73. Ellie’s Passion for Fractions Taught Right

Brittany 0:00

Hello, Ellie.

Ellie 0:20

Hello there.

Brittany 0:22

I have a question for you. When you were in the middle grades and learning fractions, did you like them as a kid?

Ellie 0:28

I honestly can't remember, but if I don't have a strong memory of loving or hating them, I guess they were just okay for me.

Brittany 0:37

Well, welcome to the Teaching Toolbox Podcast today, Ellie.

Ellie 0:43

Oh, hello,

Brittany 0:44

Ellie 1:07

I'm sure there are many reasons, but I don't think every teacher who's teaching math necessarily wanted to be a math teacher, especially in the upper elementary grades. And what I've heard from many teachers in upper elementary and early middle school, like fourth to sixth grades, is that they either really dislike teaching math or they don't feel prepared to teach math in general. In many cases, teachers were never specifically taught how to teach adding, subtracting, multiplying, and dividing fractions in ways that students really understand, and so they just do their best with the algorithms and the materials they've been given in order to get through the unit and then move on. And these days, they might pick up incorrect methods or shortcuts that they've seen online or on social media.

Brittany 1:55

Do you think more professional development or classes specifically on fractions would help the instruction. Or do you think it's more a general scare of math that's the problem?

Ellie 2:06

I think it's different for every teacher. There might be teachers who like math in general but really dislike fractions. And I know some teachers just hate fraction operations, because it seems like no matter how many times they show their kids the procedures for adding, subtracting, multiplying, and dividing, the kids don't get it. Or they confuse the processes like, when do you need to find common denominators and when don't you? And just as a side note, you can use common denominators for all the operations if you want to. It might make it more challenging for multiplications, but you can use it. You know, so they ask things like that, and then when do you flip the fraction, and which one do you flip? And that kind of thing.

Brittany 2:50

You can use common denominators for every type of problem?

Ellie 2:56

Yep!

Brittany 2:57

Whoa. Mind blown. Do you think teaching of fractions at younger and younger grades, like how they're doing it nowadays, will help with fraction understanding and fraction operations by both students and teachers?

Ellie 3:13

I think it's hard to tell. I think a lot of it depends on the developmental readiness of the students, and we know that can certainly be different for students who are the same age. There are definitely things that seem hard to understand when you're one age, but then a few years later, it seems so clear. And then it depends on how the concepts are taught, how comfortable the teachers are with using different methods or with adjusting their methods according to the readiness of their students. Like I know when I was taking geometry in high school, I had such a hard time with that. It's not fractions, but different math concepts. I just I had so much trouble with it. And then what like two years later, when I took it in college, it was completely different, same material, and all of a sudden it just made complete sense to me.

Brittany 3:58

Yeah, I had the exact same thing happen. So where did your love for fractions come along? I know most people don't enjoy them, and I actually find them kind of fun and quirky, but you really enjoy learning about and using fractions. So how did that come to be?

Ellie 4:14

I think I became much more interested in using fractions one year that I had a student teacher, when I was teaching sixth grade. She was doing a fraction division lesson that her supervisor was observing, and at the end of the lesson, the supervisor asked me if I taught fraction division using common denominators. Up until that point, I didn't even know you could do that. So she sent me information from a textbook about how that works and why it works, and that hooked me a bit more. From that point on, I taught my sixth graders both ways to divide fractions, both multiplying by the reciprocal and using the common denominators. And then I let them decide which made more sense to them, and they could use whichever method they wanted. And then another big moment for me was when students started coming to sixth grade using the butterfly method to add fractions. And there was one particular experience with that that really started getting me concerned about the shortcuts teachers were teaching students. Because even though they might have taught the traditional algorithm and maybe used models and did all of that, the students remembered the butterfly method the best and ended up relying on it since supposedly, supposedly it was faster and easier. I do have a blog post that I wrote about that one and why we should not be using that method, but that was another thing that really hooked me into fractions.

Brittany 5:36

When teaching fractions, teachers often love to use shortcuts like the MAD wheel for converting mixed numbers to improper fractions. I actually had never heard it called the MAD wheel before. We just always used to say multiply, add, and keep the denominator. But duh, MAD wheel makes perfect sense. And then there's everyone's favorite: copy, dot, flip for division. But what you and I have learned is that students have to understand what is actually happening behind the scenes to truly understand the fractions and what they're dealing with.

