Math is Figure-Out-Able with Pam Harris

Ep 35: Multiplication Facts: The Good, the Bad, and the Ugly Pt 2

February 16, 2021 Pam Harris Episode 35
Math is Figure-Out-Able with Pam Harris
Ep 35: Multiplication Facts: The Good, the Bad, and the Ugly Pt 2
Show Notes Transcript

When choosing tasks to teach multiplication facts, what are the pitfalls to avoid? In this episode Pam and Kim discuss ways teachers may inadvertently 1) overemphasize speed, 2) introduce shame into their classrooms, and 3) focus on learning facts in isolation.  We've all made mistakes, and this episode is about learning and growing for our students.
Talking Points:

  • What the research says about the negative effects of timed activities such as multiplication fact tests
  • Shame is not a motivator to learn facts (harder then you think!)
  • Why learning facts as isolated ideas is not helpful


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'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. That mathematics class can be less like it has been for so many of us and more like mathematicians working together, we answer the question, if not algorithms, then what?

Kim Montague:

Y'all last week, we began an important series about multiplication facts.

Pam Harris:

Very important.

Kim Montague:

And shared some clarification around the words

Pam Harris:

Yeah.

Kim Montague:

We're gonna try to bring some awareness to the memorization, automaticity, and fluency. You'll definitely want to check out Episode 34 for some important background information. In today's episode, we want to talk about some of the more common routines that we see happening in classrooms to help students become fluent with multiplication facts. And we difference between what your goal is, and what might actually want to shed some light and some current research on why we believe some of these routines aren't maybe getting you the results that you really want. be happening because of the ways that you might be trying to achieve your goal.

Pam Harris:

Yeah, so we invite you to think about three main ideas, three indicators that describe efforts that will be

less successful. So number one:

if that effort is using shame to

motivate. Number two:

teaching the facts in isolation as isolated things to be rote, memorized. And number three: it's all about timing, that it's about being fast. That to be good means you're quick. So three things: shame, facts in isolation, and speed.

Kim Montague:

Yeah, so if these are important things to consider something that we don't want, we would invite you to have these indicators in mind as we discuss some activities today. Ask yourself, do these routines have the potential to embarrass kids? Or to make them feel ashamed for their knowledge or lack thereof? Are they focused often on speed? So that it appears that quickness matters most? And are the activities that tend to view facts in, something learned in isolation, rather than connection to the other facts?

Pam Harris:

Yeah, now, this episode is not about shaming anyone, we just mentioned that we don't want you to do shaming activities in your classroom. We also don't believe in shaming adults. Shame doesn't work. It doesn't motivate.

Kim Montague:

Right.

Pam Harris:

We're all about motivating positive growth. And we think you are too that you want to motivate positive growth in your students. So we're going to discuss some of the prevalent ways that teachers try to help students learn their facts, that because they're focused on shame, isolation, and speed, they will be less successful than other equally fun, much more motivating activities that we can do with students that get really helpful results, much more helpful results, like the relationships between the facts, and students who are knowing multiplicatively those relationships. And they'll also know the facts better than just in isolation.

Kim Montague:

Oh, absolutely. So listen, I used some of these routines. when I first began teaching, right? They were things that I participated in as a kid. And so it was what I was familiar with, and what I thought were maybe some good ways to practice when I taught facts in isolation. So it's okay to have been there. It's also okay to do better when you know better.

Pam Harris:

Right, exactly. It's all about doing better when you know better. So today, we're going to sort of help shed that light on how we can all know better a little bit more.

Kim Montague:

Yeah. So let's talk about one of the most common routines, time tests.

Pam Harris:

Dug-ta-duh.

Kim Montague:

Yeah, time tests are also maybe known as Mad Minutes or Fat Tests, you know, the kind, right?

Pam Harris:

Yeah, absolutely. Yep.

