# Ep 59: Why not manipulatives?

August 03, 2021 Pam Harris Episode 59
Math is Figure-Out-Able with Pam Harris
Ep 59: Why not manipulatives?

Are manipulatives sometimes overhyped? When are they useful, and when can they actually get in the way of the mathematics? What role do they play in our discussion about the modeling framework? Pam and Kim discuss these tricky questions, and discuss the power of contexts and developing models as tools for reasoning.
Talking Points:

• What are manipulatives?
• Making decisions based on our goal as teachers
• Do manipulatives embody mathematics?
• How to choose appropriate 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 we make the case that mathematizing is not about mimicking steps, or rote memorizing facts. But it's about thinking and reasoning, about creating and using mental mathematical relationships; that math class can be less like it has been for so many of us, and more like mathematicians working together. We take the 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 this episode, we are continuing the conversation about models and modeling, the idea that we use those words to mean lots of things, but that we need to parse out and be more particular about words, what we're saying, so that we can understand each other and therefore make more progress and making more math more Figure-Out-Able. So Pam, last week, we talked about a variety of meanings for the word model.

Pam Harris:

Yeah, and the most important takeaway is this important sequence of modeling? First, it's sort of a model of the situation, as kids are in a context, we want to be able to model that situation and really understand what's happening. But it's an important model of that situation, because then that model of the situation then sort of morphs into where as the students are solving problems, then the teacher represents their thinking, we make a model of their thinking, make the thinking visible. And as the teacher makes that thinking visible as students say, oh, when my brain does that, it could look like that, then we transition to have students then use that model to represent their thinking. Then we ask students, hey, when your brain does that, how could you make that visible? How could you like, show me your thinking? But that has to come after we've sort of used a model to represent their thinking, given them ideas of how they could represent that. And then lastly, after lots of experience, and really using that model a lot to represent their thinking, then that becomes a tool for thinking. Then they can actually use that model in order to think. So that's kind of this really important sequence or progression of modeling that we like to think about when we work with teachers. Now, Kim, there are some popular progression videos out there. And even when I just said progression of modeling, you're like, Oh, yeah, I've seen some progression of videos, those are cool. And they're very well made, and they sort of show a progression of manipulatives through the grade levels. And they end with wallah, that's why the algorithms work. They're really well done. And they're entertaining. And they do explain well the algorithms and maybe many people understand the algorithms for the first time because of these progression videos. Which might be noteworthy about the usefulness of understanding the algorithms. Just saying. So you might find it interesting that we don't promote these progressions, because remember, the algorithm is not our goal. Nope, nope, not our goal. So today, I'd like to discuss another reason that we don't promote those progressions. And it's about the way those videos use manipulatives. So today, let's focus more on one of those things we said in Episode 58 that we don't mean, we do not mean when we use the word model. When we talk about how important it is to use models in math class, in math teaching, we don't mean manipulatives, at least carte blanche.

Kim Montague:

Manipulatives. So I was on Facebook recently. And, you know, I keep seeing these posts, lots of posts in different teacher groups about people changing grade levels or starting teacher, and they're asking things like, what's the best manipulatives that I need for this particular grade level? Y'all give me some ideas? Or, you know, I got a couple hundred dollars as a new teacher, and I'm trying to hear from others what manipulatives I should get? What do you recommend? And I find that so fascinating that that's the question that they're asking.

Pam Harris:

Yeah, like Kim, let's talk about manipulatives. Give us some examples of what we mean - we have high school teachers on here - what do we mean by manipulatives?

Kim Montague:

Oh, there's so many right. So there's base 10 blocks. We've got counters. We've got two sided counters, little colored teddy bears maybe in younger grades. Yeah, there's unifix or centimeter cubes, dice, little clocks, tiles, algebra tiles, hundreds charts, students size hundreds charts, all the things right to get students holding, moving, manipulating.

Pam Harris:

Kim Montague:

Yeah, that's so good. So let's describe a little bit of what she might have been seeing. Right? Let's say it's time to be working with negative numbers. And so we'll see teachers take out integer chips, which are counters that are red on one side and yellow on the other. The CRA approach, would have kids build the numbers, and talk about zero pairs. And then the kids start moving tiles around. And then the teacher has kids draw the same things. And then the abstract, right, then they write the numerals.

Pam Harris:

Kim Montague:

So good.

Pam Harris:

And we agree. So let's talk about contexts. You might notice that I use some very specific context for integers, they need to be contexts that translate, in this case, to number lines. So it's not just about any random context to get kids interested, sometimes people hear Oh, you've got to make it real so kids are interested. It's not about that. It's not about real world. It's about context that make the mathematics realizable. And then we can translate to those really important models. So again, the sort of modeling that we think about is that it's first a model of the situation, then the teacher models student thinking so that then students can model their own thinking, and then we transition, and this takes time and experience, to a model for thinking or in order to think.

Kim Montague:

So listeners, if none of this makes sense, think of an analog clock. The math is clearly in that clock. You and I know that right? What the numbers represent and what's going on. We've already messed with those relationships in time. But do kids understand that analog clock by looking at it or even messing with one where the hands move? Or do they need to have experience with the relationships? Absolutely. Just having that manipulative does not ensure - we can't you just hand it to them - and ensure that they understand time.

Pam Harris:

Especially if we just hand it to them and say, do this, now do that. And you got it down? Okay, got those little steps? All right. All right. Now you understand time. What? Ah!

Kim Montague:

Yeah, so are we suggesting that manipulatives are bad? Absolutely not. But we so want to be particular about which ones and how and when we use them, and in the next few episodes, we're going to take a bit of a deeper look into what we do recommend.

Pam Harris:

So if you want to learn more math and refine your mathematics teaching so that you and your students 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!