on different strategies is, is that we're, all of these school districts have been asked teachers to go like, I want you to teach like Peter's classroom. I want you to do this, this open middle problem. I want to do this, but you're asking teachers to go like, wait a minute. I, I only have been doing the lecture because I'm not sure how all this works. And if a kid asked me stuff, or I'm not sure exactly how to phrase it differently or, or even model it differently because I just have this script that I've been following for years. And that's just what I was taught when I was a kid. And instead of going like, we want you to stop that. We want you to actually like give kids the freedom to solve problems, and you now have to not only allow that in classroom management in the classroom to do those things, but you also have to be ready and knowledgeable enough to interact with the way a student does solve a problem that's different than the way you know how to solve the problem. What happens if they solve it this way? How do I know that that's wrong? Now it's scary for teachers to do that. So what we're saying is like, when we've been partnering with school districts, most are asking teachers to change instruction to this, but not equipping them with the background knowledge on understanding how to solve problems differently, what models or strategies that those teachers can use that help create fluency different than just showing standard algorithms, and then building that conceptual understanding so kids can move towards procedural fluency, which is like, I can do this, you know, with, with my eyes closed, but real fluency, like I can do this with my eyes closed this way, but I could pivot over here and model it and show you this way. Like that's real fluency, like being able to like switch in between different, uh, representations of the mathematics. So that's like a long winded way of kind of, I think, saying what Kyle is saying, but Kyle, why don't you give the example.

What does "understanding" mean?

Kyle Pearce 18:15

Well, here, here's, I'm going to share at least one of the biggest challenges that we have in order to do this well. And it's really does come down to conceptual understanding. So Jon talks about this fluency and flexibility, which is, which is a part of the conceptual understanding. And the reality is, is that most of us, and Jon, you said middle and, and lower, I'm going to argue that like, all of us, like K through 12, and beyond in many cases, actually don't necessarily, like there

Vanessa Vakharia 18:45

I, 100%. I'm a high school math teacher and I have no, like seriously, I, no one ever told me why flipping and multiplying is what you do with division. Deborah Peart taught it to me two months ago and I was like, like, I, I didn't even know and I didn't need to know and I've never even questioned it.

Kyle Pearce 19:01

Yeah, totally. And, and this is the thing and it's the kids who trust blindly. I was that kid. Jon that kid. It sounds like maybe you were that kid, right? The kids who trust blindly, and are able to memorize steps and procedures, traditionally have been what we call the math people. And people say, there's no such thing as math people. I'm like, heck yes, there is, in that world where math is only memorization. Of course, there's math people because not everyone's going to be able to memorize something blindly right? That's the reality of the situation. I believe if we do it actually holistically, like you're saying, but then also looking at all five proficiencies of mathematics, we can all be amazing mathematicians. But the difference is, is that you can't just turn that on. It's not like all of our teachers in the past have been like, you know, we don't want to pull out the whole conceptual understanding thing because like it might, be, you know, it might like let everyone understand it, you know, like it's like, no, we just don't know it. The example that's so easy. You talked about why flipping and, and multiplying for dividing fractions, why we've never known it. Well, I'm going to go even earlier and say, I never knew that there was two types of division. Right? Like dividing two whole numbers, you are always dividing with one of two structures. Use that word again, structures of division and what you might be like, what the heck are you talking

Vanessa Vakharia 20:28

I, my face is saying, what the heck are you talking

Kyle Pearce 20:30

Exactly, this

Jon Orr 20:31

Wait, don't I just divide two numbers and boom, there's an answer?

Vanessa Vakharia 20:35

Yeah, what are you talking about?

Kyle Pearce 20:37

Absolutely. Absolutely.

Vanessa Vakharia 20:38

Like 10 divided by five.

Kyle Pearce 20:40

Yeah. So now let's think about with context, right? With numbers. Here's the crazy part. If you use naked problems like 10 divided by five, what you'll tend to do, tend, not ten to do, tend to is you're going to use you're going to naturally do the division structure that fits the numbers easiest, without even knowing it, right? So in certain cases, like you'll be like, okay, let's do, let's, let's pick an easy one. Uh, let's go 10 divided by two. How, like, you know, the answer, I know, you know, the answer, but you had to actually like explain how you're going to divide that, tell me how you're going to do it.

