Pam Harris  00:00

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

Kim Montague  00:08

And I'm Kim Montague.

Pam Harris  00:09

And we're here because mathematizing is not about mimicking or rote memorizing. It's about creating and using mental relationships. 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  00:11

To start off this episode, we're gonna read a five star review on Apple podcasts.

Pam Harris  00:20

Five stars! Woohoo!

Kim Montague  00:20

Because it's a great introduction to what we will talk about. The subject is, "Always thought I was dumb" and Creeksea writes, "Until Pam showed me what Real Math was I was stuck thinking I was just plain dumb. Thanks Pam, for helping me see the truth!"

Pam Harris  00:20

Oh, so important. Like, whoa. When we read that we were both like, "Ah, yes! yes!" Because it's so to the point right? So thanks tons for the five star ratings on Apple podcast. We love reading your comments and ah-has that you're having. This one was so great for our subject today. Y'all, we never want anyone to feel dumb. We're so glad that we were able to at least make a little bit of a difference in Creeksea's life, not thinking that you're dumb, just because fake math made you feel that way. So we've been talking for the last few episodes about why everyone doesn't teach math the way we recommend.

Kim Montague  00:20

Right.

Pam Harris  00:34

We've been discussing certain perspectives that we might have had as young learners of mathematics that potentially color the way we see the nature of mathematics itself, and how to teach it. So we talked about the X perspective, that you should be able to pick up on the Real Math in spite of being taught fake math, and that everybody should be able to do that. We've talked about the Z perspective, that math is steps and stuff to memorize, and that a student's job is to mimic the teacher; and y'all that's fake math. So we talked about those two perspectives. In today's episode, we are going to talk about potentially my favorite perspective, and maybe it's more of my favorite people, I don't know. And we call it the 'Y perspective'. So why do we call it the Y perspective? Because these are the students who cannot do it unless they understand the 'why'. Yeah, so we did a little play there. When we decided to call these perspectives by variables we, you know, might as well use X, Y, and Z. But for sure, we wanted to make sure that the Y represented this perspective of like this, it's like this psychological, it's like this soul need to understand why. So when I said they can't do it, unless they understand why, to be clear, it's not about ability. It's really more about a frame of reference or a state of being that says, they believe that if they can just understand why, they'll be able to hang on to it and then do whatever it is correctly. Y'all these guys can absolutely mathematize and they might be able to mimic too, just to be clear. In fact many of them are fine, but they just don't want to.

Kim Montague  01:01

Right.

Pam Harris  01:01

It's like somehow they know that it's mimicking. They're like clear, I'm just like repeating what you told me to do. And they don't want to do that. They want to understand. They actually believe that math is Figure-Out-Able, and they want to understand. They believe that if they can understand they'll actually be able to do it. So they just sort of have this refusal to mimic. It's kind of curious. So Kim, we both have people with a Y perspective in our lives.

Kim Montague  01:01

Yep.

Pam Harris  01:01

Tell us about one in your life. Close to you.

Kim Montague  01:01

Okay, so my Y in my life is probably my most important Y. And that's my husband, and he is, oh my gosh, such a Y. He had an experience with school math and did not love it. He just had to get through. He just was not about the school math. Because it was fake math, right? But he is an amazing builder. And a woodworker for fun. 

Pam Harris  01:01

Y'all you should see what he makes. He is a craftsman, it's beautiful work.

Kim Montague  01:01

He does really great stuff. And he does that just for fun, which obviously has a lot of math and he's a firefighter and paramedic, so he does a lot of medicine calculations.

Pam Harris  01:01

And let's just pause right there. We thank him for his service. We're really grateful for first responders and especially for Bo.

Kim Montague  01:01

Yeah. And so Pam, you and I actually kind of figured based on the fact that he's talked about not loving school math, and the fact that he does a lot of math just in his daily life. We figured we knew what he was, right? And so we asked him to take the quiz that's available on Pam's website. And he came back and he said that he was a Y. And I asked him if the description of a Y fit him, and it totally did. 

Pam Harris  01:01

Bam! We called it!

Kim Montague  01:01

Right.

