Ep 88: Getting Correct Answers or Building Relationships?

February 22, 2022 Pam Harris Episode 88
Math is Figure-Out-Able with Pam Harris
Ep 88: Getting Correct Answers or Building Relationships?

Most of us are probably teaching the way we were taught, to get correct answers to problems. But we aren't actually helping students understand and reason about the math. Which is more important? In this episode Pam and Kim discuss answer getting versus relationship building.
Talking Points:

• Phil Daro's research on patterns of math instruction from across the world
• Student success from answer getting instruction vs instruction that focuses on outcomes from reasoning
• The real purpose of math class
• Now that I know different, how can I do different and help kids reason?

Resources:
Phil Daro video: https://vimeo.com/79916037

Pam Harris:

Hey fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able. (pause) Oh shoot! What is wrong with me? (laughs)

Kim Montague:

Pam Harris:

And we make the 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 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:

So in this episode, we thought we'd continue the conversation that we've been having for a couple of weeks. We've been talking about algorithms versus relationships. And now we want to talk about correct answers versus relationships. So this actually came up because we were talking about an email that we got from one of our journey members, so your membership site, and she said, "I have to share with you what my husband said during a car ride this past weekend." He was describing doing some math, he handles the finances. And so it's probably about taxes or something. And he said, "So I thought to myself, What would Katrien do?" And I said, "What?" This is her talking. He said, "I've heard those math webinars that you've listened to where that woman shows those other strategies. So I thought to myself, hmm, I have to subtract 75 from something crunchy. And so I thought about subtracting 80 and then adding back five. So I've been trying that for a while. Every time I have a math problem, to see if I could do it. And it's really cool." Isn't that interesting? She says, "A wholly unexpected influence. You're rewiring the brains of 55 year old dads, the over strategy for the win." Isn't that great?

Pam Harris:

Oh my gosh, when we got that email, I was like, sweet. So Katrien, thank you for sending that story. And that's fabulous. I'm so glad. Like, that's amazing. Um, I'll be honest, I, how was my husband? 58? Like, we've got a 58 year old guy over here. And he's sort of rewiring the same way that we've been rewiring him for a while. And I mean, of all the people. Rewiring me, like, I was the one who just mimicked procedures and just did what the teacher told me to do. I tried to make sense of it. I wanted to know why and how. I did the best I could to figure out which step went next. But now I have a slightly different perspective. That I'm not just a mimicker. I'm not just the button pushing monkey. I can mathematize. And I love that. I love how that has set me free.

Kim Montague:

Yeah. So this question about correct answers versus relationships actually comes up pretty often because people ask you all the time where you stand. Right? And so I am going to ask you to share a little bit today. One of the things I've heard you talk about before that relates to this is about Phil Daro. And I think one of the first time you ever shared his research and what he had to say about this topic really blew my mind. So I am going to sit back and listen a little bit today, and let you share with our listeners.

Pam Harris:

Kim Montague:

Yes. Reasoning, not just a multiplication algorithm. But reasoning, oh, you know, what I know, I know, there's going to be some students who are going to try to use Additive Reasoning here. That's not gonna work. So I might look for students trying that. And we might bring that out in a very positive way. "Oh, look at the student," as a canary in the mineshaft. "Look at how this student is going down this rabbit hole. Let's check it out. Will that work?" And because it's probably in context, we can reason about how, "Oh, you can't like, if you subtract a pizza, you can't subtract \$1. Because a slice of pizza didn't cost \$1. We don't know what a slice of pizza cost, but we know it wasn't \$1. So I can't just subtract a slice." And I'm using a context that we've used before, where we have four slices of pizza for \$5. Kids will sometimes subtract a slice of pizza and subtract \$1 In order to solve, say, for three, the price for three slices of pizza. If they use that Additive Reasoning, we know that's going to be a thing that's wasted to been reasoning. And so we know that. We know the sort of the landscape of what's happening. We know that the Development of Mathematical Reasoning. And so we say, "Okay, we're gonna look for that, we're going to highlight it, and we're going to discuss it, we're gonna use context to make sense of it. Oh, now look, now my students are reasoning more sophisticatedly. Nice, how am I going to continue that? How am I going to help them continue to reason more sophisticatedly?" Now in that classroom, at the end of the day, I might not have all students solving that problem correctly. Now, I might, one problem by the end of the whole class period. But in that, we might have some struggle. Okay, we are going to have struggled, if we're doing it well, students are going to be like grappling with these ideas and trying to make sense of how the relationships work differently than they sort of were thinking about them, especially if they were thinking additively. And in that grappling, that's a little uncomfortable. That's a little disconcerting. You're off balance, because it's not all just like, fresh in front of you. And you might be like, "Pam, can we just give it fresh in front of them?" No, it doesn't work. Learning doesn't work that way. I mean, they might solve, if you can see my hands, I'm kind of on this side, the American side, where I just gave him that one little bit to memorize. And by the end of the day, they're all like, "Yeah, okay, we did the thing." What you don't get is satisfied students. You get satisfied students now, maybe not that day. But as they use those relationships, and it starts to actually make sense. Those students are like, "Okay, I can do that. That makes sense to me. I am clear on those relationships. I was intrigued. And now I'm like," but that's not an overnight process. That's not a five minute. Let me, I do. I just did it. Now we're going to do together. Now you go do it. Oh, good luck, how... It's not that, humm, what? Easy?Like it takes, learning takes effort. And that effort is then rewarded, not effort, just repeating stuff 29 times, but effort in making sense of what's happening, because in that making sense of what's happening, I am now a more sophisticated reasoner. And that is the goal of math class. So I love his research. So we have some American teachers listening and maybe maybe some other countries as well, who recognize, "Maybe I'm a little focused on getting answers because that's just what I've been used to." Right?

Pam Harris:

Sure. Sure.

Kim Montague:

What does this mean for them? What does this mean when they say, "Oh, I recognize that and I'd like to make a shift."

Pam Harris: