Math is Figure-Out-Able with Pam Harris

Ep 28: Real Mathematics Perspective

December 29, 2020 Pam Harris Episode 28
Math is Figure-Out-Able with Pam Harris
Ep 28: Real Mathematics Perspective
Chapters
Math is Figure-Out-Able with Pam Harris
Ep 28: Real Mathematics Perspective
Dec 29, 2020 Episode 28
Pam Harris

This week Pam and Kim wrap up their discussion on the Perspectives that Impact Math Pedagogy. Understanding the X, Y, and Z perspectives not only helps us understand one another better, but empowers us to choose to take on the real mathematics perspective. Listen in as Pam and Kim discuss the need for mathematics to be experienced, and the power in developing mathematical reasoning.
Talking Points:

  • How do each of the perspectives benefit from real math?
  • All people can do more real math than fake math
  • What pitfalls do each of the perspectives have to avoid when teaching real math?

Take the XYZ quiz here! mathisfigureoutable.com/XYZ
Find this episode's transcript HERE.

Show Notes Transcript

This week Pam and Kim wrap up their discussion on the Perspectives that Impact Math Pedagogy. Understanding the X, Y, and Z perspectives not only helps us understand one another better, but empowers us to choose to take on the real mathematics perspective. Listen in as Pam and Kim discuss the need for mathematics to be experienced, and the power in developing mathematical reasoning.
Talking Points:

  • How do each of the perspectives benefit from real math?
  • All people can do more real math than fake math
  • What pitfalls do each of the perspectives have to avoid when teaching real math?

Take the XYZ quiz here! mathisfigureoutable.com/XYZ
Find this episode's transcript HERE.

Pam Harris:

Hey fellow mathematicians. Welcome to the podcast where math is figure-out-able. I'm Pam.

Kim Montague:

And I'm Kim.

Pam Harris:

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

Kim Montague:

So for the last few weeks, we've been diving deeply into the idea that there are different perspectives we bring to our work with mathematics. If you haven't caught the last four episodes, you should check them out when you have some time. But real quick, we believe that there are three major viewpoints. We think there's the Xs of the world, those who kind of mess with numbers a bit naturally and saw math for what it is, despite being taught super traditionally, there's the Zs of the world, those who were like, give me the rules and procedures, and that's what math is. And then there's the Ys who wanted to know why. Because they believe that when they can understand they can do all the things.

Pam Harris:

Today, we are going to wrap things up and give you all a, "So what?", some final thoughts for this series. You might be tired of it but we got some new things that we're gonna bring in. And we think some really important things that kind of underpin the reason that we did the series to begin with. So this is kind of our finale, to make our big punchy point here. You may have identified with one of the perspectives that we shared about or taken the quiz to help you determine your existing viewpoint. If you have not yet taken our really cool, super cool, super quick - it'll take you less than two minutes - super cool quiz that will help you determine which perspective you kind of bring to mathematics and mathematics teaching, you can find it on the website mathisfigureoutable.com/xyz. We're putting it on social media, take it, have your colleagues take it, have your kids take it, it'll be great, you can identify the perspective that you're bringing. When you take that quiz, you might recognize that you identify with one of those perspectives we shared. So now what? Well, first thing, whether you're a parent, or a teacher, or a leader, the most important thing to remember is that your perspective about mathematics may not be the same for those that you're working with. And we can't assume that we know the perspective of others.

Kim Montague:

Yeah, yeah. That's so important. Just to know that there there are these perspectives, right? It's a great start.

Pam Harris:

Yeah, so the goal isn't to leave people where they are, this is probably the biggest upshot of this entire five part series. The goal isn't just to recognize people's past perspectives. No, don't leave them in those perspectives. The goal is to pull them all out of those three perspectives and teach real math and do real math. Y'all real mathematics is for everyone. I'm gonna make a bold statement. All people can do more real math than fake math. Let me say that one more time. All people, all of us, can do more real math than fake mathematics

Kim Montague:

Preach.

Pam Harris:

Kim I ever heard you say that one of the great things about real math is that there's something for everyone.