Kim Montague:

So there might be a full page of basic multiplication problems. It could be all the same kind of facts, like a page of sixes or page of sevens. Or maybe it's a full page of mixed problems. But either way kids are maybe passed out a page. And then once the teacher says it's time or maybe says go, they turn it over and have a certain amount of time, like maybe a minute or two or five, to complete as many of the problems on the page as they can before the timer goes off, or the teachers that stop.

Pam Harris:

Or they might be on a computer and same sort of thing. Like it's like, go and then they have so much time to do it and stop and it's this time thing.

Kim Montague:

Yeah. So the intended outcome is that students maybe know they have these practices. And as they work on their facts, they get better and better over time. They have a measurable way to determine their progress. Definitely a speed component involved there.

Pam Harris:

Right? But the actual outcome is at worst math anxiety and so many students who never really get good at the facts. And at best, its facts in isolation for almost all the rest of the students.

Kim Montague:

Yeah.

Pam Harris:

That's a ton of students who never learned the facts but learn to have anxiety around math, or students who have these disconnected facts and rote memory but can't actually use them to reason multiplicatively which is our goal. Right. So Jo Boaler from Stanford University has a great article out called Research Suggests Timed Tests Cause Math Anxiety, that's the title of the article. Okay, she clearly states, "Evidence strongly suggests that time to tests cause the early onset of math anxiety for students across the achievement range." She found a study that found researchers now know that students experience stress on time tests that they do not experience even when working on the same math question in untimed conditions. And then in a different study of first and second graders, researchers measured students' levels of math anxiety, and they found that students as young as first grade experienced math anxiety. And that levels of math anxiety did not correlate with grade level, reading level or parental income. Now, that might sound kind of jargony. But let's get down to why that happens. Why do time tests cause math anxiety? When researchers analyzed brain imaging data for seven to nine year olds, while they were working on addition, subtraction problems and found that those students who felt panicky about math also had increased activity in brain regions associated with fear. Right. They're feeling panicky, that makes sense. Right? Fear, okay. But when those areas are activated, researchers found that decreased activity took place in the brain regions that are involved in problem solving. That's important. Literally, students couldn't think as well. How does that make sense? Researchers use brain scans to show that when students compute with math facts like those in time tests, they recall information that's held in working memory. Researchers found that when people are stressed, the pressure blocks their working memory. And so facts that people are familiar with can't be recalled. You've probably felt this happen when you're in stress or pressure, like in a public situation when your mind goes blank. Right, Jo Boaler says, "This is the impact of stress blocking the working memory. When students who experience stress in timed conditions find they cannot access their working memory they underachieve which causes them to question their math ability, and in many cases, develop further stress and anxiety," unquote. So now we've got a ton of people who think they're not good at math, but in reality, they just aren't great at recalling disconnected facts under pressure. Y'all, that's not math.

Kim Montague:

Yeah. So it's funny that you are mentioning this research, because I can remember the one time that I ever cried in math. I was so young, I was probably in second grade. And I was brand new to a school. And first day, literally first day, the teacher says, "Oh, it's so great to have you in class. We're just about to do our fact practice." And I was like, "Sweet, I know my facts." So get out a piece of notebook

Pam Harris:

So you're actually feeling really confident at this paper. point.

Kim Montague:

I was like, "I'm gonna do great." Right?

Pam Harris:

Wahoo.

Kim Montague:

She calls out the problems. And in the previous school that I had been at, you write the problem in the answer.

Pam Harris:

Okay.

Kim Montague:

But in this school, apparently, you just write the answer. And I could not write fast enough.

Pam Harris:

You didn't know that. Ahhh.

Kim Montague:

I didn't know the rules, right? And she's calling out so quickly. And I couldn't write fast enough. But here's the thing. I also could not recall the answers to the problems fast enough. I was so flustered, and I remember, tears just coming down. I was panicked. I was absolutely panicked. And I felt a little ashamed. So we mentioned time with timed tests. But also can...