Pam Harris  01:32

We were pretty darn clear that he can do an awful lot of Real Math and does do a lot of Real Math. But he has this perspective, or had this perspective as a learner, that we're calling Y perspective today. So let's describe this perspective a little bit more. I saw it as a high school math teacher. So in my classes, I had some Ys, this is what it looked like. I'd be explaining something, we'd be talking about it. And then everybody would dutifully pick up their pencil and start working except a couple of students. And they'd be like, "Um, like, I don't understand." And now this is back in the days where I was pretty much a Z. So I was teaching rules and procedures. With a lot of understanding  of rules and procedures! But they were still all about rules and procedures. And so I'd already like discussed and described and helped them understand the rules and procedures, all the steps and when to do it, like three times already. So the kid would like, "I still don't know", I'm like, "Listen, I've explained it three times. Love you, pick up your pencil." and the kid would be like, "Ah, but -" I'm like, "Oh, seriously." Like, if you could see me right now. I'm like, my hands are clenched, I'm like ah! Like a little crazy maybe. I'm like, "Just pick up your pencil, just like do the first step." "But I don't know-" and I'm like, "Oh, just like -", because they just had this thing that they didn't want to just mimic, they didn't want to just do. They wanted to understand. They really felt like they would have to give up part of their soul to just like, do what I said. Because they believe that they can actually understand and then they wouldn't mess it up. For example, one of them said to me one day, "Look, I can just do your thing. But then when we come in for the test, or tomorrow, whatever, I'm gonna be like, I won't be able to repeat it, because I don't understand it. You got to help me understand it better, and then I'll own it.". Well, at that point, that didn't even really make sense to me. Sorry, sorry for all those Y students I had. I didn't know any better. Yeah. So let me keep going. You gave a really close Y to you, I'll give you my closest Y in my life. So God gave me three boys who came out of the womb mathematizing. They were Xs. They were seeing relationships, connections, up the wazoo, and in a huge way I credit them with helping me get out of fake math, because I was so enamored with the kind of Real Math that they were doing. And frankly, they were bored at school. But then God gave me my daughter. So my daughter, Abby, is amazing. I'm so grateful. I love being a mom of boys. But there was something about giving me that girl, thank you God. And I love, love, love her. But whoa, so different in so many ways. And in one way, the way she viewed sort of this mathematics experience. And she had a few reasons. There was a teacher who she should have had in third, fourth, and fifth grade.

Kim Montague  02:00

 I'm never living it down. 

Pam Harris  02:00

You're never living that one down. Kim could have been Abby's teacher in third, fourth and fifth grade. But she left the school to go open a new school with the principal who we both loved and respected. And I totally understood... kind of... It was that moment, like, "don't leave my kid". And because she and a bunch of other teachers left, my daughter was sort of left with teachers who had never been trained. At that point I wasn't working with the district anymore. And unfortunately, the district wasn't keeping the training going. And so she had teachers who taught fake math, and up to that point, she was doing brilliant. And I'll never forget the day that she came home in third grade. And she'd recently been diagnosed with dyslexia, which doesn't really have anything to do with fake math. So don't get that confused.  But she just recently been diagnosed with dyslexia. And so she's a little frustrated with the whole reading thing. And she was kind of, you know, like, beat yourself up a little bit. But she's brilliant in math. And she came home one day, and she said, "Mom, Mom, I'm really frustrated. Because I, you know, I've always struggled in reading a little bit, but I've always been great at math. But I don't think I'm good at math anymore". Oh! Like, there was a moment where I was like, "Well, wait, wait, wait, hang on everybody. I mean, we're gonna fix this". Because she is brilliant in math. And I said, "What did you guys do today?". And sure enough, her teacher, bless her heart with all the meaning that means the south, had just reverted to the traditional alogrithm for addition, and Abby literally said, "I don't understand those little ones and stuff". And I said, "What are you thinking about?". Y'all she's thinking about the magnitudes. And she was using strategies. I said, "You just keep going.". Because when she could understand what was happening, when she could use relationships and connections, she mathematizes with the best of them. But  if she can't understand the rule, the procedure, the thing to mimic then she can't do it. It's just it's like a part of her psyche just decides I should be able to understand that because it looks like all the rest of you are understanding and I can't. And she just feels like she can't just perform steps if she doesn't understand them. It's so interesting, right? Because so many of the rest of us were just happy to perform the steps. 

