# Ep 184: Revisiting - But I'm Required To Teach Algorithms

December 26, 2023 Pam Harris Episode 184
Math is Figure-Out-Able with Pam Harris
Ep 184: Revisiting - But I'm Required To Teach Algorithms

Happy holidays! Pam and Kim invite you to revisit Ep 87, it's super important! How do you navigate teaching math that is figure-out-able if your standards include the teaching of algorithms?
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.

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Pam  00:01

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

Kim  00:07

And I'm Kim.

Pam  00:08

And you are in a place where math is not about memorizing and mimicking, where you're waiting to be told or shown what to do. But it's about making sense of problems, where you notice patterns, and reason using mathematical relationships. We can mentor students to think and reason like mathematicians do. Ya'll, not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keeps students from being the mathematicians they can be.

Kim  00:35

It's holiday season!

Pam  00:36

Whoo-hoo!

Kim  00:37

Pam  00:39

Oh, sure enough. That's coming up. Yay. Hey, and this is a particularly good birthday because I have been 29.

Kim  00:46

Oh, yeah.

Pam  00:47

Forever.

Kim  00:48

For awhile.

Pam  00:48

And I told my kids, like just since I've been 29. Pretty much I just stayed 29. And I told my children, "As soon as you give me grandchildren, I will be 39.

Kim  00:56

Oh! Okay.

Pam  00:57

So, this year, I'm 39.

Kim  00:59

You're turning 39. Fantastic.

Pam  01:00

I am a grandma twice. And yeah, it's been a great year for.

Kim  01:03

Super, super good year for your family.

Pam  01:06

Loving it.  Yep.

Kim  01:06

So, we're wrapping up this year and looking forward to 2024. And this week, we decided to do a throwback to a really important episode that we want to be sure that you have not missed. If you've already tuned in, give it a listen anyway because sometimes hearing it twice is fantastic. We're all learning and growing, and you might hear it differently this time. So, this one is about a real argument or concern that many teachers have.

Pam  01:33

Yeah. Many, if not most teachers, have standards that say something like, "Students will use algorithms and strategies based on place value and properties..." blah, blah, blah "...to multiply and divide (unclear)."

Kim  01:43

Yep.

Pam  01:44

Or something like that. So, it's a real question. How do you navigate that if I'm suggesting, we are suggesting at Math is Figure-Out-Able, that students do not ever need to be taught algorithms as a thing to do, how do you navigate that standard?

Kim  02:01

Yeah. And that's a really important distinction that you just mentioned. It's as a thing to do. So, does that mean that students are taught them some other way?

Pam  02:09

Kim, it's almost like we're on the same page. Yes! And you are going to want to listen to this episode to hear all about that. So, here is episode 87. But, "Pam, I'm required to teach algorithms!" Alright, ya'll, enjoy. Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able! I'm Pam.

Kim  02:33

And I'm Kim.

Pam  02:34

And we make the case that mathematizing is not about mimicking steps or rote memorizing facts. But it's about thinking, 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  03:04

In the last episode, we talked about how pouring algorithms into kids 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  03:21

Kim  10:40

Yep.

