Ep 56: For Parents: Why Does "New Math" Look Different?

Pam Harris  00:01

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

Kim Montague  00:09

And I'm Kim Montague.

Pam Harris  00:10

And we teach math teachers. In this podcast, we help teachers refine their math teaching so that more students are more successful. 

Kim Montague  00:22

In this week's episode, we're again talking directly to you, parents. We know you have questions, so we decided to make a few episodes just for parents. Last week, we discussed a bit of history to explain why math teaching might be different today. Today, let's talk about why math teaching looks so different.

Pam Harris  00:42

Yeah, welcome parents. Super great to have you listening. So have you seen more pictures and drawings in math class? What is that all about? Why would we dumb down math for your kids? I could imagine that it might make some of you feel a bit unsure, uncertain to see that teachers are making math more fuzzy, or in many cases, it looks much more complicated. 

Kim Montague  01:07

Right. 

Pam Harris  01:08

Why are teachers doing all this weird stuff instead of just clearly showing kids the steps? Isn't that a whole lot more work? Just do the line them up steps already.

Kim Montague  01:19

Yeah, that could certainly be frustrating and unnerving. So let's talk about it. Well, remember that in the last episode, we discussed that the nature of math hasn't changed. That mathematics is about using relationships to solve problems. 

Pam Harris  01:34

But historically, teaching has left out the real essence of math, and it has just kind of taught kids how to get answers. Line the numbers up, do the steps, get answers, right? Today, we are attempting to have our kids make better sense of what math really is. Consider that there are times where you do what we would call Real Math, when you do things like have to think about what time you have to leave in order to get somewhere on time. Or when you figure out how much change you should get back. Or when you decide what's the better buy when you're choosing between two boxes of cereal. All of these could use relationships among numbers to figure out what's going on. Let me give you a further example of what we mean. If I were to ask you a problem, like, I don't know, random 99 plus, say, 37. You probably learned 99, 37, you lined those numbers up, then you added the digits by columns, you started with the small numbers, and you just added the digits. And then you carried when you needed to and - right? Like that's kind of how we learned that. You may never have thought about the numbers 99 and 37. You might just have dutifully done the steps because that's what addition quote unquote, means. But we're trying to help your students think about the numbers and use what they know, to influence how they might solve that problem. So think about 99... like when I say it that way, when I go 99... you are tempted to say 100 right? And everybody just was like 99, 100. Well, yeah, so I'm just trying to like ping on some prior knowledge of yours. 99, 100. If you're thinking about the problem 99 plus 37, could you think about 99... 100? Well, now I've already added one, I was supposed to add 37. So 99, 100, I still have 36 left. What is 100 and 36? Well that's just 136. Could you use what you know about 99 and 37 to just think about 100 and 36?

Kim Montague  03:43

I love that. And what's even more important to me is that when you and I lined up 99 and 37 we found an answer to that one problem. But understanding that 99 is close to 100, and that we can use that understanding or that kind of generalization, we can solve anything plus 99 all day long.

Pam Harris  04:02

Yeah, like more problems are accessible to us. Yeah, really, you can think about 98 plus anything or 97 plus anything. Or for heaven's sakes, 999 plus anything. Right? And check out how that influences how we could think about problems like 99 times 37. What? No way. We could think about that problem? Like could we think about 99 37s? We learned to line those up and then do a bunch of little multiplications. Right? And then you kind of got line one and then there was this magic zero and then you got line two, and then you had to add up a bunch of stuff. That was sort of the way to multiply numbers like 99 times 37. But could we think about 99 being close to almost 100 and then instead think about 100 37s? Could that help us? For sure to estimate. Right? If we're thinking about 99 37s, we can estimate that it should be close to 100 37s. What is 100 times 37? Is that just 3700 or thirty-seven hundred? Like 37 times 100 is thirty-seven hundred. So we now instantly know that's a bit too much. But now we have a great estimate for what 99 37s should be. Well, could we also if we know a 100 37s is 3700, so 99 37s, we just need one less 37. So what is 3700 minus 37? Kim, I'm gonna put you on the spot. What is 3700 minus 37? How might you think about that problem? 

