Ep 93: Partnering With Parents: Do Correct Answers Matter?

Pam Harris  00:01

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

Kim Montague  00:07

And I'm Kim.

Pam Harris  00:08

And we're here to make the case that mathematizing is not about mimicking steps or rote memorizing facts. But y'all it's about thinking and reasoning. It's about creating and using mental relationships. We take the strong 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  00:39

So for the last couple of weeks, we've been talking about partnering with parents. We did an episode on listening. We did an episode on over communicating. And last week, we did an episode on parent math nights. In this episode, we want to talk about some do's and don'ts when working with parents.

Pam Harris  00:56

Yeah, it's so important that we work with parents, we partner with parents, we don't separate parents from their kids. So what are some things that we're thinking about as we finish up this series that we feel like we want to include, things to think about, maybe some things to sort of do less of and some things to do more of? So let's start this off with something that I saw happen as I was working with my kids' teachers, the district that my kids were going to school. I started, I was doing the professional learning with teachers. I was kind of the facilitator. And I started to hear teachers say things like, "Well, yeah, I'm telling parents or I'm telling my kids, don't worry about the correct answer. That's not important. You know, it's just the process." 

Kim Montague  01:40

Yeah. 

Pam Harris  01:41

Kim, I will never forget the look on your face when somebody said that at a training once. 

Kim Montague  01:47

I'm sure it was a good one. 

Pam Harris  01:48

There's a part of me that was like, "Well, kinda." Like there's a nuance to that, right? But you had to second your face like, "No." 

Kim Montague  01:56

Yeah. 

Pam Harris  01:57

Tell us more about that. Like, why were you so...?

Kim Montague  01:59

So I think we spent a lot of time focusing on strategies and thinking and reasoning. And we knew that that was where the conversation really was focused. And so I think that some people took that to mean like, "Oh, whatever the answer is they get like, it'll be okay. It'll work out." And absolutely, the answer matters, right? If you do need to get a correct answer, it's just that it wasn't the only thing that mattered anymore, right? And so we don't want parents to hear-

Pam Harris  02:30

Well, and also sorry I'm gonna interrupt. And it's also that when you are thinking and reasoning, when that's the emphasis in the room, in the experience, in the mathematizing, the correct answer is already there. Like, the criticism sort of takes care of itself. Now we're talking about how you got there. So it's not like there's all these wrong answers. And we're just in the weeds and we're fuzzy. No, it's like everybody we have we have the right answer. And now we're focused on how we got there. And the reasoning and thinking. So do right answers matter? Yeah, yeah.

Kim Montague  03:05

Well, how many times have you started to explain your thinking and realized your own mistake? And how many times have you been like, "Oh, no, I meant 239 instead of 249," or, you know, whatever, something like that.

Pam Harris  03:18

But so thinking that was important comes out as we explain the incorrect answer. Yeah. So it's not about like, that there are never wrong answers that come up in a mathematizing classroom. There are, but we don't necessarily pounce on them right away. We let the student explain their thinking, "Oh," and then 99% of the time they catch their error. And so when you catch your own error, it's as if you didn't make it to begin with. And because the emphasis is on the major thinking involved, not the little tiny, you know, something that just went a little right oh, that that we fix up. Sometimes we even highlight an error so that we can kind of as the canary in the mineshaft, we can all like go down that road. So that nobody, then kinda can figure out why that's an error. So nobody, everybody's really clear about oh, okay, that's how that doesn't work. But to the end, of course, we want correct answers. 

Kim Montague  04:11

Of course they matter. Right? 

Pam Harris  04:12

Yeah. And I feel like I interrupted you. You were gonna say something. 

Kim Montague  04:15

Well, I don't remember now. But I think it's important that we don't just say a blanket statement like, "The correct answer doesn't matter." Because parents could hear that at a couple of different ways. Right? They could hear it like, I don't really care if your kid does well on the test. Or I don't really care if your kid gets put in some sort of intervention program. Or I don't really care if they have to repeat the year because those are measures that correct answers are measured for those kinds of situations.