Pam  10:40

So, now, they're going to think 9 times 4, right? And so, she'll say, Now, they'll say 9 times 4, and then they'll get 36, and they'll add 6 to that." So, 9 times 4 is 36, add 6 to that, it's 42. "And then, they'll just write that 42 down next to the 3. Whoa! That's weird. Ya'll, what are they doing? Does that work? Why does that work? Draw an array. Find those pieces that just happened. Like, can you find something that is 400 and... Help me. 23? Can you find like some chunks of area that would add to 423? Where does that 6 when they just do the 9 times 4. And then, the kids, because they have great place value, because they have been developing place value all year long, look at that, and go, "Oh, it's like they're sort of doing 9 times 4 to help them get 9 times 40. But they know they've got that extra 60 hang along. But they're doing 9 times 4 and adding the 6. Wow, that is like 9 times 40 and adding 60. But wow, the meaning is kind of hidden behind that. I mean, that's really cool. Woah, I wonder who figured that out. Okay." And then, Kim will show the next step. And the kids, because they have great place value, will be able to figure out why it works and how it works. And by the end of sort of showing some steps, the kids will say something like, "Whoa, that is interesting. Like, all those... I mean, okay. Like, all the meaning is kind of behind the scenes. And it's kind of hard to like feel the place value. Like, somebody has to be really brilliant to figure that out. But are you saying people actually do that every time? Bleh! Like, for that problem, wouldn't it just be easier to find one hundred 47s and subtract a 47? I mean, that's a lot of steps! With all that meaning that's kind of hidden and all the... Wow, that's really. Like, why would anybody do that if they could just think about it?" Now, you might be like. Listeners, right now, you might be like, "Pam, really. Her kids said that?" Well, I'll tell you what. Really, my kids said that. My personal kids that had Kim as a teacher literally would look at an algorithm after seeing some steps, and they would literally be like, "Whoa, that is really intense. All that meaning sort of shoved behind the scenes. You can't really tell what's going on. I mean, I guess you could do that. But why would you if you can just think about it? Why would you stuff your memory full of all that stuff to rote memorize? Why not just think about the numbers? Just use what you know to solve the problems. Okay." And then, they would just move on. And it doesn't bother them because that point there's such good thinkers that it's just one more sort of thing to make sense of, and then kind of move on. And it doesn't become this crutch. But it doesn't become this sort of thing that takes over their life. Now, listeners, you might be like, "Well, Pam, if that's true, I'll just show them the algorithm way earlier in the year, and then they'll just have the same reaction."

Both Pam and Kim  13:34

Mmm.

Pam  13:40

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."

Kim  13:53

Mmhm.

Pam  13:53

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. 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 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 of that it just becomes this thing to do and could stop thinking, and that's not what we want in math class. That's not our goal.

Kim  14:40

Yeah.

Pam  14:42

So, you might be... 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, "Oh, yeah. I got something. I have relationships I can use to solve that. Yeah, no problem." Then, I'm totally okay that you're going to meet your standards by putting that algorithm in front of them, dissecting it, studying it. They're going to 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 tests because they're thinking and reasoning, and everybody wins. We have kids that are mathematizing. We have teachers that feel 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! (unclear). There you go.

Kim  15:45

That's a good place to be.

Pam  15:46

That's a good place to be.

Kim  15:47

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.

Pam  15:59

Over and over.

Kim  16:01

Over and over. And then, sometimes 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 have 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 going to 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  16:46

Absolutely. And another place you're going to 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 is a symptom of sort of not teaching real math. 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 it 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 say?

Kim  17:39

And, well, I was going to say, we're not saying that there aren't things that you don't want to review or circle back to, right?

Pam  17:44

There are some. Yes.

Kim  17:45

There are some things.

Pam  17:46

But not the steps of the multiplication algorithm.

Kim  17:48

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

Pam  17:58

Hey, before we go there. I think I know where you're going to go. Sorry. So, briefly, can we mentioned some things that you might want to review? Like...

Kim  18:05

Okay.

Pam  18:06

...vocabulary. Is that where you were going? Were you going there?

Kim  18:08

Pam  18:08

Okay. So, vocabulary. That's a rote memorize thing. That's a social, conventional thing. We're going to memorize vocabulary. Notation might be a thing. "Hey, guys, on the test you might see a division problem that looks like this. 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. Now, you should have been 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 test is to remind you of things that you might have de-emphasized. "Oh, that's right. They should see this division symbol. They should see that form of the equation of an line. They should... Oh, 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 going to review. Okay. Sorry, Kim.

Kim  18:59

No problem.

Pam  18:59

I hope you didn't forget where you were going.

Kim  19:01

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

Pam  19:26

Kim  24:15

So, in summary.

Pam  24:17

Kim  24:18

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

Pam  24:23

Nice.

Kim  24:24

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

Pam  24:31

Bam! Nicely said. Oh, 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.