Ep 40: Homework Pt 1

Pam Harris  00:03

Hey fellow mathematicians. 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  00:12

And we're here to suggest that mathematizing is not about mimicking or rote memorizing, but it's about thinking and reasoning; about creating and using mental relationships. That mathematics 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  00:37

Hey, y'all, we're on episode 40. We've been thinking ahead and planning about all we want to do in the podcast. But we thought Episode 50 would be a great time to just answer some questions that you guys have for us. So if you have a burning question for us to tackle, we'd love to hear it. You can email your wonders to me at Kim@mathisFigureOutAble.com. That's Kim@mathisfigureoutable.com. And we'll see what we can do.

Pam Harris  01:13

Alright. So this is gonna be a little bit of fun. Listeners, Kim and I usually get together to record a podcast by planning a little bit of an outline. Sometimes we put in quotes we want to quote, but at least we have some idea of the flow. But when we decided to do an episode on homework, which is today is on homework, and Kim paused and said, "I'm not actually sure what you think about homework. Oh, let's do this one live without planning" with that snarky dare-devil glint in her eye. Because if you've ever met Kim, there's definitely a little snark involved. So I said, "Let's do it." Alright, so y'all, here we go. We're gonna talk about homework.

Kim Montague  01:59

And I'm gonna just start, okay, so, I'm gonna start by saying... Can I do this? Can I just say, in general, I am not a fan. Is that okay?

Pam Harris  02:08

I mean, that's interesting. What do you mean, you're not a fan of what exactly?

Kim Montague  02:13

I'm not a fan of homework in general, um -

Pam Harris  02:16

Like you'll just never give kids homework? 

Kim Montague  02:18

I have given homework. There have been, you know, we can talk about this later. But there are times where I've had administrators that said, you'll do homework. 

Pam Harris  02:26

Like, thou shalt give homework?

Kim Montague  02:29

Yeah, as a grade level, you'll give X amount of homework per night or per week. And so I have given homework. But both as a teacher, and as a parent, I have appreciated the years where homework is not a part of our family time.

Pam Harris  02:47

Well, so let me backup just a minute. You just said that, when your principal said you had to or grade level or whatever, are you saying that you only gave homework when you had to? Like as a teacher, if there was no mandate to give homework would you not have?

Kim Montague  03:03

That's a good question. Okay, so here's the thing, there are times where I have sent things home with kids, which is way less often than I think lots of other people do. So maybe I'll tell you what those things were?

Pam Harris  03:18

Okay. 

Kim Montague  03:19

If a kid -

Pam Harris  03:20

Hey, I'm gonna pause you for just a second. I can actually tell you some of that, because remember, my kids had you as a teacher? 

Kim Montague  03:27

They did. 

Pam Harris  03:27

And you and I have had - now that was a few years ago - you and I've had a conversation about the fact that like, you're kind of confident, right? But there were a few times where you sent something home that, am I right, you wondered a little bit what I thought?

Kim Montague  03:38

Oh, sure. 

Pam Harris  03:39

Like you'd tell me later, you were like, "Yeah I was kind of wondering when I sent that home." Like Pam's looking at what comes home, which was true. I did. I mean, honestly, I looked less at any other subject. When my kids come home from school, listeners, I would say, "Hey, guys, how was school?" In my in my head, I would be like, how's math? Like, it really was all about how math class was, how math is going. And it was a little bit about all the rest of it. Okay, Kim, I totally interrupted you. 

Kim Montague  04:03

That's okay.

Pam Harris  04:03

So tell us what you did send home for homework. What kinds of things?

Kim Montague  04:06

So if a student was confident that they knew what to do, how to solve, what was expected, but just needed more time, then they could take it home. 

Pam Harris  04:21

Okay.

Kim Montague  04:22

If a student was needing help, struggling working on it, then I did not send it home. Because I don't think that it is a parent's responsibility. Now I absolutely want them involved. And so if I had a good relationship with a parent, and they felt confident and wanted to give some assistance, okay. But I don't think it's my job to assign work, and then say, "Oh, you're not done.... And you need help with this... Take it home."

Pam Harris  04:53

So let me parse that out. You're saying that if a kid was like, going. And they're going, going, going, but they just needed more time, they may be a little slower processor or something, then you're like, "Sweetheart just take it home," no problem. But if a kid was like struggling and frustrated and or maybe not even frustrated, but just needed more of you, more sort of that, what's the word I'm looking for... Vygotsky... Guidance? Or more knowledgable other, yeah. The more knowledgable other needed some help, then you're not like, "Hey, go tell your parents, who aren't math teachers, go make them help you."