Kim Montague:

Oh, sure. Right. So if you're a Y, then you get to know why with real math, right? If you're an X, you get to play around and look for patterns and relationships. But there's a structure to mathematics that makes Z perspective happy too. Everyone can enter into real math, everyone can communicate, and everyone can grow, we get to mathematize together as mathematicians,

Pam Harris:

Isn't that wonderful? There's something for everyone. So the most important things we would love for you to have as a takeaway from this series is that there are these three perspectives in the world - they exist. And we feel like it's super important to pull people out of these distinct viewpoints by teaching real math for all. If you're not sure how to teach real mathematics, well keep listening to the podcast. That's definitely one way to do it. So parents and teachers, what are some things that we can do? Well, maybe start by finding out where your student is, or your students are, how they viewed mathematics. Kim let me tell you a quick story. So I'm in physical therapy had this knee whatever, surgery blah blah blah. So I was doing physical therapy for my knee, and I had kind of an interesting experience just the other day. So my physical therapist, who I like, they do a great job, was doing some calculations. Like at her computer while I'm doing my exercises off on the side. She came over and we started talking and I said, what kind of calculations were you just doing? And we talked a little bit about her billable units and the minutes and how they're not always the same and how she sort of messes around with like a total number of minutes dividing it into these billable unit sizes and how that all works and fits and stuff. Near the end of it, she looked at me and she kind of paused and she said, No one has ever asked me how I think about math.

Kim Montague:

Oh, that's horrible.

Pam Harris:

I think that is so interesting, right?

Kim Montague:

Yeah

Pam Harris:

No one had ever asked her. I mean, how many of y'all have ever been asked? What are you doing with those numbers in your head? And it was kind of fun to listen to what she did. She did some great things.

Kim Montague:

Yeah, did you happen to ask her if she grew up thinking that she was good or bad at math?

Pam Harris:

No. But I'll do that, and then I'll report back.

Kim Montague:

Okay, please do. So what I find is that a lot of people who have to do math regularly in their jobs are coming up with things that they didn't necessarily believe that they could do early on. I actually had a conversation with my hair girl the other day, and she was talking to me as well about how she mixes color. And she said that she didn't feel like she was very good at math growing up. And listen, their perspective doesn't mean good or bad at math, right?

Pam Harris:

Right.

Kim Montague:

Perspectives present differently. And so you're going to need to dive in to figure out where your students are coming from, you could have 10 Z's in the room. But they all look different. Thier grades are different, their work looks different.

Pam Harris:

Yeah, totally true. So you might have a kid with a Z perspective, who is say super quick and can recall fast from rote memory, memorize well. But you could also have students with a Z perspective, the ones who think that math is about steps and rules, who don't memorize well. They need time to copy down the teachers work and might not be having as good of grades, even though they have the same perspective about what math is what doing math means. Some might resign themselves pretty quickly, that they're never going to be very good at math, and there are others that might excel at mimicry. Some of your students might believe that it's all just this bunch of stuff. It's rote memory, and it doesn't matter. So they're not interested to put forth the effort if their perspective is that's just all fake math. This has nothing to do with me. It's not interesting. Then do we blame them for not wanting to - like, sometimes as math teachers, we get a little bit ugh, when the kids go, when am I ever going to use this? We get all frustrated like who cares? Just do the thing! Well, you know what we can we can get rid of that question forever. If we just do real math. If we do real math with our students, we never get that question. Because it's interesting. It's intriguing. It's, perplexing, and in really positive ways students dive into that, they like puzzles,

Kim Montague:

Right. So if you know that there are these three perspectives, then you have some insight into your students, right? And you have even more reason to get into conversation with them to get to know them, and how they've approached math. So now you have questions that you can ask. So you might be asking, what do we do with each of these students with different perspectives?

Pam Harris:

Yeah, so are you ready? Get ready? So I'm gonna tell you what to do with each different group of students and each different perspectives.

Kim Montague:

Perfect.

Pam Harris:

It's actually the same! Teach real math!

Kim Montague:

Okay.

Pam Harris:

Like, there's one answer, one answer that meets the needs of all students, it really boils down to that. Real mathematics hits everyone. Like I said, before, all people can do more real mathematics than fake math.

