# Ep 122: How to Help Students Choose Which Operation in a Word Problem

October 18, 2022 Pam Harris Episode 122
Math is Figure-Out-Able with Pam Harris
Ep 122: How to Help Students Choose Which Operation in a Word Problem

When dealing with word problems it can be tricky for students to decide which operation to use, so we need a way to help them memorize what to do in any given situation... right? In this episode Pam and Kim discuss how reasoning empowers students to skip rotely memorized steps to choosing operations and get straight to problem solving!
Talking Points:

• Word problems feel unfair to students who have only experienced fake math.
• Students with reasoning develop intuition for what relationships a problem requires.
• Rich Tasks and Problem Strings with mini-contexts prepare students to apply their reasoning to real world contexts.

Pam Harris  00:00

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

Kim Montague  00:07

And I'm Kim.

Pam Harris  00:08

And you found a place where math is not about memorizing and mimicking, waiting to be told or shown what to do. But y'all it's about making sense of problems, noticing patterns and reasoning using mathematical relationships. We can mentor mathematicians as we co-create meaning together. Not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keep students from being the mathematicians they can be. So podcast listeners, did you hear our first MathStratChat edition last week? Ah?

Kim Montague  00:43

Yeah.

Pam Harris  00:43

Whoa. Okay. So Kim and I are having a blast doing those. We just take the MathStratChat question that comes out that week. And we hope you all solve it, and post your solution, chat about other people's strategies, and then pop on and listen to the second Math is Figure-Out-Able podcast of the week where we share each other's strategy. So Kim will solve it and share what she's thinking about. I'll solve it, share what I'm thinking about. Double the fun. The math is Figure-Out-Able podcast, just doubled. Bam! Dah-ta-dah.

Kim Montague  01:18

Very cool. So make sure you subscribe to the podcast, so you don't miss those too.

Pam Harris  01:22

Absolutely. So if you missed it, there's your clue to go click that button, subscribe to the podcast. So you'll get the notifications when those come out as well. Totally fun.

Kim Montague  01:31

Very fun. So last week, we answered Amanda's question and talked about how we think that there are very specific major strategies that everyone should own for each operation. But that there's some other cool strategies as well, even ones that we use, but they're just not the most important ones. So in this episode, we're going to answer some more questions or comments that we received from people who have tuned in. And actually Pam, the first place that I went to look for some questions and comments was our teacher Facebook group.

Pam Harris  02:03

Yeah.

Kim Montague  02:04

It's a really great place for some conversations. Teachers leave their thoughts, their questions, and then you know, we you and I go in there and we leave some thoughts and we get some conversation going with other teachers who are also trying to build numeracy in their students.

Pam Harris  02:18

Yeah. So if you're interested in conversation with other Math is Figure-Out-Able teachers, join the Math is Figure-Out-Able Teacher Facebook group. Love to have you there. Yep.

Kim Montague  02:28

Yep. So in that group, Jessica said, "Teaching kids in a math is Figure-Out-Able way in fourth grade, after they've been taught in a sit and get, mimic the teacher way since kindergarten." That was a struggle. That was like, "Oh, this is what I'm dealing with right now." And Carolyn said, "How do you help middle school kids who are comfortable with algorithms to do Real Math? If they've been taught the traditional way all along it's really hard for them to switch."

Pam Harris  02:54

Kim Montague  07:02

Yeah, absolutely.

Pam Harris  07:04

Kim Montague  09:27

Yeah.

Pam Harris  09:27

Kim Montague  11:30

No, yeah.

Pam Harris  11:31

They don't do that. They're figuring out the question, they're reasoning as they read the question. Now, Kim, I want to ask you something. So don't let me forget. Just mention that. I'll remember. One other thing I want to bring up is, this is why we don't, we don't have a big emphasis on word problem strategies, like...

Kim Montague  11:55

I can't believe you said that! I was just about to say something about that.

Pam Harris  11:58

Well say it go. Then I have something else.

Kim Montague  11:59

You know, I was gonna say that if you are in a traditional situation where you feel like you have to like kind of spoon feed, "This is how you do it." You might also, 'might' also be somebody who feels like code words, or a particular do these steps in a word problem is also helpful. And so..

Pam Harris  12:18

Shade these words, underline those words, circle the numbers, cross out...

Kim Montague  12:22

For these particular words. And they mean to do multiplication. This word means to add. This word, right?

Pam Harris  12:29

Those key words.

Kim Montague  12:30

That's a very elementary thing to circle keywords, and then the words, as if the words tell you what to do. And so that tends to be the way that traditional, very traditional teachers would solve the problem of their students struggle with word problems, because they hit the thinking for the very first time maybe. And they're not sure what to do.

Pam Harris  12:53

And it's bloomin hard to mimic how to solve a word problem.

Kim Montague  12:58

Yeah.

