Pam and Kim continue from Episode 2 to discuss what it means to do and teach real mathematics. When we teach reading, students read. When we teach writing, students write. When we teach math, students mathematize, because we need a verb that describes what mathematicians do when they do what mathematicians do. And when we teach students to do what mathematicians do, they are mathematicians. So teachers are mentoring mathematicians.

Talking Points

What Pam means when she says Math is Figure-Out-Able

Mathematicians do not mimic to do math, they use their understanding of mathematical relationships

What does it mean to mentor students to become mathematicians at their gradelevel?

Pam and Kim continue from Episode 2 to discuss what it means to do and teach real mathematics. When we teach reading, students read. When we teach writing, students write. When we teach math, students mathematize, because we need a verb that describes what mathematicians do when they do what mathematicians do. And when we teach students to do what mathematicians do, they are mathematicians. So teachers are mentoring mathematicians.

Talking Points

What Pam means when she says Math is Figure-Out-Able

Mathematicians do not mimic to do math, they use their understanding of mathematical relationships

What does it mean to mentor students to become mathematicians at their gradelevel?

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

Kim Montague :

And I'm Kim Montague.

Pam Harris :

And we're here to suggest that mathematizing is about thinking and reasoning about creating and using mental relationships. We answer the question, if not algorithms, then what?
In today's podcast, we're going to talk about what it means to teach real math. So Pam, you say math is Figure-Out-Able? What is that all about? Yeah, so Math is Figure-Out-Able is kind of my tagline. It's the website: MathisFigureOutAble.com. And what I mean by that is actually it's kind of my story. So of course, you're listening this podcast, you're like, well, Pam, we all teach math. Of course, we believe that math is Figure-Out-Able. However, I'm going to admit that as a student, and far too long as a young teacher, I actually believed that math is rote memorizable like
If you would have asked me at the time, I would have said, Of course math is Figure-Out-Able, I do a lot of figuring. And I did, I did a lot of figuring. I worked hard at math. But what I worked hard at was following steps. I worked hard at knowing what rule to apply when and how to make sure that I did all of the correct steps in that rule, and that then I circled the answer, like, the math I was doing was really more about rote memorizing what someone told me to do and knowing when to do which rule and it was really less than what I think math is now. Now I'm really clear that math is Figure-Out-Able that it's a whole lot more about using relationships and connections to solve problems. So it's kind of a big deal to me that math is Figure-Out-Able not rote memorizable.

Kim Montague :

I've also heard you mentioned real math and fake math. What do you mean by that?

Pam Harris :

Yeah, and sometimes it gets me a little bit of trouble because real math fake math. So I define real math as using relationships and connections you own to solve problems. And in the process creating new math. Now, not maybe new math for the world that the world has never seen. But for sure new math for the learner, like you've created new neural connections, new networks in your brain about how you think and reason because as you solve problems, then you notice patterns. And you use those to solve problems that creates new connections in your brain. So real math is about using relationships and connections you own to solve problems. Fake math, on the other hand, is that stuff that I learned in school, fake math is a disconnected set of facts to memorize, and rules and procedures to mimic. That's what I did. That's I think what most of us did in school, or at least most of us put on paper in school. Like, Kim, for example. I don't think you were doing fake math in your head, but you for sure were clear that what your teachers wanted you to show on your paper was the fake math, right?

Kim Montague :

Absolutely yah.

Pam Harris :

But you're doing real math, the kinds of things in your head Am I assuming correctly, that you
kinda thought the rest of us were too.

Kim Montague :

Yes. Yeah, I thought everybody was messing with numbers.

Pam Harris :

Yeah. And some of us wern't. But I do now and the exciting part is, now I can, I can do every bit of mathematizing that you were doing, anybody else is doing. I just needed to know it was a thing I needed to know that it's not about mimicking. It's more about what I was thinking and what I am thinking and the relationships I'm using.

Kim Montague :

You know, it's almost like we need a verb to talk about what we're doing when we do that real math.

Pam Harris :

Nicely said, Yeah, so I'm going to quote Kathy Fosnot right now, Kathy Fosnot is one of our favorite elementary math researchers. She coined a word mathematize. She said that we need a verb. Exactly like you said to describe what mathematicians do when they do what they do. Because y'all think about it. When we teach kids to read, they read. When we teach kids to write, they write, when we teach kids to do math, they... like we don't have a verb for that. So could we say they mathematize I think
we can we need a verb that represents what mathematicians do when they do their thing. So like picture. What does a mathematician do when they go to work? So picture whoever you think a mathematician looks like, I don't know, maybe Mr. Rogers kind of looking guy now it doesn't obviously have to be right. I'm a mathematician, I'm a woman, it could we could have any kind of picture sort of what you kind of think a mathematician looks like and they're going to work. They go to work, they open the door, they walk in their office, they sit down, what is the work of the day for a mathematician? Does a mathematician look at one through 29 odd, they say to themselves, I need to solve these problems today. And they look at the problems that they have to solve. And they say, Oh, yeah, let's see, how do I do these? Yeah. And they reach up and they grab a textbook off of their shelf, and they open it up to the page and they see a rule in a box that will exactly solve those problems. And they see three worked examples and all the steps are there and so so for their work of the day, that mathematician sits down for one through 29 odd.
And they say to themselves, Okay, for number one, I'm going to use this rule, I'm going to follow these steps. And I'm going to show each one of these, I'm going to mimic what someone has done before by following these steps. And I'm going to circle the answer. And at the end of the day they kind of put their papers together, they stack them up and they've done their work. They put the textbook back on the shelf, and then they leave for... is that what a mathematician does when they go to work? Of course not like you're like ridiculing me right now, of course, a mathematician doesn't do that when they go to work of course, mathematicians don't mimic. Like the epitome what they don't do. No mathematician would get paid for solving pre solved problems using someone's pre determined set of steps to use. That would be ridiculous. No one would pay anybody to do that. So what do we pay mathematicians to do when they mathematize? Mathematicians solve problems. Mathematicians look at relationships and connections and they use what they know they
bring their unique backgrounds, their creative juices to solve problems or maybe to prove already solved problems, but but when they do that they seek for clever, elegant, sophisticated solutions. They absolutely don't just repeat what someone else has done, no one would pay him to do that. So we think that we can get kids to mathematize at their grade level, that they can actually use what they know to solve problems. And mathematize just like mathematicians are.

