Ep 24: How Do you See Math?

Pam Harris  00:01

Hey fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.

Kim Montague  00:08

And I'm Kim.

Pam Harris  00:10

And we're here to suggest that mathematizing is not about mimicking or rote memorizing. But it's about thinking and reasoning, about creating and using mental relationships, that math class can be less like it was for so many of us and more like mathematicians working together, we answer the question, if not algorithms, then what?

Kim Montague  00:33

Today, we're starting a really exciting five part series that we're going to call Perspectives Impacting Pedagogy. In other words, how your perspective might be impacting your teaching practice.

Pam Harris  00:45

Yeah, so I've been a mathematics teacher educator for about 25 years. And I've seen lots of Ah-has. I've worked with parents, and teachers and students. And I get sort of a haunting question. There's a point where I work with people where they really are like, on fire, and it's clicking and they're using what they know, and relationships, and they're seeing the vision of how they can do it with students, and how they could create mathematicians. And then they sort of get this look, this very intense, personal look. And they ask me this hunting question, "Pam, why doesn't everyone teach math this way?". If it's so good, if it's so like this is the way we should do it, why don't more people teach mathematics this way? 

Kim Montague  01:34

Why doesn't everyone teach math this way? 

Pam Harris  01:37

Alright. So y'all, I've been thinking about this and interviewing people and polling people and I want to share what we've found. We've really been working on this for a while.

Kim Montague  01:48

So actually, you might hear this question, why doesn't everyone teach this way? And you might think to yourself, I don't really have any options, my admin or my instructional coach doesn't really give me a choice about my day to day lessons, or the routines or homework. And that's unfortunate. But that's not what we're talking about here. And we aren't addressing how to buck the system that you're under. 

Pam Harris  02:08

Yeah, no. So you might actually have more options than you think. It might actually be that your perspective is pigeonholing you into teaching certain ways. Like, for example, you might read your standards and because of your background, infer that it means, the standards mean to do certain things in certain ways, when in reality, you could be teaching more and more real math and actually hitting the standards in a more authentic way.

Kim Montague  02:34

Yeah, speaking of authentic, I think we're actually going to be sharing some details of ourselves in the next few episodes that will resonate with some of our listeners as well. You and I grew up with different math perspectives. And we're actually raising kids with different and changing perspectives. And I suspect that many listeners over the next few weeks will be hearing some of the comments and perk up thinking 'that is so me'. So let's just give everyone a brief overview of the three ideas that we're going to share in more detail over the next few weeks.

Pam Harris  03:05

Okay, great. So one idea. Some people think that the way they were taught is the only way. That's just what mathematics is, that's how to teach it, even though it did particularly work well for them. 

Kim Montague  03:18

Right. 

Pam Harris  03:18

So one of the perspectives we call the 'Z perspective'. So I'm a mathematician, so XYZ variables, mathy, whatever. So we're just gonna call this the 'Z perspective'. And that perspective is that mathematics is this thing I call 'fake math'. The teacher tells you what to do. you memorize it, you mimic the teacher in your work. you're solving the problem with those steps. That mathematics is all about steps and things to do. If you relate to this perspective, if that sort of feels like the way that you looked at math as a student, you might even be listening to this podcast and saying, "Oh, okay, Pam. All right, this sounds cool. So tell me the steps to do it."

Kim Montague  03:59

Right.

Pam Harris  03:59

So this is the perspective I grew up with where I memorized and mimicked, and I follow the rules.

Kim Montague  04:06

But that was not me. 

Pam Harris  04:08

Nope. Not at all. We call Kim's growing up perspective, the 'X perspective'. So mine was the Z. Kim is the X or was an X.

Kim Montague  04:18

Yeah. And so on paper, I looked like someone maybe with a Z perspective. I followed the rules for school math, but in real life, and especially once I left the classroom, in my head, there were a lot of patterns and relationships connecting, lots of like wondering and manipulating of numbers and shapes. And I asked myself a lot of questions and then made sense of things by solving and resolving.

Pam Harris  04:45

It's so interesting, like I did a lot of math right, but I did it when I was supposed to be doing math. And you were like looking at the world and wondering things and solving things and resolving and it's just such an interesting perspective and people with this X perspective tend to think that it worked for them. 

Kim Montague  05:05

Yeah

Pam Harris  05:05

That the way that you were taught worked for you because you were doing all this cool stuff. And so they continue to teach the way they were taught, even though in reality, they could have been doing far more and faster, if someone had been actively helping them develop all that real math, those relationships going on in their heads.

Kim Montague  05:23

Yeah, so X and Z. But then there's a last perspective. Talk about the 'Y perspective'. We both have people in our life with this one.

Pam Harris  05:32

Yeah. So it's funny, because when we were coming up with ways to describe these perspectives, we actually first called them A, B, and C, and then realized that people were thinking we were talking about grades. like, Oh, if you want to get an A or B, or C. No, no, it's not about grading at all. So that's why we kind of went to variables. So we've talked about the Zs and the Xs. The Ys are the group who cannot do it, unless they understand why. Now, caution, it's not about ability. I'm not talking about people who can't do it unless they understand why because they don't have the ability to do it. They could absolutely mimic. But it's more like this psychological thing. It's like this thing in their heart and their soul where they know they can understand. And they want to understand. And they also know that if they don't understand they won't be successful. So it's all about knowing why. And they just keep asking why. And they keep asking why. And if they don't understand why, they kind of throw their hands in the air frustrated, because they know they're not gonna be able to like, pick it up tomorrow. Some of them don't memorize well, but in a huge way, they don't want to have to memorize. They realize that if they could understand why, then alright, I can do your thing. And so they get really frustrated when we don't tell them why. Because typically, as a profession, we haven't taught the why. And so they've been left frustrated, and sometimes left behind.

