# Ep 87: But I'm Required to Teach Algorithms

February 15, 2022 Pam Harris Episode 87
Math is Figure-Out-Able with Pam Harris
Ep 87: But I'm Required to Teach Algorithms

Do your standards require you to teach algorithms? What then? In this episode Pam and Kim discuss how they prepare their students for success on high stakes tests without ever teaching a step by step algorithm or process.
Talking Points:

• All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems.
• Students can and will perform well on standardized tests if they have been thinking and reasoning, experiencing new situations all year.
• Students will approach a standardized test with confidence and less stress if they have been given opportunities to struggle productively all year and become good mathematicians.
• Introduce the algorithm as a study of why the algorithm works for the very end of the year. Introducing the algorithm too early in the year risks giving students the option to turn their brains off.
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, and about creating and using mental relationships. We take a 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:

In the last episode, we talked about how pouring algorithms into kid's heads and then having them use them is not mentoring mathematicians, it's not really helpful in teaching math. But Pam, teachers are required by standards to teach algorithms. So...

Pam Harris:

Kim Montague:

Mmmm...

Pam Harris:

Do Kim and I hang out or what? So the earlier you show them the algorithm, the more you run the risk that they say, "Oh, I can just turn off my brain here. Like thinking is hard." Thinking is hard. Like thinking takes effort, building your brain to think more and more sophisticatedly takes some struggle and some sense making. And that takes effort. It takes, like you have to work at it and some sweat. And if they see the algorithm too early, and it becomes sort of a quick scapegoat, then you run the risk that they then just do that. Especially if you haven't quite got the knack yet of not making it not about answer getting and making it about thinking and reasoning in your class. Which we're going to talk about answer getting in an upcoming episode soon. So make sure you pay attention, tune into that one. But if you do it too soon, you run the risk that it just becomes this thing to do and kids stop thinking. And that's not what we want in math class. That's not our goal.

Kim Montague:

Yeah.

Pam Harris:

So let's see if we can recap just a little bit. Teach thinking and reasoning all year long. Get kids really developing their brains so that they can look at any problem and go, "Yeah, I got something, I have relationships I can use to solve that. Yeah, no problem." Then I'm totally okay, that you're gonna meet your standards by putting that algorithm in front of them, dissecting it, studying it, they're gonna understand it far better than anybody who's ever just doing the steps. You have now met the standard. You've got kids that are doing great on your high stakes test, because they're thinking and reasoning, and everybody wins. We have kids that are mathematizing. We have teachers that felt satisfied and fulfilled, because good stuff is happening in their class. Kids are - I was about to say, happy to be there. We want them happy to be there because of the relationship they have with you. But also, like satisfied to be there. It's a satisfying thing, to really use what you know, to think and reason. And everybody's - what did I miss? In that list I just did? We've met your standards, we've got good scores, kids are happy, teachers are fulfilled, bam! There you go.

Kim Montague:

That's a good place to be,

Pam Harris:

That's a good place to be.

Kim Montague:

And, you know, I think one thing that you left out while you were talking was that teachers spend quite a bit of time showing the steps of an algorithm and then having kids practice them over and over and over. And then sometimes they say to me I don't have time to focus on these alternate strategies and like relationships and stuff. So one of the things that you and I've come back to several times is that this idea that if you can remove that time, where you're practicing, and teaching, and over and over again, the steps of the algorithm and replace that with the thinking and reasoning, then when you get to that last week or two and you're exploring the algorithm, then kids really do go, "Oh, that makes sense. Okay, well, I'm gonna use it or not, but it makes sense." But you've given them all the time they need in your year, to make sense of something that actually matters.

Pam Harris:

Absolutely. Another place you're gonna save time. You taught me this Kim, everybody in - this was so new to me. Everybody in my kids school, what a month, and then it was like two months. And then it was like, I mean, the time just kept growing before the stupid high stakes test. Everyone would stop teaching. They're like, "Oh, no, we have to get everything taught by February because then we're going to review until the test." And I'm like, "What? No, no, that's terrible. Let's just keep building all year long until the test." Like if you feel like you have to do this huge review. Maybe would you consider that that is a symptom of sort of not teaching Real Mmath. That's a symptom of that you're treating math like a bunch of things to memorize. And so we better go over and over and over and over again, because that's what you have to do for things that are rote memorized. But if you're just continuing to build sophistication, then we can use that time to continue to build sophistication. Sorry, what were you going to saying?

Kim Montague:

Well, I was gonna say, we're not saying that there aren't things that you don't want to review or circle back to. Right?

Pam Harris:

There are some. Yes.

Kim Montague:

There are some things.

Pam Harris:

But not the steps of the multiplication algorithm.

Kim Montague:

Yeah, yeah. So you have mentioned state tests a few times. And I want to speak to - I can hear teacher's saying...

Pam Harris:

Hey, before we go there, I think I know where you're gonna go. Sorry.

Kim Montague:

Yeah.

Pam Harris:

So briefly, can we mention some things that you might want to review? Like, vocabulary, or was that where you were going?

Kim Montague:

No.

Pam Harris:

Okay. So vocabulary, that's a rote memorizing, it's a social conventional thing we're gonna memorize vocabulary. Notation might be a thing. "Hey, guys, on the test, you might see a division problem that looks like this. Or remember, we've done that." You might see a, I mean, help me, let me get to other grade levels, because I've been really focusing on fourth grade. "You might see a proportion setup like this. You might see the equation of a line written like this. You might see a quadratic equation written like this." Like notation like that, now, you should have been like dealing with that notation. But maybe you dealt with one more than another. That's a good moment. Actually, when you're looking at your high stakes test. That's a decent purpose for high stakes tests, to remind you of things that you might have deemphasized. "Oh, that's right. They should see this division symbol. They should see that form of the equation of a line. Okay. Next year, we'll do more to actually develop that and keep it in our repertoire as we go." But especially vocabulary, is a thing you're gonna review. Okay, sorry, Kim. I hope you didn't forget where you were going.

Kim Montague:

Okay, well, so I'm the teacher right now listening, saying, "You don't know my state test. These algorithms that you just said to teach or whatever, show, in the last week or two, they're on my state test. And so I am required. And I want to be responsible as a teacher in helping my kids make sense of them, because they're tested on them."

Pam Harris:

Kim Montague:

So in summary,

Pam Harris:

Kim Montague:

Please. Teachers we're saying relationships over algorithms. Yes?

Pam Harris:

Nice.

Kim Montague:

And we're gonna argue that you spend the time that you have building thinking over practicing procedures.

Pam Harris:

Bam! Nicely said, Ah, I knew I liked you. 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!