Pam Harris  00:02

Hey, parents and teachers, welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris.

Kim Montague  00:10

And I'm Kim Montague.

Pam Harris  00:11

And to introduce us just a little: we teach math teachers. In this podcast, we help teachers refine their math teaching so that more students are more successful.

Kim Montague  00:25

But in this week's episode, we're talking directly to you, parents. We know you have questions, so we decided to make a few episodes just for parents. So, welcome!

Pam Harris  00:35

Yeah, thank you so much for joining us. You are so important. Your child is so important. You might be listening today because someone recommended this podcast to you. We are so grateful that you're joining us for the next few minutes. We've decided to tackle the really difficult conversation around why math instruction has changed. Why does it look so different? You might have seen The Incredibles movie, Incredibles 2, where there's this great scene where the dad is trying to help his son with his homework and he's excited and frustrated. "Math is math! You can't change math!" Some of you have seen that scene. I love that movie. Maybe you've felt that way as well. So what is going on with this new math? Why does it look so different than maybe what you were used to?

Kim Montague  01:29

Yeah, we hear you because we're parents, and we're also teachers. We get calls from friends who are frustrated and trying to help their students. So we're aware that you want to be supportive to your kids and to your kids' teachers. We're also aware that you may feel frustration about math looking so different these days. So let's talk about that.

Pam Harris  01:49

Yeah, and let me just say, we are so grateful that you care about your student's education. We want you to be involved. We love the fact that you're listening. Thank you so much for caring about you and your kids and how that's all going. And both Kim, you and I just said that math look so different. And we said new math. But let's actually do a little history about math and math instruction that you might find helpful, parents. I'm going to keep this super brief. But I want to give you a glimpse of the 'what' and help you understand the 'why'.

Kim Montague  02:25

Yeah, the 'why' is so important for you to understand. That it's not actually 'new math' that's going on. What's maybe new is that what we're actually asking of kids is more than ever before, because we can. If you would briefly think back to the way you and I were taught how to add numbers. So parents, we would have been told to line them up underneath each other, and then add in columns starting from right to left. And that's a way that adding can be done.

Pam Harris  02:54

Right. But it's not the only way. Like- and that might blow your mind just a little bit that there are other ways. It's not the definition of doing math is to do those steps. Like for example, let's take subtraction. Same thing. We were sort of taught to line the numbers up, borrow when needed, etc. However, there are other ways to subtract. So for example, Kim, how might you find, say 36 minus 19? 

Kim Montague  03:22

Oh, okay. So for 36 minus 19, I would actually think about 36 minus 20. And I know 36 minus 20 is 16. But I actually subtracted too much, just one too much. So instead of 16 then my answer would be 17.

Pam Harris  03:42

Bam. And we kind of call that an Over Subtraction strategy. Now parents you might be thinking, Okay, well, that's actually what I would do. But, you know, that's not the way the teacher showed me. So on the paper, I might have done all the crossey-outies and borrowing and what they now call regrouping. You might have sort of done what the teacher said. But in your head, you were doing what Kim did. Well, to be clear, I wasn't. I was just dutifully doing what my teacher told me to do. So the math that we were taught was a way. Procedures. Steps. Where you line them up to add or multiply or you do that house top division. That gave many people the sense that procedures, that that procedure was the only way. When in reality, those procedures were only one way to get answers. And you might find it interesting that that one way is not actually typically the way that mathematicians solve those problems. Or sort of mathy people like engineers, that they do more like what Kim did, where they use relationships to solve problems. So the procedural way, the step by step way to get answers is a way to get answers. But what it doesn't do is help you understand numbers or mathematical relationships. Or how to reason better, how to solve problems, like Kim just did.

Kim Montague  05:05

Yeah, some of you may use your intuition and relationships to solve problems when you're in the store or maybe other areas of your life. But some people don't. Why is that?