Pam Harris:

Kim, I'm so sorry. Like I'm feeling for you. But in reality, how many people listening to this, like, relate to that?

Kim Montague:

Yeah, yeah, we have kids who also can relate to it. Right? At a very young age.

Pam Harris:

Yep.

Kim Montague:

So we mentioned time, but there can also be a lot of shame, as well as, you know, based on how this activity is facilitated by asking kids to call out how many they got correct in front of their peers.

Pam Harris:

Yeah.

Kim Montague:

Can have some shame, right? Or by announcing or marking which page of facts, if it's a six and then a seven, and then the eights page, asking kids to tell what page number they're on.

Pam Harris:

So like, the whole class knows. Everybody's real public.

Kim Montague:

Can be super shameful, right?

Pam Harris:

Yeah, so this reminds me of my daughter's elementary class. So she was in fourth grade. And they were doing this fact practice stuff in ways we don't prefer. And her thing that year was that she was earning an ice cream sundae. So if she could pass off a certain facts, like the eights or whatever then she would, if she got enough right on time test, then she could add the hot fudge topping. Or if she got the fours then she could add the sprinkles or whatever. So there was like, and it was very public. The ice cream, the picture of an ice cream sundae was hanging on the wall. And when they got it, they could color it in and everything. And then at the end of the year, or sometime or whatever, then whatever you earn, then they actually had this like ice cream sundae party. Can you imagine the kid who didn't get any of the, or you know, had ice cream only or whatever? I mean, it was a very public, shaming, kind of task that we're not recommending.

Kim Montague:

Well, and it seems like the goal is to motivate or encourage students with these activities. But for so many students, it's not. Now some of you might be Right. Uh-huh.Yep. saying, "But kids love competition. They love earning things." So let's break down why these maybe are not so helpful.

Pam Harris:

Right. Because again, a lot of us experienced them. Some of us had success in those things. So it feels like you know, let's keep doing these things. Even, it's funny, sometimes we talked to parents who were like, "Well, no, I hated that. But I know my kid needs to do it." And you're like, "Ah, maybe we can rethink that." So remember our three

things:

shame, time and isolation. So first timed means that we're emphasizing speed is so important, and we don't think it is. But notice how these activities we just mentioned, all like make it be all about time. And then second, when you're competing in front of everybody that has high shame potential. Everybody can see who's on what part of the Sunday or when the teacher calls come get your sevens, if you're on the sevens. It's all very public. And if you're the kid still on the fours, it doesn't help you be more motivated. Shame doesn't work that way. And these tasks are so focused on facts in isolation, not our goal. We want to learn the facts through relationship. Another thing that I saw that we'd like to talk about today, I walked into my kids' third grade classroom. It was one of those moments watershed moments when I realized I needed to get involved in my kids elementary math education. It was honest, hard working teachers who are just sort of missing what math mathematics facts could be and should be. So let me describe these posters were all about rote memorization of the facts. They were rhymes or pictures and in fact, when we threw out on Twitter, "Hey, what are your, what are the some of the worst ways that you guys suggest that kids can learn facts?" Harvey, no excuse me, Richard Harvey Swanston gave us an example of a poster I had not seen. So this is not exactly the poster that was on my kids third grade wall, but it has the same bent. So he tweeted some pictures of these posters. Let me describe one of these not so mathy posters. Alright, ready? Alright, everybody. This is how you're gonna learn this fact. So get it down. Here we go. There's a door and a sign next to the door. And the sign is covered with a bunch of sticks like sticks off a tree. Right? There's like a bunch of sticks are like all over the sign. Okay, there you go. Like that invokes math. Right? We got it. Kim, what in the world is that supposed to help us?

Kim Montague:

I saw that poster. So the door represents the digit four. The door is four.

Pam Harris:

Okay.

Kim Montague:

And door time sign, sign is nine. So door times sign equals, obviously dirty sticks.

