Pam Harris  00:01

Hey fellow mathematicians! 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 make the strong case that mathematizing is not about mimicking steps or rote memorizing facts. But it's about thinking and reasoning about creating and using mental relationships. We take the stance that not only are algorithms not particularly helpful in teaching, but that mimicking algorithms actually keeps students from being the mathematicians they can be. We answer the question, if not algorithms and step by step procedures, then what?

Kim Montague  00:40

So we're in the holiday season for a lot of us and you may be home with your kids. So last week, we talked about some of our favorite games and suggested some things that maybe you wanted to add to your list. 

Pam Harris  00:52

For gift giving.

Kim Montague  00:52

For gift giving, right, and so we want to share a little bit about ways that you can bring math into your family-time while you're home with your people.

Pam Harris  01:02

So if you're spending a little bit more time with your people, this time of the year at home, I know I'm going to be, we're gonna have all of our kids here this holiday season. I'm so excited to have them whole home. We're kind of empty nesters a little bit. And so having all four plus the two new is just going to be really fun. What kinds of things might you do if you have littles at home and you want to kind of bring math more into your home and your experience with them? We often get questions from teachers about what they can do with their own littles and what they can tell their parents, so parents of their students, what can they do as they have their students at home with them? And so we thought we'd spend just a minute talking about some of the things that we've done in the past, some of the things we think that would work well, as you're just sort of going about your normal everyday stuff. So I'm going to just say I like to bake. And I don't bake a lot, but I do around December. So when it gets near Christmas, for me and my family, I'm a baking machine, which also means I do tend to put on a few pounds, I'm not going to do that this year. This year I'm gonna exercise.  There's some math! Yeah, there you go. I'm gonna exercise, exercise, exercise so that I can imbibe just a little bit. But anyway, I do like to bake, we like to make fudge. We like to make sugar cookies and decorate them. And in fact, a colleague of ours, Holly, has just told me a new recipe for frosting. I'm excited to try it. And as I try that new recipe for frosting, I'm going to be talking out loud with my kids. I'm going to say things like, "What if we were only making half of this recipe?" So especially when you're talking with students, or kids that are just starting to learn fractions, grab something that needs like a half a cup, or a half a teaspoon and say things like, "What if we're only making half a recipe? What is half of a half?" And when they say, "Well, we could just eyeball it." You could say, "Well, sure we could. But do we have a spoon or a cup that is that measurement? Like could we think about that?" I know, I've been talking to a friend in South Africa that measures things in milliliters. And she was talking about how they're often thinking about a quarter of 1000 milliliters. And so what does that look like? Well, what is a quarter of 1000? Can you think about a half of 1000? Can that help you find a quarter of 1000? So instead of just using the cup that it says start wondering about half of a batch, you don't even have to make half of a batch. Just wonder about it out loud. Or triple it or quadruple it or you know, in some way, kind of - and then when you're tripling and quadrupling recipes, and even if you're actually doing it or wondering about it, don't choose the thing, where it's like, hey, we need one cup of flour. If we triple this, how much are we gonna-? Like don't use that one. Ask the one where you need three tablespoons of something. If we triple this, how many will we need? And then - let me just stay there for a minute. So I don't make pancakes very often. Except when all my kids are home! Then I'm like, "Hey, let's have some waffles or pancakes or something." Well, I have a homemade recipe that calls for three teaspoons of baking powder. So three teaspoons of baking powder. Well, if I'm going to quadruple that batch, I can put in three times four, 12, teaspoons of baking powder. I can do that. At one point I said to my son, I was like, "Dude, figure out what other measurement that is. I don't want to sit here and measure 12 of those, like, can we figure out is there some..." can it be a quarter of a cup plus another teaspoon? Like there's got to be some kind of - and honestly, we wrote it down. I don't remember what it is anymore. But that's the kind of conversation that you could just have just like sort of raise it like, I'm lazy. I don't want to measure all these out, could you kind of help me think about that.

Kim Montague  04:42

Yeah. So I I'm not a real big baker.

Pam Harris  04:47

Okay, you're not a baker at all. 

Kim Montague  04:49

It's not my thing. But I do have a son who loves the things. He loves dessert. And so I have started saying to him, fantastic. I'll buy the stuff, but you're going to help me and it's been wonderful. He has his own little cooking set with, you know, spatulas and the measuring cups and things. And he's really, because it's for him, and because he's invested, then he has spent more time talking about measuring tools and different amounts and fractions probably earlier than he would have had he not been involved. So just involving them in general, I think gives a lot of opportunity to have those conversations. Also, my kids often, thanks grandparents, get money around this time, and they spend time planning out what they think they want to get for spending on their money, right? So because they have Amazon, they can look on the Amazon. Find out how much something costs, and they want to know, are you covering tax for me? Which is the answer: no. So they have to calculate how much money do they have? And how much are they gonna have left when they spend it? Do I want to spend it? So lots of adding and subtracting decimals considering, you know, saving and spending every year.

Pam Harris  06:07

I'm sure they're also doing some estimating and rounding and making sense of things. 