Kim Montague  06:53

Yeah. So why spend several episodes on this topic? Because we want to acknowledge that in any given classroom, there's going to be a variety of perspectives. Probably all three, right? In a family or in a friend group or teaching team, there's probably going to be all three perspectives. And so it may be a part of why the conversation about how we should teach or why we should teach a certain way can get heated at times. 

Pam Harris  07:20

Oh, yeah, that's a really good point. We're coming up to the holidays here in the states. So you might be spending time with family, though during COVID I don't know who's traveling. But anyway as you spend time with families, or teachers, or when I work with teachers, as a teacher educator, the conversation can get heated. We've had crazy stuff on social media where the conversation gets heated. And we would suggest it's possible that we are actually talking past each other. That it's possible that because we're working under different paradigms, we can be saying words to each other, but not really communicating. So we'd really like to spend these episodes in a huge way helping people understand  the paradigm they may be working under, because then once you understand that paradigm, with that understanding, then you can make a choice. Now we can communicate better. Now we can have better conversations, and really actually understand what we're talking about. In fact, the most important thing to take away from this podcast is that we don't advocate any of these perspectives. So you might have, like, heard me say, "Well, I'm a Z," when actually I'm not a Z any more. That was my perspective about what math was growing up. And Kim was an X. That was her perspective growing up. But we hugely now, not advocating any of those three. We want to advocate teaching Real Mathematics. So helping people understand what mathematics really is, and how we can teach it to help students really do Real Math and mathematize, and open up the possibilities for everyone to do what they actually want to because the math isn't holding them back. Let me explain that a little bit more. I've done lots of work with teachers and parents and people around the world. And it is interesting to me that once they get this vision of what teaching Real Math is, what Real Mathematics is, what it's all about. I have gotten people to respond by saying, "Oh, you mean, I could have actually done blank?" And I'm like, "Whoa, what do you mean"? And they're like, "Well, that's what I really wanted to do. But the math held me back." Oh, man, if we could open the gatekeeper, like math is such a gatekeeper. If we could open that gate for people to actually be able to do what they want to do. Wouldn't that be like a wonderful thing? And so we really want to spend some time diving deep, delving into these three perspectives, opening them up, giving you examples about what that might have been and how it looked to you as a student, and then how that translates into how you might be teaching now and how that affects the way that the conversation that we're having about math teaching. So that we can actually make some real change. So in the next few episodes, we're going to parse out these perspectives in detail. We're going to discuss the ramifications that those perspectives have on how you do math, how you view mathematics, how you teach mathematics, how you learn mathematics, all the things. For teachers, it can really impact how you work with students. For leaders, it can really impact how you work with teachers, and even parents. And parents, how you talk with your kids. We think these episodes could really help all of us choose the way we want to approach mathematics. Because when we know, then we choose. Then we have the freedom and the ability to choose what we actually want to do.

Kim Montague  10:30

Absolutely. Some of you might right now already be thinking, "Oh my gosh, when Pam earlier was talking about the Y perspective - or a different one - that sounded just like me." Or you might be thinking, "Hmm, I'm not really sure which one of those feels like me." We are super excited to share that you can head over to mathisFigureOutAble.com/XYZ, or click on the link in the show notes and check out a super super cool quiz that will walk you through just a handful of questions to help you determine what your perspective might likely be.

Pam Harris  11:07

Yeah, it's excellent. So we've been working on this quiz for a while. We're really excited about it. It's really short and quick. And when you take it will just ask you some questions about how you viewed math as a student, as a young person, and I can help you identify, like Kim said, the perspective that maybe you likely have. And tune in over the next few weeks, we're going to dive deeply into those perspectives and help each other all learn and teach more Real Math. You can also read more about it at that blog - same same reference math is mathisFigureOutAble.com/XYZ. The blog is going to talk all about the different perspectives and how it impacts the way that we view and teach mathematics. Y'all remember to join us on #MathStratChat on Facebook, Twitter, or Instagram on Wednesday evenings where we explore solving problems with Real Mathematics.

Kim Montague  11:55

We are so grateful for the five star ratings on Apple podcasts. Y'all, we love reading your comments and Ah-has you're having. Hey, check out what Nate said with his five star rating that he titled "Do not listen to this podcast while operating a motor vehicle.". He said, "Let me explain. This podcast engages your math brain. Even if you're not a math teacher, you'll love the episodes. Pam and Kim offers new ways of reasoning about common math relationships. You don't want to be driving when you're listening. You'll want a pen and paper to jot down your own thinking. I've tried to listen and drive but it's not advised. It's worse than texting and driving. This podcast has made me excited to talk to my middle schoolers about the reasoning skills needed to really get math. I love being reminded why we teach mathematics to kids. Good show. Great show." 

Pam Harris  12:45

Alright, so that was hilarious. So we do want you to be safe everybody. We want you to be safe. So no writing down your thinking while you're driving. Feel free to listen to the podcast while you're driving and then go home and re-listen to it with a pen and paper if you want to jot down your thinking. I loved how Nate said you want to jot down your own thinking. I love it because it's not about mimicking stuff. Alright, 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 mathematics is Figure-Out-Able!