Pam Harris:

Oh, I forgot to mention that the sticks were

Kim Montague:

So door time sign, four times nine, equals dirty. obviously dirty sticks, 36. And it shows a sign with the four on it. And the sticks are covering the picture. Right? It's all about memorizing this other thing that doesn't have anything to do with math much like songs or rhymes that kids listen to over and over again. And what happens, right, if they memorize the song wrong or mix up the posters?

Pam Harris:

In fact, one of the things that I sometimes say when we're working with teachers is I'll say, "Hey, like a rhyme like this, like six times eight, like the garden gate is made of six. So it's 50, wait, shoot I have the wrong... Right? Because it's not 6 times 8 isn't 56. It's seven times eight. But if I memorized that rhyme wrong, yeah.

Kim Montague:

Yeah. So rote memorizing facts in isolation leaves students without any recourse when they can't remember it.

Pam Harris:

And it's when, not if they can't remember it. Y'all memory fails for everybody at some point. Okay, so let's talk about another kind of thing that meets our three criteria. How about Round the World? Now maybe you call this something different in your class. Around the World for me looked like the teacher would say, "Okay, two students stand up." And she would flash a fact and whoever got it right then got to stay up. And the other person was sort of shamed and sat down and you know, bummer. And then we kept going around the world. The person who stayed standing, went and stood next to someone else, and they continue the thing. So your goal was to be the kid that was standing and keep going and whatever. So all the things like time, it was all about who could get it quicker. Shame, you had to sit down if you were the one that didn't get it right. And facts in isolation, it wasn't anything about how the facts are related to anything. It wasn't about their connections and multiplicative reasoning. It was just like this cold fact in front of other students, Not an ideal for all the three reasons Around the World does not win.

Kim Montague:

You know what?

Pam Harris:

Go ahead, Kim.

Kim Montague:

I was gonna say the most interesting part about this activity for me is that the kid who probably knows their facts the least and needs the most practice, a really good way is the one who sits down right away.

Pam Harris:

And that's why you wanted to talk about it.

Kim Montague:

That's so ironic to me.

Pam Harris:

Yeah, because it was totally you that pointed that out to me. Like we were talking about all these things not to do. And I was like, "Oh, Around the World fits our three." And you're like, "Oh, if it's a fourth."

Kim Montague:

Yeah.

Pam Harris:

Like the kids that need the most practice are sitting down and the kid who doesn't need the most practice is the one who gets more practice because they're, yeah.

Kim Montague:

Well, and I was gonna tell you that I was actually having a conversation with one of my sons and apparently it's a thing that if you know you're gonna play this game, you just get out the first round if you feel like you're not successful and then you just get to sit there.

Pam Harris:

Oh, wow.

Kim Montague:

You just get to sit there while all the other kids...

Pam Harris:

How come I never thought of that in elementary school? Man, I just kept myself like tensed and and primed, ready to go. Ah, yeah.

Kim Montague:

So when you're choosing a computer program, or a game or an activity for students, don't choose those who are all about speed and being fast, or those who shame students who are slower, or those that are all about rote memorizing facts in isolation.

Pam Harris:

Exactly. So what should you choose? Well, so listen to the podcast next week. We try to keep these podcasts manageable, that you can listen to in your commute or when you get a moment of time. We know you guys are busy parents and teachers. So next week, in next week's podcast, we're going to give you examples of our favorite tasks, activities, and games to promote Real Mathematics and Learning the facts at the same time.

Kim Montague:

Remember to join us on MathStratChat on Facebook, Twitter, Instagram on Wednesday evenings where we explore problems with the world.

Pam Harris:

Yeah, and please share with your friends and colleagues the podcast. Give us a rating and review so that more people can find the podcast so we can spread the word to the world that Math is Figure-Out-Able. So if you're interested to learn more mathematics and you want to help yourself and your students develop as mathematicians then don't miss the Math is Figure-Out-Able podcast because Math is Figure-Out-Able.