Vanessa Vakharia 21:19

Well, this is so interesting because I was just teaching a grade 8 kid the other day and realized he didn't know what division was because when I said 10 divided by 2, he did this. Oh, sorry. I'm, I'm, I'm making a splitting motion with my hand and he was like 5. And then when I was like Okay, what's 20 divided by 2, if I said 2 he could split it, if I said any other number he didn't know what to do. What I'm doing, when you say 10 divided by, I don't know what I'm doing, 10 divided by 2, I mean I just I know it's 5, but I think I'm thinking like 2 groups of 5, I think.

Kyle Pearce 21:49

Interesting. So two groups of five. So now let's think about this. When that student went like this, that student actually really understands one of the two types of division. That's partitive division. You put

Vanessa Vakharia 22:00

What the fuck, I've never heard this.

Kyle Pearce 22:03

Yeah, I know. This is the crazy part. Neither have I. I mean, now I do, but I just said it, but I went and I got a math degree and I never recognized the fact that sometimes ten divided by two means make two groups and other times it's like make groups of two and count how many groups there are.

Vanessa Vakharia 22:22

What? Pause. Pause. When it mean that? What? Ten divided by two is making five groups of two. Like, I know that works, but like, why would you think of it that way?

Kyle Pearce 22:34

So now let's think about this. Now let's layer in context. I got 10 apples and I have two people, right? What are we going to do if there's 10 apples and there's two people, even very young children know what this is. They're like, you don't have to say it's division. You say there's 10 apples and I want you to give them fairly to all the people. And they go, Oh, one for you, one for you. That's called

Vanessa Vakharia 22:58

Uh, what's that called?

Jon Orr 23:00

Fair sharing

Kyle Pearce 23:01

Yeah. Fair sharing. It's like here, one for you, one for you, one for you, one for, Oh, each person ends up with five each, but that, what that is is that's one type. Because the other option is you could say, Hey, I got 10 apples and I want everybody to get two apples each. Hmm. Now it's different. I can't fair share that, or at least share in the same way. I could, I could go like two for you, two for you, and then I just keep going until I run out of apples. Before I was going, okay, one for you, one for you, one for you, till I ran out of apples. Which might seem like it's the same thing, it's actually very different.

Vanessa Vakharia 23:41

This is the most math we've ever done on this podcast. Like, this so crazy for me and our listeners.

The roots of math trauma

Vanessa Vakharia 23:47

So, okay, Kyle's been talking for this entire time, so now it's Jon's turn to speak, because we can't tell your voices apart. How do you think, this is a podcast about math trauma. and math therapy. How do you think all of this stuff, I mean, this is actually really blowing my mind, but all, one thing that really stuck with me is you said, because you know, teachers are so strapped for time. And the biggest conversation right now is like, I love it, but I don't have time. I love it but I don't have time. How does the way we currently teach math versus this idea of true understanding, how do you think that actually affects kids when it comes to the development or triggering of math trauma? Like, is this something you've thought about?

Jon Orr 24:23

This is, I think why so many students develop that math trauma, is because they're not being brought through this process of going like, I'm put in a position to want to know the answer to this. And then I also want to be put into a position where it makes sense to me. And I think, I think that's where the trauma ends up coming from. We end up saying like, you just should know it because the teacher also doesn't know it. They're not saying like, like, well, why do I flip and multiply or why, you know, in this particular thing. And the teacher's like, that's just the way you do it. But then that creates like a lot of conflict in us to go like, but I want to know the answer. And then all of a sudden there's like an animosity towards the teacher, there's animosity towards mathematics itself. Going like this, but there's no good answer, now it doesn't make sense to me, math doesn't make sense to me, math is not for me, I hate mathematics. And it's because, if we don't have good answers to these wonders, these questions, this connection towards why this makes sense, like as long as you can make it sense for a student, this is why it's like, it made sense to you because you were like, I can follow that pattern, right? For you, it was probably like, cause that was true for me becoming like, um, you know, a math teacher is like the teacher might say, do it this way, and I would say, Hey, look, if I do it that way every time, it works, that makes sense to me, because I'm not really like seeking, I wasn't back then, seeking like the real understanding answer. And it was only until I met students who were like, but why? Like I need to understand the why. And talk to adults who have that like animosity towards mathematics also were like, I always wanted to know why, but no one could explain it to me. And then it hurts, it hurts. So I create this, like this barrier that I can never get over, and then that's, that turns into that trauma.

