23. Why the Butterfly Method is NOT the Best Method

Ellie 0:05

Hey, Brittany, how do you feel about butterflies? Do you like them?

Brittany 0:24

I love them. Their patterns are so beautiful and intricate. They're so delicate looking.

Ellie 0:31

I love them, too. I like to watch them flit from flower to flower, fly around the garden. They're so pretty. But as beautiful and helpful as butterflies are, do you know where they don't belong?

Brittany 0:43

Where's that?

Ellie 0:45

In math class.

Brittany 0:47

Welcome to the teaching Toolbox Podcast. I'm Brittany, and I'm here with Ellie.

Ellie 0:54

Hey there.

Brittany 0:55

And today we're going to talk about one of those popular shortcuts that some teachers use to try to help their students learn some fractions skills faster, in a fun way. And that shortcut is called the 'butterfly method.'

Ellie 1:10

Have you heard of the butterfly method, Britany? Do you remember when you first heard about it, If you did?

Brittany 1:16

I actually learned the butterfly method when I was about in fifth grade.

Ellie 1:23

You did?

Brittany 1:24

Yeah. I remember learning it in math class, when we were doing fractions. And they taught it to us as just one method that we could use to solve fractions. And I didn't really need it that much, because I was pretty good at math. And I saw that it just wasn't very helpful when the numbers got really big and huge. I preferred to do some other methods instead that kept the numbers small. But yeah, I learned it in fifth grade. How about you, Ellie?

Ellie 2:00

Wow, I had not heard of it until maybe my, like 18th year of teaching. I do remember very clearly the year that I learned about it. I was teaching sixth grade math. And we were really technically only supposed to teach fraction division. But I would always go back and review the other operations just to make sure that students remembered what they had learned in previous years and didn't end up confusing the different methods as we started with fraction division. So this particular year, we had reviewed the operations briefly. And then I had students working on some problem solving. And I had them work in groups. So it was a collaborative effort. And it required them to use all of the operations in different parts of the problems. And so for one of the problems they had to add four fractions, and this one group used the butterfly method to add two fractions. And then they were trying to add on the third. And then they were trying to add on the fourth. But as you mentioned, their numbers got so big, that they just got stuck. They had huge denominators, because of this method. And they just didn't know what to do. They had apparently learned the butterfly method the year before to add fractions. And even though they were perhaps taught multiple methods, like they were taught how to find the common denominator, this was the method they use the most. And it was the one that they remembered, and that they were told would always work. And so they were convinced that that's what they should use. And so even though the numbers were really getting big, they stuck with that method, because, you know, they didn't remember how to do anything else. So that was very eye opening for me.

Brittany 3:45

Yeah, before we get into the reasons we shouldn't use this method, let's try to explain how this method works in case our listeners haven't heard of it before, or they haven't heard it called the butterfly method. So without showing a visual, you're going to have to try to visualize as we describe this. So if you have two fractions to add, the way this works is that you multiply the denominator of one fraction with the numerator of the other and you write that product above the numerator. Then you multiply the other denominator by the numerator diagonal to it and you write that product above the numerator. Then you add those products together, that becomes the numerator of the answer. And then you multiply the two denominators together. That becomes your denominator of your answer. So for an actual problem, like 5/6 plus 3/4, we'd multiply four times five, and six times three, and we'd write the 20 and 18 above the numerators. We'd add them together to get 38. Then we'd multiply the denominators, six and four, and we'd get 24. So then our new answer would be 38/24, then we'd need to simplify that.

Ellie 5:11

Now, if you were doing it in class, then you would draw some pretty butterfly wings around those numbers that you're multiplying. And then like the make the little butterfly antennas and the little butterfly body to show which ones you're multiplying so that you have a pretty butterfly when you're done with the problem. And so it sounds pretty easy and fast for students to be able to find that answer. And it sounds like it's fun. And you might have seen this method on some really big Instagram or Tiktok accounts. I came across one not too long ago, somebody who had like a million followers, and I found that they were teaching the butterfly method. And that's pretty upsetting to me, because it's not the best way to teach students how to add or subtract fractions, because you can actually do the same thing with subtracting.