Pam Harris  12:59

Because the word problems change.

Kim Montague  13:00

Yes.

Pam Harris  13:01

Right? Like, if you've been in an atmosphere...

Kim Montague  13:02

No symbol.

Pam Harris  13:04

Say it again.

Kim Montague  13:04

And there's no symbol to tell you plus or minus.

Pam Harris  13:06

Yeah, exactly. There's no thing to mimic. If you're in an atmosphere where everything you've done in math is here, when you see this symbol, you write the numbers this way, line them up, and then move the decimal, butt cheek at the end. And that's what math is, is mimicking the steps. Now you get these stupid word problems. You're like, "This isn't math. Like, what? This isn't math. How am I supposed to think about the, where's this symbol? It's not lined up for me? I don't know. Just tell me, just tell me the steps to do." If students say things like that, that should ping, ping, you have, that they have been in a fake math atmosphere. And they haven't been reasoning the whole time. So that's why we don't advocate all of that, all of those, help me, Kim. What are they called? The BEAMS? No, like I can even think.

Kim Montague  13:56

Acronyms names. Yeah.

Pam Harris  13:57

All those acronyms that suggest all of these ways to help kids, ready? 'Mimic', think about it that way. All of those acronyms, all of those step by step procedures to solve word problems are just that. They are an attempt at teachers who don't understand what mathematizing really is to say, "Oh, well, if math is about mimicking, we've got to come up with a step by step procedure that kids can mimic to solve word problems." That just should be a hint that we're stuck like heavily in fake math land when we do that. Kim, the thing that I wanted to remember, not to forget is let's say that you have a student who reads a word problem that maybe traditionally or typically might be solved by subtraction.

Kim Montague  14:47

Yeah.

Pam Harris  14:49

Kim Montague  14:50

Well, so I mean, it depends on the situation in the problem. But we know that there are a variety of ways to solve subtraction problems, right? You could think of subtraction as removal, but you can also think about subtraction as finding the distance or the difference between two numbers. And so a kid might look at it and say, "Oh, for these numbers, I'm going to choose to find the distance. And I'm going to find it as a missing addend problem."

Pam Harris  15:15

Absolutely.

Kim Montague  15:16

So those mimic these steps for subtraction might not even make sense to them in that problem.

Pam Harris  15:23

And the same thing can be true for a quote unquote, division problem. A student might think of that, see that problem and vision it, feel it as a missing factor problem. And if the teacher is up there going, "Okay, so did you choose the right operation? It should be division." And the kids like, "Oh, crud I did it wrong again. I was thinking multiplication. Oh, I'm not a math person. Okay, I guess I'll just..." And then we have that, we continue that sense of if it doesn't follow my intuition, I'm not a math person. And so I'll just try to memorize your stuff. And now we're back in this mimicking land and students trying to mimic that don't even feel like they can. We want to avoid those moments at all costs. Especially that when the student's intuition was brilliant, right? That missing factor problem, missing addend problem could absolutely be the way to solve a nice problem. Then we don't have to worry. Yeah, help me, Kim, finish that sentence I was on.

Kim Montague  16:18

Oh, gosh, well, I mean, we want kids thinking, right? And so we got to give them opportunities where their thinking is valued. And when they can trust their intuition, rather than just continuing to say, "Do these steps rotely." We want to put them in situations where they're thinking is important, maybe in a naked number situation, so that when they come to those word problems, then they just go, "Oh, I'm just thinking now about a situation rather than just the numbers."

Pam Harris  16:43

Absolutely. Absolutely. Nicely said. So, Tad, it's not that I don't ever work with context problems. In fact, we work with contexts a lot. We'd like to have many contexts in Problem Strings. We'd like to have some major contexts in Rich Tasks, or what Cathy Fosnot calls truly problematic situations. We deal with context a lot. In my work with teachers, what you might be seeing me put out a lot in social media, is to help teachers develop mathematical relationships. It's to help them develop their Additive Reasoning, help them develop their Multiplicative Reasoning, help them develop their Proportional Reasoning, their Functional Reasoning with the numbers so that they are thinking and reasoning mathematically, so that then they can help their students think and reason mathematically. And if we all get in that vein, we don't need to spend so much time at all helping students decide quote, unquote, which operation to use.

Kim Montague  17:44

We love questions and comments. Right? We're so excited to be able to answer those. Hey, listeners if you have any questions or comments, you are so welcome to send those to me at Kim@mathisFigureOutAble.com. We'd love to hear from you.

Pam Harris  17:57

Or throw them in the Math is Figure-Out-Able Facebook teacher groups, and we will get to them there as well. Thank you so much for joining us on this podcast. Thanks for tuning in, and teaching more and more Real Math. To find out more about the Math is Figure-Out-Able movement, visit mathisFigureOutAble.com Let's keep spreading the word that Math is Figure-Out-Able