Kim Montague  05:37

Oh, so I would think about 30 less. So 3700 minus 30, is 3670. And then I've already subtracted the 30. So then I need to subtract the seven. So I don't have a piece of paper. I mean, I would want to write something down. So I have 3670. So then it's 3663.

Pam Harris  06:02

Yeah, in some nice figure-out-able steps. Now you guys might want to have written that down, as Kim was talking about it. I kind of almost wanted to, just to sort of keep track of the relationships she was using. But notice that we can absolutely do that in just a couple of steps, in some figure-out-able, reasonable - reason-out-able? I don't know if that's a word- ways of using relationships between 99 and 37. 

Kim Montague  06:30

Yeah.

Pam Harris  06:31

Y'all parents, that's what we want to create in your kids. We want to create in your kids students who can think to themselves, "What do I know?" Like, can I use what I know about these numbers to solve this problem? And when they can, just use those relationships to solve the problems. So we recognize as math educators, that there are connections that can happen naturally in the brain. And we are trying to capitalize on those connections, just like you just heard Kim, capitalize on those connections.

Kim Montague  07:03

Yeah. So some of you have maybe never ever thought about how 99 is close to 100 and used that to solve problems. But because we just brought it out, you might be like, "Oh, my gosh, I can use that." And that's why this kind of conversation is so important. Or maybe you had, and we could have helped you do that so much earlier and deeper if we had been actively helping you develop things like that.

Pam Harris  07:28

Yeah. So regardless of whether you were sort of naturally doing things like that on your own or we just sort of mentioned it right now and you're like, "Wow, that's a new idea." This is the kind of conversation we want to have with your students in math class. But when we say things like that, we can't necessarily see what's happening in their heads, right? Like, if they're just sort of doing what Kim just did in their head, we can't see it. So we're trying to pull that stuff out, that could be happening naturally in their head or happening as we suggest it, and we're trying to pull that out of them and get it on paper, get it on the board in order to communicate with others. And that helps then all of us build thinking. Because remember, we need thinkers these days, not just calculators. So what we see on paper can look really messy, because it's actually but - let me be clear. When we pull it out of kids, it could look messy on paper. But it's actually not that messy in their heads. It just gets messy as we try to make it visible. We try to make it something that we can all talk about. So when we try to pull it out of what's happening and represent it on paper, that can look kind of messy.

Kim Montague  08:38

Yeah. So you even heard us today, have you ever had a thought and you try to talk about it, and you kind of stumble over your words a little bit? It takes - right we've done that today - it actually takes a minute to get clear on what you're trying to say. And that's what's happening as we try to transition from what your student is thinking, to putting it on paper. But it's an important step. Making the thinking visible allows us to help students refine their thinking. And we can all discuss the relationships and get better at using them.

Pam Harris  09:09

Yeah, that's a really important point.

Kim Montague  09:11

Yeah. So parents, you might be seeing hops on a line or rectangles that are cut into pieces, like when your students are doing some work. And those might look super strange, like what in the world are you doing? Those representations are an attempt to model the thinking that is happening inside their heads. The thinking that's happening in their heads, the strategies, those are what we call strategies for messing with numbers, that's what we care about the most, the thinking.

Pam Harris  09:40

The thinking, absolutely. And so what we are advocating for might be different than what your student is actually experiencing. And we recognize that. We're advocating really to focus on this thinking and reasoning and using representations to make that thinking visible and we recognize that might not actually be what's happening in your student's classroom. So parents, we invite you to help us help teachers. The more that we all understand Real Math and what it means to do real math, the more we can all advocate for better and better teaching. And we can open up the mathematical gateway for so many more students. 

Kim Montague  10:23

Yeah. So we've got one more episode for you, parents, just for you about how you can support your students, some steps that you can take to help your students in their journey to succeed in this math endeavor.

Pam Harris  10:35

So parents, 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. So stay tuned to help make more sense of today's math teaching, and really math itself, because Math is Figure-Out-Able!