Kim Montague:

Yeah.

Pam Harris:

So Kim, you just encouraged us to communicate with your students like to talk to them and find out what they're thinking about. We also listeners want to encourage students to communicate with each other and learn to navigate these different perspectives.

Kim Montague:

Yeah, that's so important, right, communication and mathematics. So I was just thinking that we often group students in lots of different ways, right? We should be having students working together. And sometimes teachers will put kids together based on like grades, or what they perceive is their ability or processing speed, friendships, behavior, whatever. We could consider grouping students, sometimes that have had different perspectives, maybe in the past, so that the groups can take advantage of the positive qualities that different backgrounds bring right? To take advantage of their different strengths.

Pam Harris:

Yeah, so important. And another thing that we can do to make a really big impact is helping students in times of frustration. So let me give you an example. If you have a kid who got a Z perspective, they think math is all about rules and procedures and mimicking, and a Z gets frustrated, then help them lean into the discomfort of not being given a rule and steps to memorize, right? Like help them know it's okay, I get it. This isn't what you're used to. But this is real mathematics and this discomfort you're feeling that's normal. It's normal to have a little bit of positive confusion that we can work through this until, ah see? Now your successful. So we want to help them lean into that discomfort a little bit. And so that they can have productive struggle and help them know that that's a positive part of math class. Well, what if you have a student that had a Y perspective? What if that students frustrated? You know, if I find a kid who had a Y perspective who is frustrated, then I'm looking at the group dynamics. I'm pretty sure there's somebody hanging around them, that's just telling them. Someone who is just satisfied with an answer.

Kim Montague:

Oh yeah.

Pam Harris:

And that Y is going to get frustrated, that Y wants to know why, right? So if you see a Y getting frustrated, you lean into that frustration. And then help them explore more and get comfortable figuring out the why so that they now understand why what's going on, and then we can help their frustration. So what about an X, if an X is frustrated. Kim is laughing because she's been frustrated. Kim has been a little frustrated in the past.

Kim Montague:

Yeah.

Pam Harris:

Kim you want to take that? Go.

Kim Montague:

Sure. So I think one of the most frustrating things growing up as an X is when a teacher would say, you have to record every step, show me your work, show me all the things,

Pam Harris:

All of them every single one all the time.

Kim Montague:

Yeah. And if that wasn't something that I needed to show me every piece of every problem, then that would have been frustrating for me.

Pam Harris:

Yeah, totally. Because you could solve the problem pretty easily. And the teacher would say, No, no, no, you must do all the steps.

Kim Montague:

Yes.

Pam Harris:

Later, you're gonna need these steps.

Kim Montague:

Yes.

Pam Harris:

And you would just like, glare at him a little bit. Like, whatever.

Kim Montague:

Maybe, yeah.

Pam Harris:

Whatever weirdo. Because you were mathematizing; you were letting the numbers and the structure influence how you solve the problem. And so you knew you didn't need all the steps all the time, even though your teacher probably did

Kim Montague:

Right. But there's a balance, right? So as a teacher-

Pam Harris:

So if you have an X who's frustrated, and maybe you want them to to show their work, not the teachers work, not mimicking what you've done, but you really want to know what's going on. I've got a great hack for you, when I walk up to a kid that hasn't written anything down. And I need to know, like, I'm trying to decide what strategy to share, which students gonna work with which students so I kind of need to know how they're dealing with the problem. And they haven't written anything down. I might say to them, Oh, cool. You did it in your head. Okay, cool. You know what, I can't see what's in your head. Can you tell me what's in your head? And so then they're freed up to just like, talk about what they actually did in their head, not like forced to model. They might not even know how to represent their thinking.

Kim Montague:

Right.

Pam Harris:

So another thing to do is, as those students describe their thinking, and I kind of help them by asking questions and pulling out their thinking, then it's the teacher's job to model that thinking. It's the teacher's job to make it visible to say, hey, when your brain does that, when you use those relationships, this is how it could look on paper. And the kid can go, Oh, when my brain does that it could look like that? Well, okay, well, I can show you that next time. Now that the student has been using relationships and connections in their head - you should see me right now I'm like pointing to my head - like, if you're using what you own in your head to solve the problem, you might not know how to represent that on paper. So it's the teacher's job to represent it first. And then you can expect students to do more representing of what's actually helping in their head to solve problems.