Ellie 6:16

Right. With the multiply add and denominator stays the same. I would often have students multiply and add the wrong numbers. They would just do it in the wrong order. So instead of converting three and two fifths to seventeen fifths, they might end up getting eleven fifths and not have any idea that that wasn't reasonable. So if students can explore with fraction strips or drawings a little bit, they can visually see how three and two fifths is equal to seventeen fifths. Like they can see it. They can count it up. If students use manipulatives or drawings to convert before they learn that multiply add rule, they would likely come up with that rule themselves, but in that case, they would understand what it meant based on the representations they used. So they do it a couple times, and then they say, Oh, wow, I could actually do this instead. And then it's not just a rule somebody told them. When they get to middle school, as middle school teachers, we often assume that they truly understand how to convert between those number forms. But then if we see they're multiplying and adding the numbers in the wrong order we should know they don't understand the concept, and they need some representations to model what is happening. And I don't think it takes a lot of time for them to do that with some models, you know. And then the light bulb goes on, as we said, and it's like, oh, oh, this is what this actually means. And especially if they do it once they hit middle school, as I just said, developmentally, they're probably better able to understand it than they were when they learned the rule about it, if that makes sense. And then I think the same applies to the actual different operations. We can use fraction strips, number lines, other manipulatives, to model what is actually happening when we add, subtract, multiply, or divide fractions.

Brittany 8:03

So you actually started a professional development program to help teachers where the focus is specifically on teaching fractions. What made you want to cover those pesky troublemakers and also narrow yourself down so much?

Ellie 8:20

Well, fraction operations are one of the topics you see so often in math teacher groups, and the issues are the same year after year. My students don't get fractions. They should already know how to add and subtract fractions when they come to me, but they can't even find common denominators. How do you get students to remember which fraction to flip? Comments like that, and many times the responses in the groups are to just give the students calculators or teach them a song or a chant or show them the shortcuts. And honestly, having had to undo some of the shortcuts in sixth grade, like the butterfly method, was always frustrating to me, and I've never really held the belief that we should just give out calculators. I know there are arguments for giving calculators, and I'm not against calculators once students understand the concepts, but when they don't understand what's happening in a word problem, when they don't know if the word problem is asking them to add or subtract or multiply or divide, then the calculator is useless. They don't know what to actually enter, or they don't know which number to put into the calculator first. So to me, that's not really a solution to that problem. So knowing these struggles, and knowing that teachers continue to struggle year after year with class after class, I thought it would be a good idea to offer teachers some professional development so they can see ways to teach fraction operations conceptually, rather than just with procedures, and also to give them ideas and resources to easily work fractions and fraction operation concepts into lessons and into daily routines. Knowing some of the methods that I incorporated into my own sixth grade classroom really helped my students, you know I know things that I did were really, really helpful to them, and I wanted to share that with other teachers and save them the time of searching all over the internet by having all of those methods and resources in one place for them.

Well, I took your course, and it was fascinating, and it's so helpful. The visuals are great. You have over 30 lessons and videos with even more discussions and notes, activities, etc, in the program to help teachers through the different components of fractions, from improper fractions to dividing fractions with mixed numbers. Did all that material come easily to you since you have a passion for fractions? Or was it hard to think about like, what else you needed? And like, oh, yeah, I need to cover that too.

It was challenging, for sure. I started with operations, but then I decided I should include some of the basics, like improper fractions to mix numbers, because I know that middle schoolers still don't understand some of the basics, and while we don't have time to go back and re teach everything that students don't remember, I figured there could be some ways to work those concepts into the fraction operations instruction. I also ended up including the ladder method and several ways to use that because it was really helpful for my students to see how numbers are related, and it can be used to find GCF, LCM, and to simplify fractions. Several teachers who have used the training have been very excited about the ladder method because they had not seen it before, and their students ended up doing really well with it.

Yeah just as an aside, I learned the cake method which moves upward, and I was pretty dedicated, but after seeing your ladder method, which moves down, and all you can glean from it, I'm pretty sold. Do you get pushback from many cake lovers on the ladder method lesson?

I have not people have told me that they call it the cake method, but I've never actually heard them say that it went upward versus downward, so they haven't really pushed back on that one.

I also wanted to say how much I loved all the videos in your course where the viewer can really see what you're explaining while you're explaining it. It's very clear and concise but thorough and shows at least one example of every type of problem that you might face as a teacher.

Oh thank you so much. I really I tried to hit on all the different things that might come up, just knowing from all the years in the classroom that there are so many different types of problems that pop up for us.

Well you did a great job.

Thank you.

You also provide notes and doodle notes. Sometimes there's foldables or activities or other ways for students to learn. Your famous math dates are explained in there. It's really just very comprehensive, and just provide such a wealth and a variety of information.

Thank you.

If you teach math and struggle with fractions, we hope you've learned some tools to put in your teaching toolbox. Or check out Ellie's program mastering fraction operations, from foundations to operations, and check out all the videos, notes, activities, games and more that she offers to help you teach fractions in a conceptual way that kids will really understand.

And if you enjoyed this episode and know someone who doesn't love math or fractions, pass this episode or the program along to them. It is listed in the show notes. Thank you. We'll talk with you next time

Bye.