Does everything have to be everything?

Vanessa Vakharia 26:17

So, I'm finding with a lot of my conversations with people, and I ask this personally, because I'm writing a book right now on math therapy, and I know this is going to happen to me too, where people, like, will read a framework or a structure, like, you talk about it, and you're like, yeah, like, it's really great, but it doesn't work unless you do this, or, like, this thing, but, like, first you got real, What responsibility do you think the person has who's creating this structure to, like, talk about every single thing that needs to be in place for their structure to work. Like, I'm finding it, like, actually really hard to navigate this space where, like, everyone needs to be responsible for everything. And, like, I guess this is just a personal thing for me because I'm like, I know people are going to read Math Therapy and they're going to be like, Okay, great, but, like, she's not talking about conceptually understanding a problem, so it's not going to, like, I don't know, I'm feeling, I need some advice. Like, how,

Jon Orr 27:04

Yeah, I think there's like, there's, there's like, what do you call it? Like, uh, like buckets, there's buckets that we all need to understand. And you know, you're talking about one bucket doesn't necessarily mean that your job is to teach all the other buckets that fits with your bucket. But as a, as a profession, you know, if we are wanting to see our change in our craft, if we are dedicated to changing instruction for students so that we can meet their needs and put away this math trauma forever, you know, for every student, I need to, as a professional, decide on what buckets I need to fill for myself. So it's like, I, I need to be like, there's the conceptual understanding bucket or, or understanding math or my roots. We, you know, Kyle and I, when we work with school districts across North America, you know, we, we help them craft a plan to meet six different areas of, of math professional development in their, in their district. So one of those is the roots, which is what Kyle gave that full example on. It's like really understanding the mathematics. We really need to fill that bucket for the teacher so that they're in a position to work on the other bucket, which is our pedagogy, our moves in our classroom. You're filling the bucket of like mindset and thinking about how to think about mathematics and beliefs around mathematics. So, you know, your filling that bucket with your book doesn't mean you have to go and go, Hey, I also need to fill this bucket, but the, these, these kinds of areas exist and they're all intertwined. And I guess Kyle's got up on the screen right now is like, we call these like the pieces of our tree. We're growing our mathematical tree. And the roots of the tree are like the way we understand mathematics at a conceptual level, and then you're talking about the math, you know, mindsets, beliefs, our connection towards mathematics, we call it the soil, the water, the sunlight, which helped the roots grow. There are other areas, you know, there are other areas of the tree as well that can see on the screen, but there's so many, so many different, you know, areas that we all can work on like, as a teacher, we should work on these areas and it doesn't mean that, you know, you just have to work on one or, or fill them all. Does that make sense?

Vanessa Vakharia 29:10

Well, it makes so much sense and I'm so glad you said it because it's way better than the way I've been saying it. Like, I just find people are really at each other's throats being like, this person's about this thing, but it's not as important as this thing. And it's like, I keep being like, no, you need all of this stuff. Like, that's the whole point. But I really like, almost the way you're saying it, of being like, this is about us in our profession, being able to be self reflective and be like, look, here are the things I know I'm really good at right now, here are the things I'm lacking, and seeking out that professional development, those resources, like help where you need it. It's like being like, look, I really need to go to a therapist for these specific issues. Like, I don't need to talk about these, you know? So like, yeah, I love this. I really love it.

Kyle Pearce 29:49

Our biggest, like, you know, what we try to advocate to those educators and in particular, the district leaders that we work with through our district improvement program is that you want to focus on everything, but you really do have to decide, like, where are you going to start? So maybe someone might be focusing on the beliefs and mindset as a start, but where I think we run into problems is as if we look at one thing as it is going to fix all.

Vanessa Vakharia 30:16

Yes. Yes.

