# Ep 165: Where Popular Things Go Wrong

August 15, 2023 Pam Harris Episode 165
Ep 165: Where Popular Things Go Wrong
Math is Figure-Out-Able!
Math is Figure-Out-Able!
Ep 165: Where Popular Things Go Wrong
Aug 15, 2023 Episode 165
Pam Harris

There is so much that is good happening in the math teaching community! In this episode Pam and Kim discuss how we can determine how much of which good things to put into our classrooms.
Talking Points:

• Going beyond nixing tricks
• Social versus logical knowledge
• Nixing the tricks is more than explaining the math better
• The dangers of going all in on any good teaching practice
• Number Talks
• Exploding Dots
• Manipulatives
• Keep asking for clarification and refining your craft in order to create mathematicians in your classroom

Check out our social media
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

There is so much that is good happening in the math teaching community! In this episode Pam and Kim discuss how we can determine how much of which good things to put into our classrooms.
Talking Points:

• Going beyond nixing tricks
• Social versus logical knowledge
• Nixing the tricks is more than explaining the math better
• The dangers of going all in on any good teaching practice
• Number Talks
• Exploding Dots
• Manipulatives
• Keep asking for clarification and refining your craft in order to create mathematicians in your classroom

Check out our social media
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

Pam  00:01

Kim  00:07

And I'm Kim.  They have a great report.

Pam  01:33

Yeah, they do.

Kim  01:34

You sent me an episode to listen to, and it was super fun.

Pam  01:37

Yeah, it was nice. So, we are going to talk about their episode. I think it was 3.6 Don't Lose the Mathematics. And they talked about kind of nixing the tricks. Yeah. And so, we thought we'd put our spin a little bit on, and add to that conversation. We would wholeheartedly agree that we should nix the tricks. There's a fine booklet out there. It's online. You can get it for free. You can order the book, if you want to actually have the hardcopy. Called Nix the Tricks. And, Kim, I think you and I would both agree that it does a fine job of identifying some tricks that math teachers have kind of maybe found over time, that unfortunately they're promoting as doing math. They're like, "Hey, here's a here's a trick to do this. Here's a different trick to do that." And many of us are saying, "Nah, let's nix those tricks. Let's actually focus on what mathematicians do, the way they think, and not teach these tricks." And so, Curtis and Joanie, in that episode, mentioned a few of the the tricks and came up with some things to think about. Do you want to mention anything else about the episode? Or, then, I'll just dive into what I was thinking about.

Kim  02:51

Yeah. So, there were a couple of things that they talked about that prompted me to revisit the Nix the Tricks website. And I had forgotten that it was kind of curated, I can't remember who it was, but a couple of people. But a lot of it was submitted by the math community in general, which I absolutely love. And it's like a collection of things. And I got to tell you, Pam, when I got on the website, I was like, "Wow, there's even more tricks than..." I mean, like, this is not the kind of thing, listeners, where we're saying, "Go check it out, and like learn a bunch of new things to do in your classroom." We would absolutely recommend that you don't go learn some things. We won't learn them. It's just people telling you like, "Here's a thing, a trick you can do." But yeah, there were several on there that I was like, "Wow, I've never heard that before." How is that? There's like 70 different.

Pam  02:52

It's not math, yeah.

Kim  03:15

Like, can you imagine being a middle school kid, and you're like, "Here's one more."

Pam  03:45

"Let's try to memorize all of those."

Kim  03:48

Oh, my gosh. Oh, my gosh. Yeah.

Pam  03:48

Which is kind of what we get, right? The older the students get, if that's the kind of math class they've been in, it just gets harder and harder to say, "Woah, woah, woah. Yeah, you get answers with those tricks. But you can actually think about that stuff, actually reason through using what you know." Oh, let's see. We might have to back up and know some more things.

Kim  04:10

Yeah.

Pam  04:11

One of the things that I thought we could kind of add to the conversation a little bit is, one of the things they talked about is how do you know if something is a trick or not?

Kim  04:20

Yes.

Pam  04:21

Kim  08:01

Right.

Pam  08:02

So, that we can add to the conversation a little bit, that if you can look at the thing you're trying to teach, and say to yourself, "Hey, is this... Is part of this social?" Well, then I'm going to tell kids that, and I might help kids rote memorize that. But the vast majority of whatever it is, is probably logical, mathematical, then bam, we're jumping in, and we're going to actually have experience learning that thing, experience gaining relationships and making the mental neural connections stronger and stronger.