Kim Montague:

Yeah. And part of the responsibility of a mathematician - all perspectives of mathematicians - is to communicate their thinking. So we need to help all students, but particularly maybe the Xs to do that. That's part of the goal.

Pam Harris:

Yeah, so totally interesting, because this actually came up because you know, you and I had these different perspectives, right? Had. I think mostly, now we're in real math. But every once in a while it rears its ugly head. When we were talking about a MathStratChat response, somebody had posted a response to MathStratChat, that was pretty, what's a good word? Sparse? Like it didn't have a lot of explanation, it kind of skipped some things. And you and I could infer what they meant, you know, we could sort of follow because we thought through the relationships, but it would be really hard to follow, it was not not well communicated. And I said something back to the person like, did you mean this or I think this is a way you could represent your thinking to make it more clear. And you poked me, you were like, Pam, they solved the problem. That person didn't need that stuff, you can see clearly, they could tell they only wrote down what they needed to solve the problem. Ah, so there's kind of two different times. If you're just solving a problem, all you X's out there in the world, if you're just solving a problem, and you just like, sort of are building the relationships, and you're gonna, you know, figure things out. Then sure, only write down what you need, just keep track of your mental thinking enough, because that's all you need. However, if in that instance, your job, your task at hand, is to communicate your thinking with others? Ooo, then we want you to fill in the blanks, then we want you to make sure that you have a viable argument that somebody else could read. And that makes sense. And so then we're going to work on that communication, then we want you to show more steps. So that's when I pushed back on Kim and I was like, wait, wait, wait, what's the purpose of MathStratChat? Is it just to get an answer? And so you're only going to keep track of the steps you need? Or is it to communicate your strategy to the world because we're chatting about math strategies. MathStratChat. Anyway, so it was a great conversation. It was interesting how it actually took you and me a couple of minutes for us to kind of Oh, that's what's going on. But that's why we're approaching this a little bit differently. Cool.

Kim Montague:

So we talked a little bit about teachers, right?

Pam Harris:

Yep.

Kim Montague:

What What can we offer as advice for leaders?

Pam Harris:

Cool. So if you're a leader, how does this help you with your work with teachers? Well, just like we're suggesting that teachers need to get to know their students, we highly recommend that you leaders get to know your teachers. Consider that when you're working with a teacher who had an X perspective that they might honestly believe the kids don't need all that modeling, all that strategy development, all those rich tasks. The X teacher didn't, at least they don't think so, right? The X teacher thinks that the way they learned was good enough for them, and it works for them. And so all that other stuff is extraneous. It's froofroo. That's not real math. That's what they're thinking. And so of course, they are going to push back on that a little bit. So what do we do? I try to immerse those teachers in a mathematizing experience, give them a taste of what it could look like to help students develop the kinds of things that they themselves were left on their own to do. Let them experience what it means to be actively, purposefully helping. And then they can go, Whoa, well, you mean, like we can do stuff that actively purposely helps students develop to think like me? Yes, Yes, we can. And so when I work with people with an X perspective, I really want to help them experience. so don't do math they own. Do a little bit of new math, bring something in that's not something that they teach every day. Now, it's great if it connects, because otherwise they get a little onry sometimes. But do something that will help them create a new connection, a new relationship, I've got some strings, you guys, leaders, you want to know? Ping me on social media, I'll tell you some things are you like, tell me what grade level you're at and I'll give you one that's just out of their reach, usually, that you can again immerse them in some experience where they're mathematizing. And they realize, Oh, we can be deliberate about how we help students develop, to think in real mathematics.

Kim Montague:

Well, and if they're an X perspective, they'd probably enjoy it right? X perspectives love to play around with numbers and structures and relationships. And so they'll probably buy in pretty quickly. What about working with a teacher with a Z perspective?