Kim Montague  06:12

Oh sure.

Pam Harris  06:13

Yeah, nice. And so rather than just a bit of trial and error, you're actually encouraging them like, let's plan this. Let's actually, you know, like, make some sense of things. Isn't this the time of the year for book orders too?

Kim Montague  06:25

Well, lots of different times throughout the year are Scholastic book order times, and so same kind of thing. You know, a lot of them are 99 cents, or 2.99. And so there's a lot of opportunity, we get holiday book orders most often. And so there's a lot of opportunity for nice round numbers, right? No. They're all 99s. But it's been so much fun, because we can have conversations about estimating or thinking about the total amount and then backing off a little bit since they have a lot of 99 or 98 cents compared at the end.

Pam Harris  06:57

Absolutely. Lots of over strategy going on there.

Kim Montague  07:00

 Uh-huh.

Pam Harris  07:00

Very cool. So another thing I'm thinking about is involving my kids, when they were younger, in wrapping presents. And just like, "Hey, this is a rectangular prism. Like are you gonna do this the long way, the short way?" And kind of the spatial sense of wrapping presents and sometimes letting them use too much wrapping paper. And then noticing that. I mean, "Wow because you did it that way, look how much extra if you would have done it this way." But also, we have kind of a funny thing in our family. My husband refuses to wrap anything that is not a rectangular prism. So whatever it is - now I'll like jury-rig it. I'll like make a big, like bon-bon out of it, you know, where you sort of like wrap it up and kind of have the ends and put ribbons on it. And he looks at me like, "Are you serious?" Because it's lumpy, whatever. And he's like, "No, then we can't stack it." And I'm like, "Why do we have to stack the presents, can't we-?" Anyways, every year it's an... argument? It's a discussion between him and me. He will find a box, no matter what. He will find a box to put it in, and then he'll wrap the box and it's whatever. So a couple years ago, I decided, Oh, yeah. Oh, yeah. So I bought a box of boxes. These beautiful, like they're already kind of like they're, well they aren't really wrapped, but you don't wrap them because they're like already wrapped. And I'm like, "Here, here, honey, here you go." And he loves it. Like it was a big joke for me. And he loves it. He's like, "I'm just putting everything in those boxes." 

Kim Montague  08:22

I might need those.

Pam Harris  08:23

It kind of saves wrapping paper too. So that's kind of a nice earthy thing. Yeah. All right. I'll give him that. Fine. Fine. Alright, so another thing that we do around our house is after we make all that stuff, like Christmas cookies and fudge, and can I even think of all the other things? Mostly those. We make a ton of different kinds of cookies though, there are kinds you can - you don't care. Anyway. So after we make all that stuff, then we will take them to our neighbors and carol. So we like to sing in our family, which I know - "Don't sing on air," my kids are saying right now. "Please, Mom, don't sing on air." So I'm not the soloist in the family. I could carry a part, I can carry a tune. And so out of us we have good four parts. So we go caroling. As we do that, I will often have the discussion. Okay. So if we're going to go carol to our six neighbors, or whoever we choose that we're going to, you know, deliver some goodies and go caroling. How many of these kinds of cookies should we make? How many batches of this should we make? Like, how many plates do we need? How much plastic wrap, like whatever, all the things, I just don't do it all myself. I just involve my kids in the conversation. It has actually been interesting to then have my daughter come back and say, "Hey, I was asked to make this stuff for this thing. And because you're always involving me when you're deciding how much to make, and how many of all the things," she's like, all of her peers - so she's at university level, she's 20 years old-  she's like, "All my peers they were like, how do you know how much to make and how much to buy?" And she's like, "We do this all the time." Anyway, so just the more you can kind of involve them in that kind of whatever it is that you do, just involve them in the conversation. You know, like I mentioned, we're gonna have a new frosting recipe, alright, like let's decide. It's new. So I got to like, figure out how much are we making, how much of the ingredients we're gonna make. All that kind of stuff.

Kim Montague  10:05

You're giving them experience, right? So that they can fall back on that experience, just like we talked about a couple of weeks ago.

Pam Harris  10:11

Yeah, that's what teaching is all about, let's give them the experience. Absolutely.

Kim Montague  10:15

So I will admit that because we are a little on the go and a little busy, we do not do a super often regular sit down dinner together. So this is especially common during this time, lots of like, face to face, fully intentional meals.

Pam Harris  10:34

So wait, wait. So when you said you don't? That's because typically -

Kim Montague  10:37

Typically it's sports and things and all the clubs and whatever. Right?  So this time of the year, there's a lot more of that. And so we actually like to play dinner games as well as board games. And so we will play games like Guess My Number or play I Have, You Need a little bit with something a little funky, a little bit different, maybe some fractions now that they're older, maybe with some decimals. Not long. Not long enough that it's 30 minutes of me, you know, drilling numbers at them. But as they're setting the table, we will play a little something. We have pulled up MathStratChat and had conversations about it. Now, that might not be super interesting to everybody. But it might be. If you've never tried it, it might be interesting for your kids to just hear you talk out loud about how you're thinking about something. And the more experience they have with that, the more natural it will become.