Kim  08:31

Yeah. I think more and more, thankfully, we're hearing people say, "These are some tricks. Don't teach kids the tricks. It's not about cutesy. It's not about a bunch of things to memorize." I mean, I think we're, hopefully, trending towards that becoming less and less of a thing. But what I am seeing, I think you're seeing this too, is that instead of those tricks than what people are doing is just explaining more clearly, or maybe explaining things with a little bit more mathematics. But it's still a little bit too much of explaining. Right, like a little too much of "Teacher has all this knowledge. Let me just tell you."

Pam  09:11

Kim  09:12

Yeah. Which is also not something that we advocate, right? We want to build mathematicians by giving them experiences, by posing important questions, letting them rustle and (unclear) some stuff, having deep conversations, letting them be a part of the process, rather than just standing at the front telling them with a little bit more meat than some of the tricks we might have done in the past.

Pam  09:35

Yeah, because we actually believe that's actual learning.

Kim  09:37

Yeah.

Pam  09:37

We don't believe that you can unzip a kid's head, and pour some stuff in, and then they own it. That's like saying, "Go ask GPT how to, and then..." Pick something that's... In fact, here's here's a way that sometimes I determine whether something's logical, mathematical, or social. If you can ask Google or chat GPT a question, and their answer actually you can own it, you can do something with it, you can run with it, then it's probably social. Like, if it's enough. If you're like, "Hey, when was..." Pick something. "When was Mount Rushmore created?" Some random social thing. That's a social thing. It happened. There's no way you can figure that out.

Kim  10:16

Right.

Pam  10:16

"Who were the signers of the Declaration of Independence?" Bam, like I'm going to go, I can ask that, when I get the answer, it's satisfying. I'm done. But if I say, ask chat GPT all the connections and relationships to build a nuclear bomb, which I don't even think it will answer that question. Or to everything about quadratic equations. It might tell me a lot of stuff about quadratic equations. But that telling, if I don't have enough to experience to own that stuff, then then I'm not going to own it. I can't do anything with the answer. So, chat GPT might give me a great answer. But if I don't have experience grappling with those relationships, then I'm not going to own them enough to do something with them.

Kim  10:59

Yeah.

Pam  10:59

Yeah, so some people are saying, "Don't teach the tricks." We're saying, "Don't just explain more. Actually build mathematicians by giving them experience."

Kim  11:09

Yeah. So, the other thing that I think is fun to bring it today is that  there are lots of educational leaders out there. And we're so lucky to have a bunch of people doing really good work to move away from tricks and to do a better job of giving kids these experiences. And so, you think that there's a lot of richness to bring to a classroom. But the one that you probably focus on a lot more, because you love them and because they're so beneficial, are Problem Strings. Right, like that's a...

Pam  11:40

That's kind of my schtick, yeah.

Kim  11:41

It's kind of an important thing. Maybe because once it becomes routine, it's a quick routine. That there's so much meat. Like, there's there's so much bang for your buck in a Problem String. So, you do Problem Strings. Some people do number talks. Some people do, you know, all these other things. And let's talk for just a second about the idea that when you go all in on a thing, like a Problem String or a number talk or whatever, there are some really good things about it, but there's also some things to be on...

Pam  12:15

Guard?

Kim  12:16

(unclear) about, be aware of. Because we've both had conversations where people say, "Well, I do this thing." But when they describe... Let's say number talks. They do number talks. But when they describe what they're doing with number talks, or how they're sharing number talks in the classroom, or what they think they're getting out of number talks, we've heard some scenarios where we feel like people were just kind of like missing the boat a tad bit. And then, let's talk about the kind of the negative to that. Like, what can happen when people go all in on one thing, and that's the only thing that they they focus on?

Pam  12:53

Yeah, and especially if they maybe misunderstand the thing or the purpose of the thing. Yeah. So, you mentioned number talks. Let's start there. So, are number talks great? Absolutely.

Kim  13:05

Yes.

