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Episode Summary:

Why do so many students struggle with fractions and how do we make math concepts stick beyond rote memorization?

This episode is for educators looking to move beyond the frustration and confusion of teaching and learning fractions. We speak with Tara Flynn and Shelley Yearley, two co-authors of the book Rethinking Fractions. 

Tune in now and learn how a deeper understanding of fractions and a focus on student ownership can make math more meaningful and engaging.

You’ll: 

• Gain insights from educators who’ve experienced both the pitfalls and rewards of teaching fractions in new and transformative ways.
• Discover practical strategies to shift from memorization to conceptual understanding, especially with unit fractions and counting strategies.
• Learn about upcoming opportunities to engage with like-minded educators and access resources that make teaching fractions approachable and effective.

Tune in to this episode of Making Math Moments That Matter to revolutionize your approach to teaching fractions and inspire deeper mathematical understanding in your students!

Resources:

• Register for the Make Math Moments Virtual Summit
• Make Math Moments Problem Based Lessons & Units

Attention District Math Leaders:

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What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? 

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Episode Summary:

Mathematics Education Experiences and Perspectives

In this episode of the Making Math Moments Matter podcast, Jon, Shelley, and Tara discussed their experiences and perspectives on mathematics education. Tara shared her confusion and frustration as a student when she was taught math using a rote memorization approach, which led to her questioning her abilities. Shelley, who retired from teaching two years ago, shared her recent experience of teaching a new grade 9 math curriculum, highlighting her enthusiasm for a student’s success. The discussion also touched on the challenges and rewards of teaching mathematics, with an emphasis on the importance of understanding and applying concepts rather than just memorizing formulas.

Math Moment and Unit Fractions Summit

Kyle, Tara, and Shelley discussed a recent math moment involving a student who struggled with fractions. Kyle emphasized the importance of allowing students to take ownership in their learning and shared his experience as a math consultant, highlighting the significance of understanding fractions through counting strategies. The group then shifted the conversation to upcoming sessions at a summit, with a focus on unit fractions. Tara and Shelley were set to present on this topic, with Tara defining unit fractions as any fraction with one as a numerator.

Understanding Fractions in Math Education

Tara, Jon, and Shelley discussed the importance of understanding fractions as a unit in math education. They acknowledged that many students and teachers might miss this concept, which can lead to difficulties in other areas of math. The team emphasized the need to shift the focus from procedures to understanding fractions as quantities, and highlighted the significance of providing opportunities for students to count by fractions to build ordinality and cardinality. They also noted that this approach could help students better comprehend whole numbers.

Enhancing Teachers’ Mathematical Understanding and Summit Plans

Tara, Shelley, and Kyle discussed the importance of helping teachers develop a better understanding of fractions and other mathematical concepts. Shelley emphasized the need for user-friendly and accessible resources that teachers could easily adopt and integrate into their busy classrooms. Kyle stressed the importance of educators learning and growing alongside their students, and Tara highlighted the role of reducing math anxiety among teachers. The team expressed their hopes for their upcoming virtual summit, where they aim to share their insights and strategies with a global audience of educators.

Discussing Research and Sharing Resources

Kyle, Shelley, and Tara discussed their work and ways for others to learn more about them. Tara and Shelley shared that they have a website for their research called the Trent math education, research, collaborative, and that people can find more about Shelley’s work on fractions learning pathways.ca. They also mentioned that they will be presenting at the makemathmoments.com/summit, which is free to attend. The session was also set to be recorded and added to the show notes for those who missed it.

FULL TRANSCRIPT

Hey there, Shelly and Tara. Welcome to the Making Math Moments That Matter podcast. We are excited to have you on. Shelly, we had you on a number of years ago, episode, think 150, which I think this episode is gonna We’re more than double 310, 310 episodes total. And we’re excited to talk with you about rethinking fractions. We’re excited to talk with you about your upcoming virtual summit session. And just to give everybody a little bit of inside info.

at OAME last year, 2023. I was in Shelley and Tara’s session and it was great as always. And I was like, yeah, we gotta have them back onto the summit this year. So welcome and fill everybody in. Tara, why don’t we start with you. Fill everybody in on your role and what’s going on in math in your world right now. Sure. So I’ve been working at Trent University in the School of Education for the last 17 years.

