# Ep 101: Strategies!

May 24, 2022 Pam Harris Episode 101
Math is Figure-Out-Able with Pam Harris
Ep 101: Strategies!

What comes to mind when someone says the word "strategy"?  There are at least four different meanings for the word "strategy" in mathematics teaching. In this episode Pam and Kim parse out the different meanings and discuss how those meanings shape the outcomes of our teaching.
Talking Points:

• Numeracy Strategies
• Problem Solving Strategies
• Teaching Strategies
• Strategies for Teaching
• Why without one type of strategy, the other strategies will fall flat

Pam Harris  00:01

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

Kim Montague  00:08

And I'm Kim.

Pam Harris  00:09

And we make the case that mathematizing is not about mimicking steps or rote memorizing facts. But it's about thinking, 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 dumb mathematicians they can be. We answer the question, if not algorithms and step by step procedures, then what?

Kim Montague  00:37

So in this episode, we're going to talk about strategies. So Pam, when I say that word, what pops into your mind?

Pam Harris  00:45

I think about how you solve a problem.

Kim Montague  00:48

Like problem solving strategies? Somebody actually asked me about that. And we've really already done an episode, it was Episode 15. If you're interested in what we think about problem solving strategies,

Pam Harris  01:00

Kim Montague  03:12

Yeah, right. So those are the ones that, like I said, we mentioned in a different episode, where somebody might say, one problem solving strategy might be to solve a simpler problem, or a problem solving strategy might be to look for patterns, or to look back to make sure that it makes sense. And we're actually, although some of those things are fantastic problem solving strategies, we also don't mean acronyms, where it says underline this, and circle this, and check for this, like some of those acronyms where it's like CUBES or STEPS And yeah,

Pam Harris  03:47

All the different, we can't even remember them. Right? They're acronyms, right? But they're kind of step by step procedures that kids have to follow all these steps every time they...  Every student for every problem. Yeah.  But that could be a meaning of the word 'strategy', that kind of problem solving strategies. We don't advocate those, memorizing a bunch of steps to solve problems. If you want to hear more about that, check out Episode 15, where we really dive into problem solving strategies, what to and not to do for those. So what's the third meaning that we might have as we're talking to each other, we're math teachers, we're interested in teaching math? What might be a third meaning about strategies?

Kim Montague  04:24

Yes. So we have problem solving and numerical strategies, but there's also teaching strategies, right? Teaching Strategies. And when we say teaching strategies, we also, I think, kind of get twisted a little bit because we might be talking about teaching like an adjective, or like a noun. Are we talking about teaching students some strategies, or are they teacher strategies?

Pam Harris  04:50

Yeah, parsing that out is tricky. So if we're talking about, doesn't seem like, you said adjective or noun and I'm, like stuck. You have to tell me which one this is. Okay. So if I'm talking about strategies like: good questioning, and wait time, and using a private signal so that all students have enough time to respond, we don't have this sort of speed thing going on. Or if I talk about partnering kids strategically and appropriately. Or if I talk about, like all the discourse moves to create discourse in my class, things that the teacher does. Teacher moves, we call them high leverage teacher moves. Those are some teaching strategies, right? Yeah. Those are teaching strategies the teacher does. Or teacher moves, teaching strategies.

Kim Montague  05:35

I guess, I kind of in my mind, I think it's less important that it's an adjective or a noun. But I think of those as their teaching. Like they're, how do I say this?

Pam Harris  05:45

Happening as you teach.

Kim Montague  05:49

I don't know how to say what I'm thinking in my head. Yeah, I don't know.

Pam Harris  05:54

For me, it's the kinds of things that we - in our deep dive workshops, we have a whole module set aside in the deep dive workshops, where we really look at everything we've worked on and the math, and we relook at how we did it. And we talk about Ooh, like was was it on purpose that I asked that question at that point? Was it on purpose that I asked every person in the room a question? Was it on purpose? Why did I say could you restate what that person said? Or does everybody understand this person strategy strategy? There are numeracy strategy. I was about to say numeracy problem solving strategy. That's tricky. Did everybody understand what could have been either? Right? Did you understand how this person went about solving that problem, numeracy wise, the relationships wise? Or did you understand how they used a simpler problem? Or how they went and asked a colleague for a hint. Like there could be problem solving strategies. There could be numeracy sort of mathematical relationship. As we sort of point those out, what teachers are doing to teach, those I call 'teaching strategy' teacher moves. We usually call them high leverage teacher moves. What are the ones that we can really get a lot of leverage out of, if we just change this little thing, tweak this to create discourse in class? Those are sort of teacher moves. Because Can I think we've got one more kind of thing that could be, we could call a teaching strategy.

Kim Montague  07:16

Yeah.

Pam Harris  07:17

But it's less about, kind of what a teacher does as the teacher's teaching.

Kim Montague  07:22

And it's not about the moves they make.

Pam Harris  07:24

Kim Montague  10:04

Yeah.

Pam Harris  10:05

Yeah.

Kim Montague  10:06

Well, and I think you and I were talking about this, because we wondered, like, in the conversations that we're having with people, how clear are we being? And how clear are other people being? And like, why does it even matter that we parse out the differences between these strategies? And it boils down to, there's a lot of really cool routines and strategies out there of all kinds. But people want to adopt them as ideas in the room, because they're interesting, and they get kids thinking. However, if you don't have the mathematical strategies to support the other three, then they all fall flat. Like there's nothing we're talking about. And there's nothing worth pairing kids for. There's nothing worth problem solving for. And so we center a lot of our conversation around the numerical strategies, because then you bring meat to the conversation.

Pam Harris  10:54

Yeah, I almost just, like want to have you repeat exactly what you said. Of those four strategies -

Kim Montague  11:01

Yeah.

Pam Harris  11:01