Pam  13:05

But I got to tell you, the first time that I heard the phrase "number talks", or the title "number talks", I pushed back on that a lot. Because I said to myself... Or maybe even math talks. People are like, "Oh, you know. Yeah, do a math talk," as if that's the only time you talk in math class. And I was like, "I want to be talking a lot in math class, not just during this one sort of thing that we do." So, a thing to consider is, if you've heard math talk or number talk, and you're like, "Oh, yeah, that's when we talk in math," I'm going to push back on that, and say, "No, no, no. No, we should be talking a lot in math class." Sure, there are times where students are quietly doing their own work. I think that is an appropriate use of math learning time a little bit. But mostly we're having conversations, were grappling, we're having kids wrestle with. We're giving students good problems to tackle, so that they can then wrestle and grapple with the relationships. And then, we're making that thinking visible, and we're pointing at it. But we're doing that not just during a number talk or math talk time. We're doing that all the time. That should be happening during almost all the work that we're doing. So, that would be an example of something that maybe we'll bring up. A tweak that we would suggest is, sure you can do number talks sometimes in your class. But that doesn't mean that you're not talking in other times of class. Cool. So, I'll mention another one, Kim, that I've been thinking about. I hear sometimes people say, "Oh, Exploding Dots is the best thing ever!" So I think Exploding Dots, depending on how you define it, is kind of cool. I like to listen to...

Kim  14:48

James Tanton.

Pam  14:49

Thank you. James Tanton. I can't believe. Whoa! I got sleep last night. James Tanton is an enjoyable presenter to listen to. He tells good stories. He's pretty funny. However, I would mention that I think Exploding Dots does its best work when we use it to think about place value.

Kim  15:09

Yeah.

Pam  15:10

Kim  16:46

I was going to say, do you remember one time we were interviewing some students, and we had a young lady who we gave her a problem. And it was a not super complicated problem for maybe her age. And we had seen her do some work, where we knew this problem was not likely to be super challenging problem for her. She had done some other things that were maybe a little bit more complicated. But because she had been using Exploding Dots so much, she did that for every problem. And, you know, I don't pretend to know James Tanton.

Pam  17:21

Well, did that. Let me describe what she did. So, it was like a problem like 7 plus 8 or something.

Kim  17:26

Yeah.

Pam  17:26

And she dutifully wrote down 7 dots and dutifully wrote down 8 dots, and then moved her paper over, and then like circled 7 plus 3 and said, "Okay, now that's one 10. And then, what's leftover?" And then, she's like, "Okay, so that's 15." And I looked at her, and I was like, "Do you know 7 plus 8?" Were you interviewing her? Both of us there I remember. And she's like, "Oh, yeah, it's 15." And we're like, "But did you have to do all that work?" "No, no, no. But that's what I'm supposed to do."

Kim  17:51

Right. So, I think that's the point, right? That's the point is that I don't know what James Tanton's take would be on that. You know, I don't. But there are things. And so, her experience with either her teacher, or previous teachers, or whatever was that "This is what you do." And so, a thing that is maybe a really good idea, maybe Exploding Dots is fantastic for a place value or whatever, but what we see happening is these really good things turn into "Do the same thing all the time," or "This is how the one way that you use them." And so, I think that's challenge, right, is hearing something and going like, "In what way do I want to use this idea that somebody's sharing about and (unclear)..."

Pam  18:35

"...and have it not go awry."

Kim  18:37

Right. And when would I not use it? And how is it not helping my students in these particular instances? Can I bring up another one?

Pam  18:45

Yeah, sure.

Kim  18:46

Or do you want to say more about that?

Pam  18:47

Kim  18:47

You get asked a lot, "What about manipulatives?" And it's kind of an interesting question because people will say, "What about manipulatives," question mark. And It's like, Wait, what's the question there? What? Manipulatives?"

Pam  18:57

What about manipulatives?" Yeah. Like, say more.

Kim  18:59

How? When? Which one? Mmhmm. So...

Pam  19:01

Yeah, yeah.

Kim  19:02

You'll need a long answer, but in brief.

Pam  19:05

Mmhmm. So, I have to tell you. The first thing that comes to mind is Gail Burrill was a former NCTM president. And when I was a young teacher, she was the NCTM president, and she did a president's message. And it was when the Wendy's commercials... I'm totally dating myself here. The Wendy's commercials had come out. "Where's the beef? Where's the beef?" And their whole thing was, you know, "We have we have big hamburgers," I guess. But "Where's the beef in everywhere else?" But her thing was, "Where's the math?"

Kim  19:34

Yeah.

Pam  19:34

And she said, as she was traveling around as the NCTM president, she saw a lot of manipulatives out in classrooms, and her concern was, "Where's the math?"

Kim  19:43

Yeah.