Kim Montague  05:27

It's so interesting to me, because I see it all the time on, you know, my neighborhood group or on a Facebook, "Hey, can somebody in the neighborhood help me with my kids' seventh grade homework?" It happens all the time. 

Pam Harris  05:40

Yeah, yeah. And you think because that kid obviously isn't understanding, and so the parents are trying to help, which, of course. Let's actually say it one more time, because I know you said it, but we would never, Kim and I feel very strongly about this, we would never come between a kid and their parents. Like we want parents' involvement. We honor parents, we would never say parents don't help your kid or parents stay out of this, we'll just handle it. That's not what we're saying at all. We love parents. We have parent meetings. We've done parent classes up the Ying Yang. Like we love involving parents, we love having parents, we want to involve parents at whatever level they have time for and want to be involved in all the things. So we would never tell parents get out, we'll take care of it. That's not the case at all. But at the same token, I think what I hear you saying is we don't also expect the parent to take our place.

Kim Montague  06:31

Yeah, "Your kid is struggling with this. So here you go teach them."

Pam Harris  06:34

Yah, "I'm done with them. I'm done with them, it's all on you." So that's interesting that you're kind of differentiating between kids who just need a little bit more time and kids who need more help. And I think that is an important distinction I fully support.

Kim Montague  06:50

I think I've mentioned this before, actually, that it's one of the things that I say to my kids: Do you need time? Or do you need help?

Pam Harris  06:56

Nice, nice. And that's a way that you think about homework. So what other kinds of things do you send home for homework?

Kim Montague  07:04

So it's certainly something that I consider how much of this kind of thing have we done in class together? Right? So when I was required to send home homework, if we had just started a particular topic, or strand, or unit, then I did not send homework with those kinds of things in mind. It would have been something that we had done previously. It would have been some kind of foundational work that kids needed to continue to work with. Lots of geometry terms, lots of social knowledge, right?

Pam Harris  07:39

Things that kids can sort of practice and you're okay with that, because we need practice with social knowledge kinds of things. Hey, that reminds me, we've done an episode on social knowledge. Kim, keep talking, and I'll go see if I can find that episode number to give everybody.

Kim Montague  07:53

Yeah, so another thing that I considered a lot, and we'll come back to parents in a little bit. But one of the problems that I have with a lot of homework is sometimes they don't have the time or the support at home, the place to do the homework, right? We have kids who come home from school, and go straight to baseball practice, gymnastics, art class, whatever, and then --

Pam Harris  08:16

Or work 

Kim Montague  08:17

Or church

Pam Harris  08:17

Or take care of their siblings. They have responsibilities around the home. They have other things that are taking place. Hey, let me just pipe in with that episode number. Episode 17 will help you sort of understand what we mean when we say social knowledge versus logical-mathematical knowledge. And so we're suggesting here that if something is social, we suggest it there as well, that we need practice with that, because it's social, it's convention, it's not something Figure-Out-Able, it's something we have to tell kids. So we want them to have lots of exposure with that. So that makes sense that you've already done it well in class, then sitting at home, then the kids get more practice with it. It doesn't frustrate parents, because it's social, they can look it up on the internet easily if they're not sure. So it's not a frustrating kind of thing that they can do. And that makes a lot of sense. 

Kim Montague  09:07

You know, it's interesting to me, because a lot of teachers that I work with will say to me, you know, I get a lot of parent complaints or parent confusion, maybe more confusion, that I want to help my kid or I'm trying to help my kid, which is fantastic that some students have that. But then we'll talk about the kinds of things being sent home and it's like, oh, yeah, you know, our parents don't have the opportunity maybe to get some understanding about math and strategies, and maybe a little bit why it's not the way that they were taught growing up. And so instead of inviting those kinds of conversations without some parents support and some parent classes, I think I generally tried to send home things that parents felt confident in. They didn't look maybe foolish or maybe didn't look as knowledgeable and then -

Pam Harris  10:01

Yeah we don't  want to put parents in that position where they're like, "I don't know what this - what is new math stuff?" And I can just picture, what is it - The Incredibles 2? "New math? How do you change math? Math is math!" Yeah, if parents have an experience, we don't want them to look foolish in front of their kids or like they don't know or frustrate the parents. And so - we were talking about delaying homework and you didn't use that word, but I kind of wrote down: Why delay? So I'm gonna ask you, you kind of said if we just started something that I'm not saying that home, but I'm gonna send stuff home that we've already done before. Why delay? Because eventually you're going to send home the stuff that you've just started, right? So why delay? Why delay what you're sending home?

Kim Montague  10:45

Well, if it's a new idea for kids, and they're still kind of like just messing with it a little bit, then I don't want them to have that productive struggle. I want that. But I don't want them to have that in a way where they could still be counting. Right? So if I'm sending home something, think about the progression that you talk about -

Pam Harris  11:05

Counting to Additive Reasoning, to Multiplicative Reasoning, to Proportional Reasoning, to Functional Reasoning, uh-huh.