Brittany 5:59

Why is it not the best method, if it gives kids an easy way to solve the problem?

Ellie 6:05

Well, for starters, it really only works well for small fractions. So once the fractions start to get bigger, the numbers that students are dealing with get larger, and then they have trouble simplifying the fractions. Like in our example, we ended up with 38/24. If students had found a common denominator, they would have found a common denominator or the lowest common denominator of 12. And then it would have been a smaller number to simplify...takes out some of those steps. And so I feel like there are times that students who struggle with their number sense and their facts and things like that are given this method. And then they have more trouble simplifying, because that's actually their area that they need to work on. So the numbers get bigger, they have trouble adding more than two fractions. So if you have to add three fractions, or four fractions, which is what happened with my students, the numbers get so big that it's, it becomes unmanageable.

And this method just totally skips any conceptual understanding. Students don't need to have any understanding at all of what adding and subtracting fractions actually means. It completely ignores the concept of common denominators. And that's something that students really do need to know as they get into middle school and high school. So you have students coming to middle school, acting like they've never even heard of a common denominator before. And maybe they haven't, or maybe they were shown both methods, but they were allowed to use either one. And so they opted for the shortcut. So I think it's not the best method because the numbers get unmanageable when students get into higher grade levels. And it completely ignores conceptual understanding.

Brittany 7:45

Brittany 8:00

Yeah, it does seem like the butterfly method is more popular in elementary school, because it's fun. And students don't run into the same issues with it, that they do when they hit middle school. Because the fractions typically have smaller denominators in elementary school, you know, the problems are made to be easier.

Ellie

Right, right.

Brittany 9:20

I've heard from many teachers over the years that it's just easier and faster, and their kids have fun with it. So they don't feel like they need to teach adding fractions any other way.

Ellie 9:30

Yeah, that can get a little. a little bit frustrating when some teachers kind of say, well, they like it that way. And it's easy for them that way, and they can get it. So that's just what I'm going to do. But it's not great for the kids.

Brittany 9:45

So how do we teach fractions and other concepts without the shortcuts that we see promoted all over social media?

Ellie 9:54

Well, to start, if you see shortcuts and tricks out there on social media, you need to take some time to question whether students need to understand the concept to do this shortcut. Or if this trick totally cuts out any need for understanding, especially if it's a concept that you yourself, as a teacher might not be super confident about. You know, you take some time to research that a little bit and see if you can find conflicting information about the shortcut. You know, maybe somebody else is saying this is absolutely not the way to go. We know that sometimes our college courses don't always give us all the tools we need to teach math well at all the different grade levels, because sometimes our degrees.... we're not specializing in math, and we're not having the courses we need to teach all of those concepts as well as possible.

Are there other social posts or reliable books or other sources out there that contradict those shortcuts and tricks? Try not to just accept a shortcut you see, just because the social accountant has a huge following....the account holder might never have been a math teacher. They may never have thought about how shortcuts can end up making math harder for kids in the long run.

Right, absolutely. One great way to teach adding and subtracting fractions is to use manipulatives, like fraction strips or fraction circles, or get students working with number lines, so that they can see fractions as numbers. There are so many ways to make the concepts more concrete for students... more visual, so they can understand what's actually happening when they add or subtract fractions. And using visuals can really help students become more flexible thinkers when they're working with fractions. There's not just one right way to add or subtract or to combine fractions. So using the different visuals can really really help them to see that.

So if you're looking for ways to teach fraction addition and subtraction, or other fraction concepts, you can check out Ellie's free fraction training, Three Fraction Shortcuts to Avoid. We'll add the link to that training in our show notes.

We hope this episode gave you a few new ideas about shortcuts that you don't want to add to your teaching toolbox and some ideas that you do. See you next time.

Bye.