I did my B. Ed. there and Kathy Bruce was my math teacher in the B. Ed. program. I started doing a little work with her after graduating as a research assistant and I just grew alongside her research program. So I’ve been the director of her research program for the last many years and have had the amazing good fortune to work with Shelly for about the last 30

15 years or so. Awesome. Awesome. So yeah, that’s fantastic. Well, it’s great to have you on the show finally. And let’s flip over to Shelly. Shelly, you were on the show. So you shared where you were from, what you were up to, but I guess update the making math moments that matter community, let them know what have you been up to lately and where are you coming to us from today? Yeah. So I’m in Huntsville still. I retired

This is my third September that I’ve been retired. just over two years ago, from teaching, I’ve been working with Kathy and Tara. Since then doing some work, continuing the fractions research. And I think we’ll talk a little bit more about that after. And then just, you know, being a mother to three children and several grandchildren and

being busy with my husband and his business. So doing math in more practical ways in many ways too. Yeah, amazing, amazing. I love the Huntsville area. We traveled up there a couple of years ago during the winter. So it was pretty awesome. Let’s flip into our math moment. Tara, when I say, what’s a math moment that you remember from?

you know, a long time ago, we say math class, something that’s probably stuck with you all these years. What would you say your math moment is? I have two. Ooh, actually, one is just a flash of round grade four or five and sort of doing whatever the you know, the practice questions or whatever in the textbook were that fun. was fun. And I remember being so

confused, bewildered, frustrated because I had gotten the right answer, but I used a different operation. I don’t know. That day we were supposed to multiply. So that was wrong. How dare you use addition. Maybe even division. And I like, but, and I sort of pled my case a little bit. said, but I did get to the right answer.

And I do remember my teacher saying, well, but you didn’t do it the right way. So that’s wrong. So I remember that was a bit of a shutdown, you know, moment for sure. to shut down. Yeah. Yeah. You’re like, I’m, I’m, I’m a little kid. So, I mean, you obviously are, are the teacher knows better. So I guess I’ll just keep my mouth shut and you know, see what happens. Yeah. It sort of takes away your ownership. think in your access.

into the thinking, right? Because for sure, your thinking is wrong, even if you’re so you know, now math is this mysterious thing. Even if you have the answer, the teacher knows the way to do it the right way. And even if you can get there, if you don’t guess what’s on their mind, you are wrong. So it just becomes mysterious and totally inaccessible. And then my other one is in around grade 10, when I had

I went to an all girls Catholic high school in Kitcher, Ontario, and sister Barbara was teaching math using a series. She had overheads that she had used for a billion years. Were they yellow? Like, they have a yellow change? Yes! Just making sure. I want to make sure I have the visual correct here. You know, I’m visualizing this here. So you can picture it exactly.

Like the writing so tiny and she’s so her her math class was just a process of slapping that on going blanks through yeah, and at one point I asked if I was bewildered I was in tears because at that point I felt like wait, I thought I knew Something about math, but it’s like they’re speaking a different language in here. I have no idea what’s going on So I asked a question and she looked at me and said

Don’t be stupid. Wow. Like, yeah. Holy smoke. She’s probably no longer with us. So yeah, but like again, I’m picturing straight face. No, come on. Like, know what I mean? Yes, exactly. Exactly. I often think about my old self because I taught for 10 years, very traditional. And especially your first, you know, your first moment there where you were saying like,

that you were told it was not the right way to do it. And I think I’ve said those words to as many students over those 10 years, basically saying, you got the right answer. kids were like, because I know that every math teacher or every teacher out there who’s taught math is going, I’ve heard kids say, well, I got the right answer, so what does it matter? You’ve heard those words. Whether it was like they showed no work, and now you’re asking the show work, they’re like, well, it doesn’t matter. Or you’re trying to get their thinking, and they say those words. Or it’s like,

what happened to you where I got it, but I’m like, but that’s like, you guessed or, know, like, or, hey, tell me like the teachers are, the teachers, like, come on, you know, like there’s something else here that they’re trying to either dig or just say, Hey, this is, this is not, this is not the way I’m going to show you the way I have the knowledge here to show you the way. So, it sticks with me that, that memory for sure. Shelly, we’re going to, we’re going to tip it over to you. math moment, you know, you would have shared, you know, in back in episode one 50, but you know, what’s

What’s a math moment lately for you? Well, it’s funny that you told those two stories, Tara, because I was thinking of a story that I shared last week with you about a young boy that I was teaching. So I had been out of the classroom for 19 years and then I went back to teaching and COVID hit and new grade nine math curriculum. And I was working in the resource room.

student success room, there’s all different kinds of names for it. But I had three students doing an independent math credit because they had been so challenged in elementary for so many different reasons. And this one little person, young man, he would write IDK for everything all day long. And so finally, would- Did he declare his variables?