Pam Harris:

Absolutely. So if you're working with teachers, with the Z perspective, recognize that they're really not doing real math yet. And then your job is to help the teachers I'm pausing a little bit, so I'm trying to come up with a painless word, help the teachers not so pain- like like, be aware that this could be a painful transition, a painful realization for Zs. So help them gently - gently is the word I was looking for- help them gently realize that they actually haven't been doing real math, yet. Help them realize that and give them the same mathematizing experiences that we just gave the Xs, it's the same experience. But watch those Z's. And as they are mathematizing, you're typically going to see the Z-ness kind of come out a little bit, they're gonna be like, Okay, that was cool. Like, I know that I made these connections. Let's see, that was a little wild and crazy. So let me straighten that up a little bit. Like Pam's kind of disorganized, that was all over the place. I'm gonna, like, organize that and I'm going to Okay, so step one, then step two, and they start turning this mathematizing experience back into steps and procedures and things for the kids to just mimic. So we sort of want to encourage Zs to mathematize, get into the real math, develop that real math themselves, and then not take that real math they just developed back into steps and procedures so that they can actually help their students develop the same way they were just developing.

Kim Montague:

So I sometimes think about Z's as being super, super helpful. They want to clean things up. They want to make it a little bit more organized. And they got to let, like, let the mess happen a little bit, right. not crazy mess, but a little bit of disequilibrium. What about teachers with a Y perspective?

Pam Harris:

You bet. Are you ready? Not a lot! Like with a teacher with the Y perspective, just keep giving them more and more math. Give those same mathematizing experiences that you just gave the Xs and the Zs. And they just drink it in. They've been looking for the Y so they love it. You probably remember we said in that episode that they're some of our favorites because there's so just like drinking it in and they're so happy. Because they're feeling like they belong in the club, because we're teaching math in such a way that they understand the why and they're being successful. And so maybe there's only one little caution when you work with a teacher who grew up with a Y perspective, just use a little caution. Sometimes those teachers are so happy to know that students can use what they know that no matter where the kids are coming from they can use relationships they understand to solve problems that the kids can be successful just doing what they understand. Sometimes they kind of leave them there. Sometimes they sort of leave those students in the the really unsophisticated -Oh the kids found success! Yay! Okay now it's time to move on and do something new rather than helping that student with really nice mathematizing experiences. I'm not suggesting we tell them but give them a nice mathematizing experience so that student can get more and more sophisticated. Remember the development of mathematical reasoning. I'm doing ovals with my hands here. Remember, there's counting to additive, to multiplicative, to proportional reasoning. It's not about getting answers to problems. It's about helping students develop their brains in such a way to think more and more sophisticatedly. So Ys, you're working with kids and you're so excited because they found success yay they have the answer!Now just don't leave them there in that unsophisticated strategy now work from there. Great. That's how you do that? Super, let's keep building and then build towards more sophisticated thinkers. Because then those kids can continue to learn more and more sophisticated thinking. Don't leave them, where then they're stuck. And they can't move on from there. So remember, it's not about getting an answer. It's about development.

Kim Montague:

So we invite you, if you haven't already, to take the quiz, we want you to compare it with others so that more people recognize that there are these perspectives in math. Get to know your perspective and those of the people around you so that you can make sense of the viewpoints. And then we can all communicate better, and actually make progress towards teaching real math. Do it! Go! Now!

Pam Harris:

So we have our notes like to end this by saying do it, go, now! And when Kim didn't read it, I was like, I just cracked up sorry. Because we just give ourselves these little notes, right? And so yeah, that's hilarious. All right, y'all. To take that quiz go to mathisFigureOutAble.com/xyz and there is our extra super cool, quick quiz to find out what perspective you had about math and mathematics teaching. Alright, we invite you to join us on MathStratChat on Facebook, Twitter, Instagram on Wednesday eves where we have a number talk for the world and we talk about problems. We'd love to have you join us on #MathStratChat. Y'all if you're interested to learn more mathematics, you want to help yourself and your students develop as mathematicians? They don't miss the Math is Figure-Out-Able Podcast because math is Figure-Out-Able.