Kim Montague  11:09

If it's a multiplication problem, and I see that I have kids who are still using counting strategies or additive strategies, then I'm not going to send that home with them to continue practice using those strategies that - 

Pam Harris  11:23

That is ingraining those less sophisticated strategies. 

Kim Montague  11:26

Yeah, absolutely. I might send that kind of work home, after we've done a little bit more work with it. And I have an opportunity to guide them a little bit more.

Pam Harris  11:37

So kids have gotten more sophisticated, they're more efficient at what you're talking about. Now, when it goes home, parents aren't going to see, "What are you drawing pictures for? What are those tally marks? You're counting. Just do the algorithms!" So parents aren't going to have that reaction.

Kim Montague  11:52

You know, I was gonna say and even then I'm thinking about the kinds of things that I would have done, where instead of a page of 15 multiplication problems, I might have done something like, "Hey, we've been working on a Doubling and Halving strategy. Here are 10 problems, for which of these problems might a Doubling and Halving strategy be a good strategy? Circle those, do two of them with a Doubling and Halving strategy, bring those back for a conversation the next day."

Pam Harris  12:21

Notice teachers, how that changes the conversation with parents, the parent-kid conversation. So we get a lot of comments from teachers that are frustrated, because the parents are frustrated, because the teacher sent home 25 multiplication problems, and the parents send back the homework with the kid doing 25 algorithms. The algorithm 25 times. And so notice how it changes the conversation. If you say, "Hey, here are 10 fine problems, don't solve them. I want you to choose the ones that Doubling and Halving would work nice for." Now the parent, if the parent is involved, which we'd love, right, then the parent gets to go, "What is Doubling and Halving?" And the kid goes, "Oh, yeah, it's this cool thing." You've done it enough that the kid understands Doubling and Halving, can do Doubling and Halving, so you're delaying until you're at that point. And now the conversation is where the parents like, well, if they don't know, I'm not saying all parents don't know, of course some do. But if they haven't then the kid gets to say, "Well check it out. This is Doubling and Halving." And the parent goes, "Woah, my kid's brilliant! Like, you're brilliant!" Okay, so we're supposed to choose one that works well for it? And now it's like a game, it's like interesting, but they get to kind of like look and see which one is better suited for that strategy. And then they still solve the two problems. At that point, it's much more likely that the parent and the student are going to mess with those two problems Doubling and Halving, much less likely that the parent is going to say, "Do it this way. This is the way I learned in school." And the kid comes back with a couple of algorithms. Y'all we're seeking for homework, we're searching for problems like that everywhere, where it's not going to inadvertently put people in positions that nobody wants to be in. Right?

Kim Montague  13:58

Yeah. And if there are no parents at home, right, which for so many kids there's not, then it's not them relying on somebody else to sit down and do the work with them. Right? It's also not about get the answers to these specific problems. It's about thinking generally, in broad terms about categories of problems. 

Pam Harris  14:16

Oh, you're just reminding me of something I have totally been thinking about. So some of the threads that I've been seeing on - this is so timely right now - threads I've been seeing on social media from teachers is the fact that kids are using cheat sites to do their homework. 

Kim Montague  14:30

Yeah. 

Pam Harris  14:30

And so one of the threads I just saw was... How did they ask it? Something about where can I find problems that kids can't use the cheat sites to answer? So for those of you who aren't familiar, there are many sites out there that you can just type in a math problem. 

Kim Montague  14:46

Yep. 

Pam Harris  14:46

And you can even put in like where it is in a book sometimes, and it's kind of interesting. But you just type in the math problem, and then it will give you the answer. Some of the sites will give you the steps to do the answer. And so a lot of students know that. I'll be honest with you, a couple of my personal kids, in college, they have - now they don't typically just type it in, get an answer, put it down and move on. Because my kids really want, they know math is Figure-Out-Able. But when they get stuck, a thing that they've done is they type it in, they see the answer. They might even see the steps, then they use that to help them figure out what's happening so that they can actually think about what's going on. Many students aren't using in that way. And so teachers are frustrated because they're trying to, well, they're trying to grade homework, which is also interesting, right? That's something we haven't talked about. And students are using these cheat sites. So if you ask questions like Kim just suggested, can you see listeners, how that is going to help your students not be able to use a cheat-site, right? Because if there's no way that you're going to be able to put in those 10 problems and say, "Hey, computer, figure out which one of these of these 10 problems is better to use with Doubling and Halving?" That's not a problem a computer can solve. That takes human intuition, which is what we're trying to develop. It's beautiful Kim, it's an excellent example. So could we write problems, homework assignments, problems in class homework assignments, that asked kids to think and reason, but we're delaying it enough so that they have confidence in that thinking and reasoning?  I'm just gonna clarify something you said a bit earlier Kim, if I may. You said, "I don't want to send kids home to have that productive struggle." I think what you really meant was you don't want to say send kids home to have unproductive struggle. Right?

