# 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:

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 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:

Yeah.

Pam Harris:

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:

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

Pam Harris:

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:

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:

Yeah.

Kim Montague:

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:

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:

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:

And boy, do I appreciate that as a former high school teacher and a university instructor. I mean, I just get them where they've been at it longer, right? Like they've just been in this place, where math is about rotely repeating steps and not thinking and reasoning. Remember the story I tell sometimes, Kim, have I told that on the podcast? I'm going to retell it. So if I haven't, I'm saying it again. We were doing some videoing. I think I have but I'll say it again. We did some videoing in classrooms where we go in and we teach Problem Strings with students, we video those, we put those in our Problem String hub in Journey, which is our online implementation support system. And in that Problem String hub, you can go watch these videos. But when we shoot those videos, Kim taught me this, very wise Kim, you always go in the day before, and you have kids create the name tents, so you can say their names correctly. Names are important, totally agree. And you do a short Problem String with them. So they kind of get a feel for what's going to happen. And then you go back the next day with the camera crew, and then we shoot everything. So I wish the cameras were on this first day, because it's a group of seniors. So 12th grade students, fairly successful 12th grade students. They've made it to this specific class in Texas, so they had to have gotten decent grades before that in classes. They're in this class, 12th grade students, I do this Problem String, I'm halfway through it. It's not really a time for kids to ask question, but this kid right in the middle, the room raises his hand, has this look on his face like, "What?" And he raised his hand. I'm like, not really time to ask a question, but okay, "Yes, yes. What do you got?" And he goes, "It's almost like you want us to use what we know to

Kim Montague:

Yeah, absolutely. solve the problem." And every other kid in the room was like, "Yeah." And I'm in the front like cracking up like, "Oh, yeah." Part of the funny story for that is, it was actually my daughter's senior class. So she was sitting in the front of the class and she looked at me and just was like, (snicker) because

Pam Harris:

Kim Montague:

Yeah.

Pam Harris:

Kim Montague:

No, yeah.

Pam Harris:

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:

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

Pam Harris:

Well say it go. Then I have something else.

Kim Montague:

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:

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

Kim Montague:

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

Pam Harris:

Those key words.

Kim Montague:

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:

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

Kim Montague:

Yeah.

Pam Harris:

Because the word problems change.

Kim Montague:

Yes.

Pam Harris:

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

Kim Montague:

No symbol.

Pam Harris:

Say it again.

Kim Montague:

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

Pam Harris:

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

Kim Montague:

Acronyms names. Yeah. 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

Pam Harris:

All those acronyms that suggest all of these ways advocate all of that, all of those, help me, Kim. What are they called? The BEAMS? No, like I can even think. 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:

Yeah.

Pam Harris:

Kim Montague:

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:

Absolutely.

Kim Montague:

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

Pam Harris:

And the same thing can be true for a quote unquote,

Kim Montague:

Oh, gosh, well, I mean, we want kids thinking, division problem. A student might think of that, see that problem and vision it, feel it as a missing factor problem. And right? And so we got to give them opportunities where their 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. thinking is valued. And when they can trust their intuition, 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 rather than just continuing to say, "Do these steps rotely." We 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 want to put them in situations where they're thinking is 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 important, maybe in a naked number situation, so that when to worry. Yeah, help me, Kim, finish that sentence I was on. 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:

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:

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:

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