Kyle Pearce 30:16

And that's really the key. So for us, it's about awareness. It's not, you know, we don't want people to be overwhelmed. That's why we use this, you know, nice tree analogy. So it's easy enough to like, remember. But it's like, hey, like Jon and I, we admit wholeheartedly that for many, many years, we focused primarily on the actual leaves of our tree and maybe a little bit about the branches, right? So the leaves being the resources, right? Like we were focused on that and how we delivered it, which was, for us, it was engaging, three act math tasks, that sort of, but we didn't know about these other pieces. And in particular, the roots, which we like the idea of the roots is that they're hidden. They're underground, but they're really, really important. So that division we just talked about, it's always been there, but it's been hidden in the background. And I'm telling you right now, you could spend the next 10 years in a district, in a school, in your own classroom, focusing only on mindset and beliefs. But if we forget why we're feeding the tree, the water, the sun, the soil, the soil, that's to help develop the root structure. It's to help develop the limbs. It's to, you know, it's to do all of these other things. And I think if we, if we look at it that way, you use the word holistic, I love it, because like, we have to look at math improvement in the same way. It's not that one thing or one structure or one idea or one area is going to fix it. I'll argue that, you know, our branches were really strong, like we had really good pedagogical moves, but ultimately, the rest of the tree was like suffering, right? Like our, our root system was weak, you know, the, the trunk wasn't developing. The, the limbs of the tree weren't developing. It was like, we were doing that one thing really well, and a lot of people actually said like, these guys are really good math teachers at the time, and our scores weren't getting better. Like it was like, kids enjoyed

Vanessa Vakharia 32:13

Oh my God, you're going to bring up test scores at the end of the fucking podcast? No.

Jon Orr 32:18

He didn't say it. He didn't say it. He didn't say it. Don't worry.

Kyle Pearce 32:20

No, I didn't. I didn't say it at all. But you know what I would say, though? Here's what I will say. And we don't have to go deeper into it. But ultimately, the whole test score thing in the long run, if we develop all six areas, those will change. I don't care what questions are on the test because kids are going to better understand the math, they're going to be confident enough to do it, and they're going to be fine. But the problem is, is we focus on, you know, we always talk to our district partners, we're like, how are we going to measure the change we're making? And they go test scores. We're like, well, the problem is, is that test scores aren't going to change this year. So how are we going to measure what we're changing now to see if what we're doing now is actually helping us move the needle. It's not going to move the test needle this year. And I'm going to guess that until you fix all six areas of that tree, we're not going to see the actual test scores change, unless you just get lucky and you got that one group of students that was going to do pretty well on that test anyway, like it has nothing to do with these things that we're doing on a daily basis in the district, in the schools, in the classroom, that's a much, much longer road for us to actually change the scores. We've got to change the details here to monitor. If you look at the tree, you're going to go, wow. The tree's greener. Wow. These branches are getting stronger. Wow. The root system's getting wider. Like all of those things are going to be what you'd measure when you see that you're working on those different areas. We can't just say, how good is the tree? You know, like how healthy is the tree at a general level? That's not going to actually do it. And the same is true for math.

Vanessa Vakharia 34:00

Wow. Snap, snap, snap. We are on the final two questions of the podcast, my friends. I mean, that was, that was just beautiful. I'm going to need you to answer these questions in 30 seconds each. Okay,

Jon Orr 34:12

Let's do it.

Q1

Vanessa Vakharia 34:13

Okay, so the first question, and we'll start with Jon, is what is the one thing you'd like to see change about math education? One thing. 30 seconds, go.

Jon Orr 34:22

I would like to see the professional development towards math education change to be more about, you know, that content knowledge, the roots of the tree. Too much of our choices are about the pedagogy and going like, we need this pedagogy to change, change, change the pedagogy, hey, we want all of you to change your pedagogy, but we're not actually preparing you to change that pedagogy by giving you what you need to change that pedagogy, which is really the understanding of the mathematics. We say pedagogy, but we really need to help teachers just grapple with the way they've been doing mathematics just with math problems themselves and not have any real, real obligation at this point to do it with students, you have to do for yourself first and really think about how the strategies and the models you've been using and how you could be doing it this way. Get comfortable first, and then you can start to think about how that, that evolves in the classroom.

Vanessa Vakharia 35:16

You guys cannot talk for 30 seconds. You can't do it.

Jon Orr 35:20

I did it. do it, it 30, I timed it.

Vanessa Vakharia 35:24

Okay. Kyle, your turn. What's the one thing you'd like to see change?

Kyle Pearce 35:27

You know what, I would say I would love

Jon Orr 35:29

Won't be able to do it.

Kyle Pearce 35:30

For us, this is hard, stop taking my time! Uh, what I would love is I would love for us to take number sense and operations, and I would love to take them out of the math program for a little while and make it its own little separate subject

Vanessa Vakharia 35:45

Wow.