Kim Montague  02:00

Right.

Pam Harris  03:03

She just feels like it's giving up a part of her soul to do that. So one day she came home, I'll never forget, she goes, "Mom! Fractions!". Oh, I totally just threw my pen across the room. I'm getting excited here. She came home and she's like, "Mom division of fractions are Figure-Out-Able, right? Division is Figure-Out-Able of fractions". And I was like, "Yes, yes, it is." She was so like, "AH!". And I'm like, "Yes, it sure it.". So then we talked about division of fractions. We made sense of what it means to divide fractions. One day, I was at a presentation actually. So I was doing a workshop with teachers. I got a text on my phone. This is my daughter. So this is when she's in 10th, grade Algebra II. And she says to me, "This is me right now: Wait, that rule doesn't make any sense. Teacher and other students: Well, that's just the way the rules are. That's how it works. Me: But that doesn't make sense. Why is it that way? They respond: That's just how it is.". And she puts that emoji with the little angry guy with smoke coming out of his nose, like, grrr. "They expect us to mesmerize all these rules." There's the dyslexia coming out as the autocorrect fixes things. "They expect us to mesmerize all these rules, instead of understanding and reasoning through it." Grrg, grr -  she puts the emoji again. I'm like cracking up like, whoa. So I respond back to her. "Goodness. What's the topic today?" Y'all if it was going to be a topic in Algebra II, that you maybe are not sure how to teach without teaching rules and procedures? What would it be? So she responds back to me, "Logs." Yeah, it's logarithms. I mean, logarithms are complicated. There's a lot going on. And if you don't understand exponent relationships, you're not going to understand logarithms. And so it was interesting. So she then sends me a picture of the board and the board has kind of the subtraction/division relationship with logarithms. And she said, "Why do you subtract, divide makes no sense. Logs are stupid." I'll never forget that day. So I responded back to her, "You make me smile. Let's talk all things logs when you get home, or at the DPS while we wait in line." Because literally, she was getting her license that day. So y'all, that day, when we got home, we talked about the exponent relationship she built the week before. We built on that, exponents to log. She growled at me again. And she's like, "What is wrong with all these high school math teachers that won't help me understand the why?". And I have to just keep reminding her, it's because they don't know why. But let's change that. Let's get to the point where we can explain or help students develop the why. So that people like Kim's husband and my daughter don't have to go through life so frustrated that we're not letting them in on the secret of what's really going on.

Kim Montague  03:59

And we have a great time, right with both of them doing Real Math. Like all the time to ask them, "Hey, what do you think about this?"

Pam Harris  03:59

Oh, yeah. All the time. Yeah. And in some ways, you got to agree with me here, Kim. They're more creative. 

Kim Montague  03:59

Oh, for sure.

Pam Harris  03:59

Like they bring in things that you and I haven't even thought about. It's like, wow, that creativity. Both of them are artists, and they bring that to bear. And not that all Ys have to be artists. But those two are.

Kim Montague  03:59

Yeah. So you talked about Abby for a bit. And I talked about Bo, but you also meet a lot of people traveling right? And have you ever met any Ys, like in your travels? 

Pam Harris  04:16

Oh, so here's fun, right? So I sit down on the plane, the person sits down next to me, they say so how you know, where are you going? Blah, blah? What do you do? I just start cracking up because I'm like so glad you asked. Because then we're going to talk math, right? Like let's do it! So then it's interesting, because I will often get this response. Where we'll sit, and go, "What do you do?" "Well I teach high school or I did teach high school. Now I teach math teachers." And they're like, "Oh, math," and sometimes there'll be this response where they kind of scoot away from me a little bit. And they're like, "Ah, you know, I was never really good at school math. I had to do these tricks and the stuff kind of behind the scenes and I didn't, I didn't get what was happening." And I will then say, "Give me an example of what you are doing sort of behind the scenes of stuff that you think makes you less than," and you guys it is examples of Real Math. Like they're using relationships to do stuff. They're like, "Yeah, I just didn't really understand that lineup stuff and all those rules and couldn't keep the steps in mind.". So they created Real Math in their own heads. I love the opportunity to be able to go, "Oh, guess what?That stuff that made you feel less than? Yeah, that's actually Real Mathematics. Way to go.". 

