# Ep 86: Are Algorithms Necessary?

February 08, 2022 Pam Harris Episode 86
Math is Figure-Out-Able with Pam Harris
Ep 86: Are Algorithms Necessary?

What purpose has and should algorithms have in mathematics education? Are step by step What purpose has and should algorithms have in mathematics education? Are step by step procedures even to be taught at all? In this episode Pam and Kim talk about our role as teachers and what students need to think like mathematicians.
Talking Points:

• One student's perspective
• What are algorithms?
• Why have we taught algorithms in the past?
• Where are algorithms helpful in today's world?
• Do algorithms help students learn to mathematize?
• From another student's perspective

Pam Harris:

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

Kim Montague:

And I'm Kim.

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 keep 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 if you've been listening to the podcast for a while, or you've heard Pam speak, then you know, we have some strong feelings or opinions or things.

Pam Harris:

I mean.

Kim Montague:

So in today's episode, we're going to spend some time here talking about algorithms and discuss are algorithms necessary.

Pam Harris:

Yeah, or even helpful or perhaps hurtful. Constance Kamii is a researcher who said the teaching of algorithms is actually hurting students. And I remember when I read that, early in my dive into research, and I thought, "Whoa, that is a strong statement to make. You better back that up." And she does. And we have carried on in that work. Not only asking are they particularly helpful, but necessary? Hurtful? Like, where do algorithms fit? To start that off, Kim, tell us about your son, Luke, the other day. This is amazing. Like, tell us about that.

Kim Montague:

Yeah. So actually, the other day really close to here. Luke was working on something in geometry. And to be honest, I can't remember exactly what it was. It was like, arc length or something that I'm not sure. And he called me over because he was really excited because he had found some relationship on his own, whatever he was supposed to be doing. And he said, "Hey, look, I figured something out." And what he had figured out, after he called Pam and talked to her, was he had figured out a formula. He had solved the problem using relationship and later figured out, "Oh, it was the formula that was in his book." It is so interesting, right?

Pam Harris:

So cool.

Kim Montague:

And what the conversation between me and Luke was that he had been told a lot of formulas and algorithms before, and then figured out why they had worked in the past. But this time, he messed with it and figured out before he even knew that that was a thing that he could get a formula for, right? And what he said I thought was really interesting. He said, "Why do they always tell us first and then we practice it, instead of helping us figure it out?" And he literally said, "It seems like they take all that learning away." And of course, I called you right away, because it was so interesting.

Pam Harris:

It's so fascinating, that this high school kid, okay, he's kind of still middle school taking high school courses, like is clear that he learns more, that learning is happening when he's using relationships, and figuring out how those relationships connect together. And how we can use those to solve problems. He's clear that that's learning.

Kim Montague:

Yeah.

Pam Harris:

Kim Montague:

So what I'm hearing you say that's applicable for teachers right now is that what we're against is handing kids an algorithm, practicing a few times and calling it math? That's not what learning math is.

Pam Harris:

That's not what learning math is. That's not what mathematizing is.

Kim Montague:

Yeah.

Pam Harris:

Yeah. Thank you for capitalizing that. Like to be helpful, we're not saying algorithms are evil or bad. We're saying there's a place for them. And it's not in the mathematics classroom. It doesn't help your students mathematize.

Kim Montague:

Yeah. So we have another colleague, right? Who's got a spunky, spunky son. Spunky's good. Yep. Yep. And he shared a story with us that I would love for you to share.

Pam Harris:

Kim Montague:

Hmm.

Pam Harris:

I think that's such a fascinating quote.

Kim Montague:

Yeah, spunky alright.

Pam Harris:

I mean, spunky, like, they're acting like we don't even have things in our head. Just like, like. Now, that's a different sort of pedagogical bent. Like, I might be, pedagogy is not the right word there. What do I mean? It's like there are different theories about learning. And so you might be the person who says, "I can unzip a kid's head and pour knowledge in. They are a blank slate." We don't agree with that. We agree with the sort of bent that we start with stuff. Like kids have, just like this kid says, "I have things in my head. Why aren't they asking me about what I know, and helping me get from where I am, what I know, to that thing that they're trying to teach?" I feel like you want to say something, a minute ago, sorry.

Kim Montague:

Well, I was just going to say we've had this conversation with a colleague. And we know that this kid has had a few experiences in previous grades where they had teachers who had given experiences where they were used to talking about math.

Pam Harris:

Mathematizing. Relationship.

Kim Montague:

Sorry, yeah. And sharing like what they were thinking about. And so it's, I think there's just an experience this year for this kid who the teacher was a little more traditional, maybe. And was, is very in the school of thought, where like, I have to tell you all these things, and like, get through all this material.

Pam Harris:

I do, we do. And then you go do.

Kim Montague:

Yeah, yeah. And the kid has some feelings, right about that?

Pam Harris:

I think it's fascinating that the kids clear. Yeah, like, "Why are they treating me like I don't have anything in my head?" They're just like, "Why is this person even teaching?" It's a little harsh.

Kim Montague:

Yeah.

Pam Harris:

"Why are this person even teaching?" Because this kid has had really good teaching and learning experiences and isn't this year. That's interesting.

Kim Montague:

Well, and it brought us to the conversation that like if this with his colleague, like their parent, during the parenting situation. And so we were talking about if this resonates with listeners, as a parent, if your students have a teacher who is pretty traditional, that they could still talk about rich problems, and talk and play about real math at home.

Pam Harris:

Yeah, so if you are that parent, you have sort of some influence over home, like you can still create that rich, richer experience with your students at home. And we would encourage you to do that. And, you know, it's kind of fun. We actually are gaining quite a homeschool following. So shout out to all of our homeschool parents that are listening in. Way to go. Nice. We appreciate you. We appreciate all of the teachers that are parents. And we appreciate the teachers that are listening to the podcast that are trying to make math more and more Figure-Out-Able.

Kim Montague:

Yeah, if you want to know how to teach so you are mentoring your students to be mathematicians, and you would like some help doing it, we have online workshops. And they actually start running today.

Pam Harris:

Today.

Kim Montague:

Whenever you're listening, check out our asynchronous online workshops at mathisFigureOutAble.com/workshops.

Pam Harris:

And all of you listeners that are in the workshops. I am thrilled to be able to interact with you in the message boards. And we're gonna have some live Q&A's. It's going to be a blast. Thanks for taking the workshop. 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.