Pam Harris  04:47

Absolutely. And that's one of the reasons why we want to really over communicate with parents. We want them to understand what we do mean, that's why parent nights that we described last episode are so important. That parents actually experienced the mathematizing to realize, oh, yeah, like we got correct answers, the correct thinking was important. So that then when we're having conversations with them about what does matter in class, it's because, of course, yeah, we have the correct answer. Now we're really focused on getting your students to think more sophisticatedly about. It's not just correct answers anymore. All too often in the United States, we have, and, frankly, a lot of places where I'm looking around the world, we've only focused on answer getting. And if that's the only focus, then we lose out on the reasoning and the helping students get more sophisticated in how they're reasoning. And then students have a harder time actually making the progress that the parents are so worried about. So we're just advocating today that we think about how you word that. It's not about, oh, correct answers don't matter. Of course, they matter. That's just not the only focus. That's not the main focus, because so much else is happening that's wonderful. Correct answers are happening, and we can build that more sophisticated reasoning as we go. I thought it was really important, Kim, when you just said that parents might hear the message, that if we say something like that, how that might negatively impact their kids. 

Kim Montague  06:20

Yeah. 

Pam Harris  06:21

Because parents do care about how well their kids are doing. Right? And so-

Kim Montague  06:26

I mean-

Pam Harris  06:27

Go ahead.

Kim Montague  06:28

Well, I was gonna say, the message could be sent that your student is just one of my whole class, but to that parent, that's their one student. Right? They're super concerned about what's happening with that one student. 

Pam Harris  06:42

Yeah, absolutely. And so another message that could inadvertently be sent in our attempt, so most of us deal with high stakes tests. Yes? I also, as I was working with teachers, started to hear teachers say, so misunderstand what I meant, as we were working with them in trainings and workshops. And so they would say something like, "Oh, yeah, the high stakes test doesn't matter. So don't worry. You don't need to worry about how your student's going to do on the state high stakes tests. It's okay, those those tests are dumb.  They don't matter." You might have heard me in the podcast, say, "On a stupid high stakes test. And now you know how I feel about the test." That's often a way I sort of joke about high stakes tests, because I don't really like them, mostly because of what the perception is that they do. The perception is that the high stakes tests help us create equitable learning experiences for kids. And that's just not true. There's an expectation that often public policymakers will say, "Well, we have to have these measures so that we insist or that we ensure that we have high, help me Kim, that we have proficient teachers, that we have really expert teachers, and that the high stakes test ensure that." And we can talk more about that someday, but that just doesn't work. If you look at what's actually happening, that the tests don't provide that. They don't ensure that. They do other things. And sometimes I think that the tests are actually not that bad as a test. It's what we tend to do with the scores that's horrible. It's what we tend to do to freak kids out, the pressure that's on kids. And I think that's the well meaning teachers, meaning the well meaning teacher is like, "Oh, let's not put all this pressure on these kids on these high stakes tests." And that's what they might mean when they say the test doesn't matter. But we have to be really careful about how we say that to parents, because parents again might hear, "Oh, I'm not going to help your kid do well on this test. I'm not because Oh, it doesn't matter. And so your kid, it doesn't, you know, your kid's gonna maybe fail this test." Again, like they might get held back this year. They might get stuck in some sort of intervention. They might have to come in after school to get better at doing that, you know, like those lots of ramifications that parents might be used to if their student doesn't do well, on the high stakes test. Kim, you mention some things that could happen at younger grade levels. From a high school perspective, I've got high stakes, my students are taking high stakes tests, like ACTs, SATs, college entrance exams, maybe even military entrance exams. That those are true high stakes. Like students need to do well on those sometimes in order to enter their chosen profession or their chosen internship or chosen university. And so very high stakes are involved. So we want to be really careful how we talk about those tests with parents. I don't know. Chime in, Kim, helped me out here.

Kim Montague  09:42

I was actually just listening to you. And I was thinking about when I took the GRE.

Pam Harris  09:47

And it wasn't that fun. 

Kim Montague  09:48

Yeah, it was super fun. And you know what my approach to that was? Let's just see what happens. Right? Like, let me just let me just see what's going on. It's been a long time since I've done any high school mathematics. And here's what I found. And I think that you'll agree with me that because I was a thinker and a reasoner, and still am, I didn't have to memorize a bunch of stuff, right? I walked in, I was like nervous about it. And I thought, well, let's just see what happens. But I was able to reason through so much of that, even though I hadn't experienced it for quite some time. And so I think that the kinds of classrooms that we are building, or we-

Pam Harris  10:28

Are advocating. 

Kim Montague  10:29

Yeah, advocating, thank you suggesting, is that we're going to have kids who we are equipping to do really well on high stakes tests. And so we don't need to say things like, "They don't matter." We're gonna say, "We're partnering with your kids," and we're going to equip them so that they do well on these anyway.

Pam Harris  10:48

Absolutely. It's not about we're going to drill. We're going to review for three months before the test. We're gonna do these crazy things, because we're focused too much on the test. But we're also not ignoring the test. We're gonna admit that it's there. We're gonna do some very intelligent things. And we're gonna have an episode coming up soon, where we're gonna focus on some ways that we can help students be successful on those high stakes tests, in ways that don't rob the thinking and reasoning, that don't take away from the time that we want to advocate that we spend really mathematizing. But they can also help your students, you know, have a little bit of a leg up on those tests so that they don't, what we don't want is we don't want students to get to that high stakes test day, and be completely unclear about test instructions, or be have never experienced a time component to a test if that's part of your high stakes test, or never have experienced the way an item might be phrased, or never experienced the way that they might have to answer that if they've never taken a multiple choice kind of a question if they've never experienced that, if they've never experienced what we in Texas call a griddable item. If they've never had to show their work and explain their thinking. Like we don't want students to land in that kind of atmosphere and be shocked and surprised. And I've never seen anything like this, of course not. So we'll share some strategies that we have to help students so that they're not totally surprised by that kind of experience. But at the same time, we're going to prioritize the way that we teach so that kids are hitting that test like Kim. They're going into that, any high success they ever take, knowing: I'm a reasoner. I can think through stuff. This stuff is figure-out-able. I'm going to read the question and I'm going to figure it out. I have confidence in my ability, that because I know it's figure-out-able. And I know that I am a figure-outer that I then can confidently with assurance: I can go into the situation, figuring it out. I know it's figure-out-able. I'm a figure-outer, I've never said that before. And so now I can just approach this test with confidence. And y'all in a huge way, my personal kids taught me that. Specially I'll give credit to my son, Craig, where he would, and it's not that my other kids didn't, but he would verbalize it so much more than the other ones, where I would say, "Hey, you know, like, what do you think about this, this high stakes test that you have to take?" And he would just smile at me, he goes, "Mom, it's gonna be figure-out-able. I know I can reason through this stuff. And I'm just gonna do that. Here we go. I'm just gonna go and reason and do the best I can." Kim, one of the things that I want to share today in the podcast is, I was in a workshop once. It was a national conference. They had this kind of short workshop during the conference, it was sort of a longer session. And I was sitting next to a participant. Hadn't ever met this person before. You know, "Hi, how you doing? What do you do?" Right before the session started. And this person said, "Well, I'm actually not a math teacher. But I write items for the SAT." And I was like, "Oh, I'm so glad I'm sitting next to you right now. Because I just actually want to like leave this workshop and just talk." But it's fine. Yeah, I just want to like drill this person. I was really fascinated to talk to an item writer, you know, like an item on it on an SAT. What their, what's behind that? Because I was pretty sure that I knew what was behind it. I actually did a paper on the SAT gender bias actually, for my senior thesis at BYU. And so I've done a lot of, you know, stuff on the SAT. Anyway, during the session, there was some time where we could kind of talk about some things, you know, like turn to your partner and have a conversation about things. I said, "Do you mind if I ask you? Tell me about writing items for the SAT." We ended up having a longer conversation later, where the upshot of the conversation was, I asked, "Do you look at