Kim Montague  04:25

Yeah.

Pam Harris  04:25

 Like, it's so fun to watch them sit up taller, a little bit like, "Really that?" "Yes, absolutely". Now, let's be clear, they have a lot of holes, because they didn't necessarily create relationships for everything. That's hard to do on your own for sure. So you know, it's not like they've created all the great math, but they certainly were doing a whole lot more math than a ton of the Z perspective people that I've met for sure. As a side note, that's also true of the X's, by the way. The X's were the ones that were sort of creating those mental relationships on their own, and then thought the rest of us were as well. They also have lots of holes. Why? Because again, they were only kind of figuring out relationships, when they sort of needed it or they could. They just kind of knew that was a thing. But they certainly did plenty of procedures and stuff when they kind of didn't have time or whatever. And they weren't able to make sense of it. You made it all the way up through high school or to high school, Kim, before you kind of did that. 

Kim Montague  04:25

Yep. 

Pam Harris  04:50

Just to be clear. So there's also a little bit of a difference then between an X and a Y perspective, because somehow those X's knew that using those relationships, that was part of Real Math. Like they were confident as they came up with relationships, the X's were like, "Yeah, that's like Real Mathematics, of course." But the Ys think they're doing it because they can't figure out the 'right way' the 'correct way'. If you could see me I'm like getting air quotes around the 'right, correct way'. That they had to do this trick because they didn't understand the procedures. Newsflash! No one understands the procedures, like even all of us were just like mimicking and we weren't understanding what was going on. Isn't that interesting that the Ys felt like, "Oh, well, everybody else must be understanding what these procedures are. I'm just like dumb because I don't understand.". No, no, no, no, the rest of us were just dutifully mimicking, we didn't have a clue what was happening.

Kim Montague  05:06

Right. 

Pam Harris  05:06

Maybe teachers, maybe as adults, you figured out the relationship behind the traditional algorithms. But let's be clear, it took you that long. We could be doing things with kids so much earlier that they actually understand relationships. And that's not about repeating steps. And then we wouldn't be losing these Ys. They wouldn't be having that feeling. They wouldn't even be Ys to begin with because they wouldn;t be having that feeling that they're not invited into the club of Real Math. 

Kim Montague  05:06

Yeah, you know what, I'm glad that you're talking about this. Because the idea that somebody could feel dumb at math, because they didn't make sense of it based on the way that it was taught is really troubling. The review at the beginning, the subject was, "Always thought I was dumb". That's so unfortunate that we leave people feeling that way. It's not true for all Ys, right, but it is for so many. My husband thought that he wasn't great at math, either. But again, that was the fake math. He's so good at the math that he does every day. And frankly, even though you and I talk math everyday. Um, I feel like he probably does more math every day than I do. I was thinking about the other day, the kinds of things that he does, right? He finds dosages based on patient weight on the fly. 

Pam Harris  05:06

Yeah.

Kim Montague  05:06

So he built this shop in our backyard. It's like a 16 by 28 huge building from scratch, like all by himself -

Pam Harris  05:06

So amazing.

Kim Montague  05:06

- with area and dimensions. It's really kind of crazy. When he builds wooden pieces, he's talking about fractions and scaling ratios for size of wood. He does more than I possibly do.

Pam Harris  05:06

Let's give an example. He does these gorgeous cutting boards. 

Kim Montague  05:06

Yeah.

Pam Harris  05:06

And somebody will say, "Oh, I want this size." And then he does that proportional reasoning to scale the size. And it looks so good.

Kim Montague  05:06

Yeah. He doesn't ask me for help. He's got this.

Pam Harris  05:06

Well he's got it down. Right? 

Kim Montague  05:06

Yeah, yeah.

Pam Harris  05:06

He doesn't need it there. 

Kim Montague  05:06

Yeah. 