Kim Montague :

That's so great. You a few minutes ago said, the word writing and writers. One of my favorite stories I've almost ever heard you share is about your experience as a young writer. Will you tell the listeners about that?

Pam Harris :

Yeah, you bet. So I'm an author. I have written several books. And so I'm a writer. Yeah, it's like I said a minute ago when we teach kids to write they write well, so how did I become a writer? Maybe you had a good senior English teacher or maybe you had a really good English experience at your university.
How did I become a writer, I became a writer, my best mentor was my college freshman roommate, which might sound a little bit silly. But as a college freshman, I had a roommate. She was a junior, she was an English major. And I had to write my first paper. And so writing that first paper, I knew how to play the game and I knew how to get a better grade, you have someone read it, they correct your punctuation and your spelling, and then you get a better grade. And so I said to my college, freshman roommate, hey, Melissa, you are an English major, would you proofread my paper and then I'll get a better grade on this paper. And she said, so ah, you know, like, we're gonna be roommates all year. And so we want to get along and so let's just lay some groundwork like do you want this to be a good paper? Or do you just want me to correct your punctuation and spelling? Well I didn't know the difference. I was like, oh, let's make it a good paper. Go for the gusto. Give me the full treatment. Let's do it. She said okay, just so like we've laid the groundwork. I'm gonna, you know, like, I'm not just gonna correct your punctuation and spelling. We'll make this a good paper. I'm like, yeah, absolutely. She read my paper. She handed it back to me. I said, Melissa, there's no red marks and crossy-outies like, what do I change? She goes, it's bad. I said, there's no red marks and crossy-outies, like, what do I change? She goes, No, it's that bad. Y'all. I was like, surprised, shocked. I mean, I've written a lot of papers. And she said, Pam, why do you want to be a teacher? The paper was about why I wanted to be teacher. And I don't know that I'd ever really expressed why I wanted to be teacher, I for sure knew it. I had it up in my head, but I hadn't ever really talked about it. I definitely had never written about it. And so she very wisely said to me, tell me tell me why you want to be a teacher. And she began to pull out of me my ideas, and I began to sort of haltingly talk about want to be a teacher. And then as I as I talk, that passion came out, I got more excited and I got more clarity about why I wanted to be teacher. I've talked about it all and she said, Oh, that that right there that go right, that. I said, That? I didn't write that already? No, that wasn't there. Go write that. Okay, fine. I'll go write that. I rewrote the paper. I handed it to her. She handed it back to me. She said Why do you want to be a teacher again, I'm like, really, it's that bad?
She says yah, just talke to me. Why do you want to be a teacher again? And so again I began to talk about why I want to be teacher. That, that! Right there, Pam, go right about that! All right, all right, all right so I went back, rewrote the paper, handed it back to her she circled three or four sentences, These are any good the rest of it's trash Why do you want to be teacher again? The more that I talked about why I want to be teaching the more clarity I got around the ideas that were floating around in my head the the passion that was really burning inside of me that I was able to then more put it on paper. Y'all, I think it was the seventh or eighth iteration, when she finally handed it back to me with all the red marks and crossey-outies and I could begin to correct the grammar and the punctuation and spelling and really make it a good paper. I wrote a really good paper about why I wanted to be a math teacher. But the way I did it was that I was mentored by a more knowledgeable other somebody knew her craft knew what it meant, was able to pull out of me something worth saying before then I could actually craft it and make it be said well

Unknown Speaker :

So how did I become a writer? I became a writer by being mentored. Could we mentor mathematicians? Could we help our students become mathematicians? Now sometimes people will say to me, pam, pam, my kids are'nt becoming mathematicians. You don't know my population. So hang on. I didn't mean mathematicians to be, not in the future. I mean, mathematicians in the here and now I want to create kids that are mathematizing at a second grade level kids that are mathematizing and a sixth grade level, algebra one students mathematizing algebra one content, it's, it's the idea that could they mathematize their world at the level that they are. So I think we can teach real math not fake math. It's not about telling math, it's about experiencing real math. I think we can get kids to mathematize at their level that they can literally use the relationships and connections they own to create new math for them. Now that's not crazy outside the standards.

Pam Harris :

I think we're actually doing this within the standards, that kids are actually solving problems that they will be solving at their grade level, but using the things they know. And as they do that they're creating relationships in their head. They're constructing literally the standards that they're supposed to learn that year. And as we do that, we can mentor mathematicians.
So, y'all, if you like the podcast, we'd love it if you go to your favorite podcast place and like it and give us a review so more people can find it. Check out our website mathisFigureOutAble.com. We'd like to invite you to join us on Tuesdays and Wednesdays for hashtag math strat chat, where we chat about strategies, I throw out a problem to the world. People throw in their solutions, and we chat with each other about how they're thinking and reasoning about how they are mathematizing so we can mentor more mathematicians. So if you're interested to learn more math, and you want to help students become the mathematicians they can be, then the Math is Figure-Out-Able podcast is for you because math is Figure-Out-Able.