Kyle Pearce 35:46

And have the rest of math kind of like be in this other little subject for a little while. And just like really make sure, really, really make sure that we help people understand, including educators, understand number sense, fluency and flexibility with numbers and operations, because I think the rest of the job gets so much easier when we do it and do it well, and I'm not talking about just memorizing facts.

Vanessa Vakharia 36:09

I think that was 30 seconds. He, that was, that was succinct.

Q2

Vanessa Vakharia 36:12

Final question. What do you say to someone, Jon, who just is like, this is really great, everything you've talked about, but like, I'm just not a math person.

Jon Orr 36:22

Well, I think we've been, we've been chatting about that, that we

Vanessa Vakharia 36:26

You're wasting time.

Jon Orr 36:27

We, I am, I am. We do need to see ourselves as math people. And if we're saying we're not a math person, then then we need to think about what does that mean? And why am I saying saying that about myself? Because we have it in ourselves to do what we want to do, if you want to become, you know, a math person, or you want to become better at mathematics or your understanding of math, you can do it. You just have to choose that. Like, like you, you could choose to go on, you know, run a marathon. Everyone could do it. But you just have to choose to dedicate yourself to making that happen. And I think, I think that's the same with mathematics. It's like, I could just say I'm not a math person, but if you're, if you're dedicated to making this change in yourself, you can make it happen.

Vanessa Vakharia 37:11

Thank you so much for that succinct answer. Kyle?

Kyle Pearce 37:14

I would love to see us focusing on making the experience one such that people won't have that problem. And what I mean by that is that means we in the education community specifically need to understand the mathematics conceptually well enough that we can teach it so that more students can understand it instead of memorizing it. And if we do that, I don't think we're going to have to convince anybody of anything, because they're going to trust the math. They're going to trust what's going on and they're going to be confident with it. You don't have people saying the same thing about literacy and reading, you know, maybe writing, some people may be like I'm not great at writing. I'll be fine if people are like, I'm not very good at writing down the math that I'm thinking about. You know, but it's like, I want them to be able to understand numbers, operations, how they work, how they behave. And if they do, then they're going to be in a much better situation where they go, yeah, like maybe I don't like math so much, like, I don't want to do it for my career, I don't want to, you know, whatever. That's fine. I'm not a big reader, but I know how to read. And I want more people to have that reality. And that really begins with us in the education community, to do the work ourselves so that we can help more students see that in themselves.

Outro

Vanessa Vakharia 38:31

So what I've noticed about your response styles, which I love, is Kyle always, Kyle's like me, where like he wants to wrap up his response in something like really clickbaity and powerful at the end. Like he wants to make sure he has a good soundbite at the end. So that's why it takes him a bit of time sometimes I think, cause you're like, I'm like this too. So I've really, I've noticed that about you and I appreciate it. Cause I'm going to have a lot of great soundbites and you both have great soundbites. But like, I noticed that you are like near the end of your response, you're like, and now how am I going to tie this into like a really good statement?

Kyle Pearce 39:07

I love it. I didn't know that about me.

Vanessa Vakharia 39:09

Well, now you know that about yourself. It's time to go. This has been fucking amazing. I, I loved it. I actually didn't know what we were gonna talk about. I was like, I just, like,

Jon Orr 39:16

We didn't either.

Vanessa Vakharia 39:17

It was, it was so much fun. It was really fun. And this division thing, like, I'm gonna go divide shit now. And I'm, I'm, yeah, thank you. Bye guys. Good times.

Jon Orr 39:26

Thanks so much.

Kyle Pearce 39:26

Thanks so much for having us, take care.

Vanessa Vakharia 39:30

Okay, wow, this episode really reminded me how important it is to inspire kids to understand math rather than just memorize it. That's where curiosity is born. That's where joy and wonder stems from. That's what matters most when it comes to students building meaningful relationships with math. If something in this episode inspired you, please tweet us @maththerapy, and you can also follow me personally @themathguru on Instagram, Twitter, and TikTok. Math Therapy is hosted by me, Vanessa Vakharia, it was created by me and Sabina Wex, and it's produced and edited by David Kochberg. Our theme music is by Goodnight Sunrise. And guys, if you know someone who needs math therapy or just needs to hear someone else getting math therapy, please, please, please share this podcast, and rate or review it on whatever podcast app you use. Those things actually make such a big difference for us. I'm determined to change the culture surrounding math and I need your help, so spread the word. Until next time, peace, love, and pi.