Pam Harris  05:06

So it's not about being smart or dumb, whether you're an X, Y, or Z. For the Y perspective, it's more about this feeling that you're being left out of the club of understanding. It's this, please let me into the secret. If you'll just tell me and help me understand. I know I can do it. 

Kim Montague  05:06

Right. 

Pam Harris  05:06

So let me just give you one more personal example in both of our lives. So we video a lot. We video in classrooms and video, some of the keynotes that I do and stuff. And so one day I was doing a keynote about this very subject. It was one of the first times I've ever talked about it. I wanted to help a group of leaders in the state of Texas understand sometimes why we have a hard time moving teachers, we have a hard time getting teachers to buy into Real Math. And so I wanted to kind of think about these three perspectives. And I was sort of talking about it and at break - we were videoing - at break our videographer RheAnne came up to me and she had a tear in her eye. Tear coming down her cheek. And she said to me, "Pam, that's so me.". Well, we talked about all three of them. Right? So I'm like, "Which one?" And she goes, "Y. Why wouldn't you tell me why?". Broke my heart. I was just like, "Oh, sweetheart,  I didn't know why.".

Kim Montague  05:06

Yeah. 

Pam Harris  05:06

Like she really felt we were kind of leaving her out on purpose. Like we were being mean. All of you who relate to this Y perspective, please know, none of us are - we all go into teaching because we like people. We like kids. We believe in helping. Nobody's like trying to mess you over on purpose, they're not leaving you out on purpose. But everybody listening, please recognize that this is important that this perspective exists and is alive well out in the world. And we have the power to do something about it.

Kim Montague  05:06

Yeah. So we've talked in detail about X and Y and Z. And you gave us some insight or how you encourage and work with Xs and Zs. Why don't you share with us a little bit about what you're thinking about when you work with the Ys in a group?

Pam Harris  06:21

Yeah, great. So when I'm working with people who have had this Y perspective, my goal is to help them understand a few things. So number one: the most important thing is that you are not less than. You are not stupid, you are not dumb. Those things that you were doing, most of them were great, and they were all about Real Math. Way to go! In fact, in many ways, you were actually doing far more Real Math than so many of those Zs who looked successful, but they were getting good grades for doing fake math. When in reality, you were doing a whole lot more Real Math and all those kids that were getting good grades from mimicking the teacher. So most important, please sit up a little taller and know that you are a valued member of our mathematics community. And then probably the second thing that I keep in mind that I really want to help people with a Y perspective understand is: please keep demanding the 'why'. Keep the rest of us on our toes so that we'll get better and better about designing and implementing facilitating experiences that help all of us develop more mental relationships to mathematize more and more and more. So you're helpful. Keep us on our toes. Demand that why. Absolutely.

Kim Montague  06:31

So really, for all students and learners X, Y, and Z Real Math is the way to go. Right? 

Pam Harris  06:31

Absolutely.

Kim Montague  06:39

We want everyone to have Real Math. You may have already taken the quick quiz for yourself, or maybe not. 

Pam Harris  06:40

Not yet? Come on!

Kim Montague  06:40

But it really might be cool for you to ask your co workers to take the quiz as well. Knowing the perspectives of the people around you can help facilitate better conversations, right? If you know the perspectives of the people that you're working with. Hey, leaders, we would love to encourage you to have your teachers take the quiz as well. You can access that at www.mathisFigureOutAble.com/XYZ.

Pam Harris  06:57

That's www.mathisFigureOutAble.com/XYZ to take the really cool quiz that will help you identify what your perspective was growing up. And that can help you identify your colleagues' perspective. And so we can all communicate better. What we really hope to engender is more productive conversations across the world. If we can all acknowledge the way that we saw mathematics and mathematics teaching as students, then we can have more productive conversations now about what to do now to teach Real Mathematics.

Kim Montague  07:02

Remember also to join us on MathStratChat on Facebook, Twitter, or Instagram, on Wednesday evenings where we explore problems with the world.

Pam Harris  07:05

So if you're interested to learn more math, and you want to help yourself and students develop as mathematicians then don't miss the Math is Figure-Out-Able Podcast because math is Figure-Out-Able!