Pam  19:44

And so, I share that concern. And here's where I would add to that conversation. We do a lot of talking about developing mathematical reasoning, in that we need kids to learn to count and solve problems using counting strategies, but then we want to advocate additive reasoning and thinking in terms of bigger chunks of numbers. If we give kids one to one manipulatives all the time, kids will not necessarily be nudged, be encouraged to build their brains to think in terms of chunks of numbers because they're counting one by ones. If we give them one to one manipulatives, they will continue to count one by one.

Kim  20:24

Right.

Pam  20:25

So, the biggest caution that I would give. It's not the only one. But the biggest caution I would give about manipulatives is to think about what is my goal here, and is the manipulatives supporting answer getting only or is it supporting the goal of building reasoning? And what kind of reasoning? So, then, we actually have to identify what kind of reasoning we're trying to build. I'll give you a quick example. Early, early, when I dove into elementary. So, I was secondary teacher. I got super interested in elementary. I started diving into research. One of the things I did was volunteer at my kids school. And one day, they said, "Hey, today, we're not going to give you that group of kids you've been kind of extending." I had a group of kids, and I was just experimenting and trying some things with them. And they said, "Today, we don't have time for you to do that. Sorry, we didn't, you know, tell you ahead of time. But today, can you just help this one student. She's really struggling." And I was like, "Oh, I don't even know what I will do with this second grade student, but sure." And so, I started chatting with this student, and they said, "Help her add." And it was like add two digit numbers. And they gave me base 10 materials.

Kim  21:28

Yeah.

Pam  21:28

And so, I wasn't even sure what to do with base 10. And so, I said to her, "You know, we got this problem. 28 plus 37. Like, what are you going to do?" And she goes, "Well, I think I'm supposed to grab these rods." And I said, "What's a rod?" Because like, this is me early, right? I'm like, I don't even know what a rod is. She goes, "Well, you know, it's this thing right here." And I said, "Well, what is this?" expecting her to say "It's 10." But she goes, "It's a rod." And I said, "Right, but you know like, if this is 1, what's this?" And she goes, "It's a rod." And now, you might be like, "Well, Pam, that student misunderstood," or whatever. But when I pulled out the 100, and she said, "That's a flat." And she goes, "I think it's called a flat." And I was like, "Um... But like, how many of these little guys are in that?" She goes, "I don't know." I'm like, "Well, how many of these little ones are in this 10." And I think I literally said, "How many of these ones are in this 10?" And she goes, "It's a rod." And I'm like, "Right, but how..." So, then, she took the little one, and she lined it up against the rod to see. And she goes, "Well, I guess in this one there's 10."

Kim  22:25

"In this one." Yeah.

Pam  22:27

Yeah, so my point is that I'm not sure what the teacher had tried to do. Obviously, you could do a better job of that. But in manipulatives, we have supposed, we've... How do I say this? We've created manipulatives to represent the mathematics that we have created in our minds and supposed that students can see the mathematics in that manipulative. And that is not true. Students cannot just look at this pre-constructed rod that we've stuck together and all of a sudden go, "Oh, yeah, that's a 10. And see, there's 10 of those in that flat,. And there's 10 of those in that cube." And so, we can't... I'm going maybe longer than you wanted me to. But we can't just assume that that because we've created the relationships, and we now know the mathematics that are involved in that manipulative, that then therefore it Woah magically appears to the students in the manipulative. So, I don't... Yeah. There's four other things I can think about manipulatives, but we won't make this too too long.

Kim  23:28

Yeah. Well, I don't know how long we want to go. But I think the big recap, the point here is that are manipulatives, or number talks, or Exploding Dots, are they bad? Absolutely not. There's value in all of those and many more other things.

Pam  23:45

Mmhmm.

Kim  23:46

What's important to keep in mind is that if you think only doing that thing is going to get you very far.

Pam  23:54

We have to do some (unclear) for everything. They have always be out, and we have to always have kids using. "Kids don't have manipulatives in their hand, you're doing a bad job teaching." We're saying no, not with that.

Kim  24:03

Yeah.

Pam  24:03

Yeah.

Kim  24:03

Absolutely.

Pam  24:04

Sorry to interrupt.

Kim  24:04

That's okay. And also, you know, there are ways that these things are being used that miss the mark of even the people who are sharing about them. Right? So, like just just recently we talked about Problem Strings and how, you know, we think we're being super clear about them, and yet there's still questions. And so, I love when people continue to ask, right? Like, "What's the value in this?" And, "How often should I be using it?" And, "In what way should I be using?" And, "How do we know if they're being effective?"

Pam  24:33