Ep. 15: Problem Solving with a Twist

September 29, 2020 Pam Harris Episode 15
Math is Figure-Out-Able with Pam Harris
Ep. 15: Problem Solving with a Twist

Have you tried teaching your students "the steps" to approaching word problems, but your students still struggled? Pam and Kim discuss a better way to help kids tackle math problems. They explain why the acronyms and problem annotation methods of the past simply won't cut it. They suggest to help your students live the problem solving process, and not just memorize it.
Talking Points:

• The dangers of teaching and asking kids to memorize "Problem Solving Methods"
• Engage students in Real Math so that problem solving is a natural outcome
• Numberless word problems can be helpful

Resources: Brain Bushart's Numberless Word Problems

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  00:10

And we're here to suggest that mathematizing is not about mimicking or rote memorizing. But it's about thinking and reasoning; about creating and using mental relationships: empowering teachers and students. We answer the question, if not algorithms, then what? In today's episode, we talk about the problem solving process with a twist.

Kim Montague  00:35

Recently, Pam got a question that sparked a lot of conversation between the two of us. And since that's kind of the point of the podcast, we thought we talked about it today. So here's the message: "Hi, Pam, I have a question for you about providing all classes from kindergarten to year six, with a visual on how to solve word problems. So if a student didn't know where to begin to solve such a problem, they would look at the chart and then work out what they might use to do or do to solve their task. What are your thoughts? The one I was given had step one, understand the problem. Step two, make a plan and so on. It was designed by George Polya. Is there any research out there about giving students a chart to work out problems?"

Pam Harris  01:17

Okay, so that's the message that I got. And here's sort of my reply. The short answer is, sure. But I wouldn't spend a lot of time or money on it, and I wouldn't expect great results from it. Okay, so, Kim, when we were first talking about this, we went back and forth a little bit, and I asked you if you knew who George Polya is, and you weren't sure. So tell us about George Polya.

Kim Montague  01:42

Yeah, I learned so much from you. Dr. Polyais a Hungarian mathematician. And he taught in Zurich and Stanford. And he had a book that he was known for called How to Solve It. And he was also known for his efforts in the wake of Sputnik in 1957, to teach math teachers how to teach math. So apparently, he was regarded as the father of the modern emphasis in math education on problem solving. And he had a four step problem solving process. And here it is, step one, understand the problem. Step two, devise a plan. Step three, carry out the plan. And step four, look back. So as you were telling me about this guy, it reminded me of a time when I was in the classroom, and we had a six hour staff development, where we brought in this woman, and she did a training for us all about her specific problem solving process. And she introduced it, she walked us through examples, we all did some math together. And we left that day with a set of, a class set of cards, that we were to hand our students. And every time they solved any kind of problem, they were apparently supposed to walk through this process. And they were required to use it every time and I struggled, I struggled with that quite a bit.

Pam Harris  03:09

You loved it, you love spending six hours and making the cards. So, I'm also around the same time, there was a school in the district that said, "Pam, we need you. We have this thing and you know, can you please?" So I booked out some time, blocked out some time, and went to the school and met the principal, all the people were there, the math coach, heads of grade levels, you know, we sat down and everybody was really serious. And they kind of ask for what that professional development person did for you. They said, "We want you to come in. And we want you to set up a problem solving process. We really think that our kids are struggling solving math problems. And so we need to help them like with this, these steps, we need to give them the steps that they can clearly." And the steps they really had decided that they wanted to underline and highlight certain words and pick out different things, like do things to the numbers, and then off to the side, they were going to rewrite part of the problem. Anyway, they had this whole system set up and they wanted me to come in and work with the teachers to make sure that the teachers really understood the whole process on and on and on and on. And I was a little stymied. Not because I didn't know what to say, well, kind of didn't know how to say it... Because I wanted to be respectful of the fact that they were, you know, very honestly coming at the fact that their students were having a hard time solving math problems. So you and I began to continue to talk about like, what do we do in those situations? Is giving kids this problem solving process? Is that the be and end all? Is that the answer to helping kids be able to solve math problems better?

Kim Montague  04:55

Yeah. So, actually I gotta tell you since we're on the topic today, of Problem Solving methods, if you will. I searched, just google searched, some acronyms you want to hear?

Pam Harris  05:06

Yeah, go for it.

Kim Montague  05:07

All right. All right. So you might be doing the STEP method or the PAWS method like, animal paws. You could do the ROCKS method because math rocks. You could be doing CUBES or FUSE or CLEAR or GRASS.

Pam Harris  05:26

Hey, at least that one's sort of mathy. You know, like graphs, like x and y axis.

Kim Montague  05:31

No GRASS, like green grass outside.

Pam Harris  05:34

Ah, it's not even mathY. Okay.

Kim Montague  05:36

RIDES because a problem solver rides through problem solving.

Pam Harris  05:40

Ah.

Kim Montague  05:42

LOVE.

Pam Harris  05:43

Yah, we need more love.

Kim Montague  05:45

RICE.

Pam Harris  05:46

Rice? Rice, like rest ice compression elevation.

Kim Montague  05:50

Yeah, I didn't really get what the steps were.

Pam Harris  05:55

I've sprained my ankle a few times. I know that one.

Kim Montague  05:57

Rucksack

Pam Harris  05:57

Oh, rucksack ok okay, that's good. Yeah.

Kim Montague  05:59

Isn't rucksack like a carrying thing?

Pam Harris  06:00

I think it's like a backpack yah.

Kim Montague  06:01

Yeah. And, oh, gee, like 11 million other options. So here's the question I have: how are kids supposed to know what to do, when they like RISE or STEP one year, and then they rucksack the next? Right? That's a problem.

Pam Harris  06:18

Kim Montague  07:48

Oh I'm sure.

Pam Harris  07:49

Kim Montague  09:02

Right and the best you'll ever get. Is that now that they've made sense of the problem, but they're exhausted, because they've had to do all these extra things to get to that point, right? They haven't even begun to solve the problem. And by giving them these cards, we're in a sense saying that we have to tell them that a part of the process is to actually solve the problem, or could they just solve the problem?

Pam Harris  09:24

Yeah, exactly.

Kim Montague  09:25

So, Pam, what does help?

Pam Harris  09:29