Kim Montague  16:31

I don't think... I think I clarified that, I want them to have productive struggle. I don't want them to have that productive struggle without the opportunity for somebody to intervene when necessary. 

Pam Harris  16:42

Right, right. 

Kim Montague  16:43

Yeah. 

Pam Harris  16:43

Got it.

Kim Montague  16:44

I actually want them to struggle a little bit. Right? 

Pam Harris  16:47

But not at home so much, right?

Kim Montague  16:49

I don't want them to feel like they can't when they're working really hard. I want there to be somebody in there that can continue to guide them a little bit. 

Pam Harris  17:01

Totally.

Kim Montague  17:01

I don't want them feeling stuck, like I can't do this.

Pam Harris  17:05

Absolutely. And then that just causes sort of unproductive struggle. And now everybody's frustrated. And now we revert to you know, like you said, we revert to less sophisticated strategies, like counting or additive, when we're supposed to be multiplying. We revert to looking stuff up in cheat sites. We revert to calling your aunt - my nieces and nephews will call me for help.

Kim Montague  17:26

Oh, yeah.

Pam Harris  17:27

Like calling somebody for help. Yeah, when instead, we could just sort of be doing some productive things that are just getting us to kind of think but without the frustration that we don't want to have as we send kids home.

Kim Montague  17:38

I wonder sometimes if some of that comes from teachers sending home homework that they haven't really looked carefully at, like it's a page in a textbook that they haven't even looked at the problems. If they just copy off a worksheet from a, you know, book that says, you know, something a great title, or it says, you know, adding two digit numbers or whatever. 

Pam Harris  18:02

Or you just Google it? I need a bunch of problems. Now, let me just say, hey, anybody listening out there? It's COVID, right? It's a pandemic. So we are not like shaming or thumbing their noses at you. In no way are we saying, "I can't believe you're not spending your last breath you know, figuring out all the things." We totally get it, there will, of course, be times where you grab something quick, because in the name of COVID, and everything, that's all you have time to do. Of course, we understand that. But if we can sort of look at what the homework is, we look at what the assignments are, and then make some choices. Kim, one of my favorites that you've ever done is to literally Google something where you're just like, just give me like you said, Give me 10 division problems, three digits divided by two digits. And you just take that random set of problems from the internet, but then it's the question that you send home with it. And then the question is, "Ooh, for which of these questions would you rather use a partitive approach?" Now you're probably not going to use that with kids. What would you say a dealing out approach? Or in some way you would say, for which of these would you rather do a multiplying up approach? And then pick two of them and solve those and bring it back. And we'll share which cool strategies you came up with. So you could take what is a sort of traditional assignment, something easy to like pull down where you don't have to create all the problems. But you create the discussion around it. Whoa, that was fun to talk all about homework, kind of off the cuff. Hope that wasn't too unorganized for anybody out there.

Kim Montague  19:39

And obviously, we have some strong feelings about homework, right? 

Pam Harris  19:42

Yeah, little bit.

Kim Montague  19:43

No shortage of things to talk about. So, so far, we've said that generally I'm not a huge fan. I'm not sure that we have gotten your opinion yet. We definitely want kids to be working on things - when homework goes home - we want them working on things that they can do, in case they're alone, right? So because of that, we want to delay homework. We want to do things that are not fresh and new in terms of practice, but need to come back up again.

Pam Harris  20:13

Yeah, excellent. And that maybe won't make people crazy, right? In general, we don't send stuff home that will make everybody crazy. So delay that homework. Okay, that was fun. And I'm gonna suggest Kim, if you're okay with it. I think we have more to say, but we're about time here on this podcast, it's actually gone longer than we'd like it to. So everybody, we're gonna have another episode, probably a freewheeling one, on homework. So stay tuned for the next episode on ideas and thoughts about mathematics homework. Remember to join us on MathStratChat on Facebook, Twitter, or Instagram on Wednesday evenings, where we explore cool math problems with the world.

Kim Montague  20:54

Hey, if you find the podcast helpful, will you please rate it and give us a review? We really appreciate that.

Pam Harris  21:00

So if you're interested to learn more mathematics and all about homework and you want to help yourself and your students develop as mathematicians then don't miss the Math is Figure-Out-Able Podcast because Math is Figure-Out-Able.