Pam Harris  05:15

So a little history. Would you consider that I think that today's generation of parents and their parents were actually taught very similarly. That arithmetic is procedures: line the numbers up, get the answers. But the older generation actually had to use math to survive. What I mean by that is grandparents were calculating the same way in school, lining them up doing the procedures, but that they learned relationships in life, because they had to. They didn't have technology. So they counted back when they were getting changed. They had to pay bills and keep their checkbook current, unlike many of us today. All without technology. They didn't have cash registers, or, for sure, not calculators, or spreadsheets, none of that stuff was around. They had to reason about numbers to survive. But consider the next generation, the parents of today's students. For the most part, that generation was still taught math as steps and procedures to get answers in school. But now they have less real experience in life because they had technology. So my generation and younger were taught the same way. But they actually owned less Real Math, because we could just pick up a calculator, punch it into a cash register, use a spreadsheet on a computer, all of those things were sort of available to us. And because of that, we were kind of less in the experience of having to mess with numbers and figure out relationships. Let me give you a quick example. During the university, I had a couple of months over Christmas, where I worked in a drugstore. And if you - so a little bit more history about me. I was the quintessential, I memorized the steps, I did the procedures, I got answers. I was not doing what we now call "Real Math". I was not doing what we advocate now that teachers do with students to help them really understand math. So you might relate to this, that as that sort of non math person, even though I was doing a lot of fake math, and I was working in the drugstore, when I would ring people up and use the cash register, and I would say okay, you owe me blank. And every once a while people would hand me a $20 bill and a nickel. And I'd be like, whatever weirdo and I would just type that in. And I never noticed that they would be getting back an even set of bills. Because they had already thought about the fact that if they gave me that extra nickel, I wouldn't give them back all those cents, I would just give them back that even bill. But I hadn't thought about that. I would just dutifully type it in, I would look at them like they were odd for giving me that extra nickel, or the extra penny, or whatever it was. I would look at them like, whatever. And I would just type it in, never realizing. I mean, it's embarrassing now for me to think about the fact that I was so not numerically powerful at all, that I would just, you know, like hand them back the bill and not even know why they had given me that change. Similarly, not too long ago, I was in a small drugstore. And I had just a few things. And I got up to the checkout line. And as I got up there, the power went out. There were big windows in the front of the store so we could sort of still see what was happening. But there was no power. Very fascinating to me that both the sort of clerk there that was checking us out and then the manager who came over - the power's out - would not let us check out. Because they were convinced we couldn't figure out what we owed. And I said, "No, no, no, we can add this up. We have the prices right here. We can add these numbers up." And then the manager goes, "But we can't figure out sales tax." I was like, "No, we actually can." Like we - and nope, they were not hearing it. You could tell they were both very nervous. And they were both not going to have us be able to check out. What I'm suggesting is that we have a generation of people who because we were never sort of put in this position that we had to figure that stuff out. 

Kim Montague  09:14

Right.

Pam Harris  09:14

We kind of can't. Sometimes we say that the kids these days are really tech savvy. I think kids today are tech dependent. So that's noteworthy, it's noteworthy that we kind of might have a generation of people who because they weren't kind of forced or highly encouraged to deal with relationships among numbers, all they have are these procedures and a step by step instructions that they got in school. So parents, I invite you to lean into the possibility that today's parents might not understand what teachers are trying to do with math these days. Because that generation never built the mental relationships to be able to recognize them in today's math teaching. Math to that generation was largely devoid of meaning and so that generation might not recognize the meaning that can be in Real Math. So we're suggesting it's not just about getting answers. Today, we have technology, we have calculators that can get answers. When we were in school, I would suggest all those steps and procedures are about getting answers. But today, technology can get those answers. So we don't need that anymore. Now, we need people who can solve problems by reasoning. Teachers today are trying to help your students, not just Google to find answers. But we want to help students, we want to create students who can create the Google of the future. Right? Not just Google to get answers. So let's create Google, not just ask Siri or Alexa for facts, but be able to use those facts to create new products and services. And frankly, to innovate. Facts are everywhere. Whatever. We can get those just on the computer, we type them in, and we can ask Siri or Alexa. We want to help your students use those facts. Now, this conversation could be a little tricky. We are not interested in bashing teachers. 

Kim Montague  11:17

Right. 

Pam Harris  11:18

But the reality is that much of implementation of what we would hope for in math teaching today is not actually what any of us sort of wishes it could be.

Kim Montague  11:28

Right. And so as we're supporting teachers, let's remember that they also grew up in the same system, where step by step procedures were also the norm, right? 

Pam Harris  11:37

For them as well. 

Kim Montague  11:38

Right. So maybe what you're seeing isn't as fine tuned as we all wish it could be. But the math behind it is solid. And we're so grateful for teachers who are willing to learn and grow along with their students, as we all work to get better at this fascinating work of raising kids who are better and better at mathematizing. 

Pam Harris  11:57

So today, we hope we've helped give you a glimpse of why things might seem so different to you in math teaching. We tried to give you a brief understanding of how math isn't just about getting an answer.

Kim Montague  12:10

Yeah. And next week, we're going to be talking more about how math instruction maybe looks so different, why you're seeing things on your papers. What's all this picture drawing? So stay tuned for more to help parents understand what we're trying to do.

Pam Harris  12:22

So thanks for listening in. Teachers, thank you for recommending this podcast to your parents who are interested to understand why math instruction needed to change. We've got a few more episodes planned to help you, parents, so tuned in to help make more sense out of today's math teaching because Math is Figure-Out-Able!