Pam Harris  11:33

Nice, nice. And you mentioned setting the table. So ya'll, if you have littles a thing that you can do is say, "Okay, let's set the table. How many - pick it - plates do we need?" And then when the little you know, I'm talking three, four or five year old, when that little says, "Well, I don't know." Then you can say, "Well, how many people do we have?" And if they say, "Well, we need lots of plates. We need 100 plates!"  So you go, "100 plates, wow!" Or if they say six, and they're just guessing, then give them six. And when they put them around the table, and there's extra, you can say, "Oh, how many did we really, actually need? How many extra do we have then? Because since you said six." Or six would be exactly what my family would need until I just got two new daughters-in-law. But yeah, the point is like estimate first, give them the number that they said, kind of build that one to one idea. How many do we need? You think that many? Let's try it out. Oh, that wasn't enough. How many more do we need? Okay, well, that's interesting. We needed five plates. We needed five cups as well, who knew? You're just sort of noticing and kind of bringing it up as you're kind of just doing the stuff that needs to happen anyway. Yeah, totally cool.

Kim Montague  12:42

I think something that you and I both do is go on walks with our families.

Pam Harris  12:47

We can do that. because we're in Texas. So the weather is usually ok. 

Kim Montague  12:50

I mean, it's like 82 yesterday, and it's December. 

Pam Harris  12:53

We can hope  it'll get down into cooler weather when it's time to go on walks. Yeah.

Kim Montague  12:57

So we do go on walks. And I don't know if you guys do anything besides chat. But a lot of times my kids are not super excited about going on walks. And so we'll play games as we're going on walks, and we'll count steps and then predict how far we've gone when I announce the time. So it's been 10 minutes, how many steps have you gone? Or we've gone this many steps, how much time do you think has gone by. Just to start estimating like, time and space and distance. So just, you know, little conversation about little mathy stuff.

Pam Harris  13:30

I'm wondering, do you ever look at the house numbers and say, "Hey, can you factor that? Or is that a prime?"

Kim Montague  13:37

That's a me running thing, not a a kid walking thing.

Pam Harris  13:39

Oh, that's only when you run?

Kim Montague  13:42

I should totally do that though. I hadn't considered that.

Pam Harris  13:45

I mean, you used to chide me a little bit, you're like, "You know, Pam when you're running."  Because yeah, I jog, Kim runs. I used to jog, until I had knee surgery, long story. Anyway. But she would say, "You know, like, when you're doing that, don't you you know, look at the license plates and begin to wonder." And I was like, no, until I built more relationships. And now I can. Now I own more. So I actually can play with stuff. So play with whatever numbers that you see, that totally can work. We also talked about things that we do on car trips. Now I'll be honest, my kids are not as excited to play car trip games. So I have tried lots of games. I think is partly because a couple of mine get car sick. And so they're like stop with making me think kind of things. We do play a game called Cows On Your Side. Whereas we're driving down the road, if you see cows on your side, then you say cows on my side and you get a point. If you first see the cows on the other side of the car, then you say cows on your side then you get two points and they have to lose a point. Oh, so you can totally keep track of points if you want to. We have totally gone on car trips with the team especially when we're going to film and so we're all in my van. And no one will play with me, which is tragic, except Sue. Sue play with me kind of. She has her own version where she just will randomly yell out, "Cows on my side," or she'll yell out things like, "Buffalo on your side or sheep on my side," or it's just kind of like it almost could be road sign on my side, it doesn't really matter, Sue will just yell out some funny thing on her side. And we don't really keep track of points. But anyway, so if you want to play points, Cows On Your Side can be fun, depending on if you're driving somewhere that has cows. So I guess I always grew up in a state that had cows. Do all of the United States states have cows? No? Alright, on Twitter, I want to hear from you if you are in a state where you will never see a cow. I want to hear from you. I mean, if you live in a city, a big city, I get it. But if you get out of the city, I've been in New York state there are cows. Anyway, moving on. Kim you actually play games with your kids in the car. Give us just a couple quick ones.

Kim Montague  15:49

So I think we've talked about this before. We wonder a lot. So my kids will, I have always tried to just wonder aloud, like we've suggested several times here. And so they will wonder aloud as well. And so we'll wonder things about mileage signs or how long until or if we're going this fast how long until we get there if it's this many miles? Yeah, I think we've talked about this before, maybe not.

Pam Harris  16:16

How far are we going? How far have we gone? So if we've gone that far, is it gonna take us you know, we're gonna speed up, slow down? Yeah, just all sorts of rate questions. Totally cool. So y'all maybe the most important thing to think about as you're sort of maybe spending some more together time if you're trying to bring some math conversation into it, is just involve everybody in your thinking, wonder aloud. Ask them how they're figuring things, share your thoughts. Just sort of put it out there and kind of see what happens. So if you want to learn more math and refine your math teaching so that you and students are mathematizing more and more, then join the Math is Figure-Out-Able movement to help us spread the word that Math is Figure Out Able!