a particular sort of topic in math and say to yourself, 'what are the typical ways that a kid who doesn't actually understand what's happening, but has memorized their way through in solving it, what are the typical ways they would mess that up? And then those are the three wrong answers.' And then what is a way that like, we're going to write a problem. So that if you're reasoning, if you're actually thinking about what's happening, if you own relationships, you can actually solve that problem pretty quickly. But if you do the typical traditional way that you see kids doing it, they're gonna mess it up in one of these three ways, it's going to take you much longer." And that test writer looked me in the eye and said, "Yes." And I was like, "Tell me more. So I make sure that we understand." And that is the upshot. The upshot is that they are looking for items that if you are reasoning, you can solve pretty readily. If you are using relationships, you're looking at how things are connected, that you can use what you know, to solve it pretty regularly. But if you are trying to do sort of the typical traditional way that we've kind of told kids the steps to do in class, that's going to take you much longer. And the answers that are there are the typical ways that kids will mess it up. Yeah, anybody feeling a little bit like, okay, I was about say, a bad word, feeling a little bit, helped me Kim, feeling a little bit. Like that wasn't nice to do. That was not a nice thing that, well, y'all, that's how they write those tests, so that they can kind of weed out people who actually understand what's happening. Now, if you're following the steps, you're going to get a bunch, right? Because you're going to follow the steps. And if you do it correctly, you're going to choose the right answer. And so you're going to get enough, right, but it's gonna take you longer. And those tests are tests of speed. And so they bank on that. The way they score those tests is they include items like that, enough of them, that again, if you're thinking and reasoning, you solve it pretty readily you move on, you're able to solve more of them. You can still do all the steps and get the right answer, but it's gonna take you longer. And since it's a test of speed, now you're taking too long, and so you don't do as well. We would suggest that if we can really help students build their reasoning skills, really mathematize, they're going to go in more confident, and they're gonna be able to solve those items more readily, because that's the way the items are written. I would suggest that many of the items on high stakes tests that I have seen at the undergrad level as well, undergrad, I just met under undergrad, not university, not the university entrance exams, but also the high stakes tests at an elementary and middle and high school, that those high stakes tests are often, those items are often the same way. That if you can reason through them, you will solve them more readily. Look at any, here's a specific item that's easy to find. Go look at a middle school test, or a fifth grade test, or even a fourth grade test, where there are decimal problems. And almost always, it is a gnarly problem to solve if they're going to do any kind of algorithmic computation, any kind of step by step procedure. But if you just reason, it actually comes out pretty nice. Most of the time, I find that to be, not all, I remember there was a test once Kim, you and I had this conversation once. It was like a fourth grade item. And it was something like 23 times 77. I mean, it was, and the worst part was it was a guess it was a benchmark test. So it was It wasn't written by the state or anything. It was like a guess of what was going to be on the year end test. And they gave it really early in the year because they said, "Well, if kids are learning two by two multiplication, they should be able to do any problem." And I'm like, "Oh, for heaven's sakes, do 12 times something" for a beginning problem, because now you got kids that are building the reasoning, that's a good beginning two digit multiplication problem and then build towards the uglier ones by the end of the year. Anyway it was just a bad guess on a test writer's part. So for the most part, there are many items that are written that way. I would challenge, listeners, here's my challenge: You go look at your, whatever your grade band is, look at those high stakes test questions. Look at those items. And notice, if kids are reasoning how readily solvable those items are. And if they're not reasoning, how much more time it will take to actually do sort of any kind of traditional step by step procedure for those. So don't tell parents that the high stakes test don't matter. Do help students become the confident reasoners that they will be able to reason through any high stakes or low stakes or any stakes sort of thing that they ever have to do in life. We just want them reasoning. Alright, so if you want to learn more mathematics and refine your math teaching so that you and students are mathematizing more and more, then join the Math is Figure-Out-Able movement and help us spread the word that Math is Figure-Out-Able.