That’s like a dad joke. I I’m getting words. So I said to him after the first or second day, you can’t say that. Like you can say something else that says you don’t know, but you can’t say that. So it took a long time for this person to actually feel confident enough to answer questions. And I remember

We did lots of fractions work and I felt really confident about that and I had the old mathies rulers that were laminated and I gave these students those and we talked about different ways to use them. And so I’ll bet you it was three months in and I would just come back to fractions every once in a while and they were working on some questions and I had given them some fairly challenging, I think, multiplication and division.

questions involving fractions and he had the answer and I said to him, well, how did you get that? And you know, this is the IDK kit, right? And so he picks up his ruler and he points to it and on the ruler there are stacked fractions, rods that show halves, fourths and everything. And he had just used the picture on the ruler to answer the question. And I was so impressed that he had.

I that little tool that we had, you know, maybe a month ago and then use it in such a creative and appropriate way and came up with the right answer. I just remember I was probably a little too enthusiastic for him. I was really excited by the way. Yes, all the classes down the hall here. I love that. Well, you know what’s interesting about it is, you know, I’m listening to, you know, I hear Tara’s one of her moments.

And then I’m hearing this more recent moment for you. And I’m just imagining, you know, like if that experience for that child happened back in, you know, terrorist story timeline or in that, you know, that time of, this math education journey we’ve been on, I bet you that teacher wouldn’t have been excited, right? Like that student probably would have got shut down. First of all, there probably wouldn’t have been a tool there that, you know, so the student may not have been able to enter this problem at all, but then also

the fact that they used a different procedure essentially is what we typically used to be looking for all the time, would really shut that student down to go back to IDK mode. And all of a sudden now, you’re in a position where that student can take that and sure that’s not gonna be the turnaround point. It’s not the TSN turning point for our Canadian listeners. It’s going to at least show them that

You know, I’m here, I can say things and I’m gonna, my voice is gonna be heard, right? And I heard, you know, earlier, Terry, you mentioned ownership, right? Like truly allowing that student to take some ownership because along the way, clearly they hadn’t felt that. So I just wanted to, you know, highlight that because I hear that right away and I’m envisioning that process and moving a student along that has very little confidence takes a really long time.

And sometimes as educators, that can be frustrating because you you’re working, you feel like you’re working hard, but it’s like, think of how hard it is on that student to, you know, get those quick wins. So good on you. And thanks for sharing that, that, math moment. That’s more recent and how fitting that that recent math moment involves fractions because friends are going to be joining us. And by the way, I said it back in one 50, your work and you know, obviously I’m going to throw Kathy in there as well.

around the unit fraction, around all of the different things using counting and additive and multiplicative thinking in the fractions world, really a huge, huge game changer for me as a math consultant at the time and really understanding how math worked specifically around fractions that we could take things that a student like you’re describing could use counting as a strategy and still be working with fractions, which I think most people, I,

you just like John, very traditional in my early goings, I would have never guessed that a student that was struggling would be able to actually think in fractional terms. So huge Bravo, but I want to flip it to you and we want to give the listeners a bit of a preview on your session at the summit coming up in November. It’s called currently, we always give people the opportunity to adjust titles between now and then, but right now it’s called a focus on unit fractions.

to change your students understanding, help people understand like what is it that you’re going to be exploring? What does that look like and sound like for those people who are like unit fractions? Maybe they’ve maybe ever been introduced to that idea or that concept in their journey. Do you want me to start, Shelly? Yeah, let’s start. You know what? We’ll start. go back and forth. So we’ll start here with Tara and then we’ll flip over to Shelly as well. We’re pretty good at that. You are. are.

So unit fraction is any fraction with one as a numerator. So that is your basic definition. any fraction with one, it could be one half, it could be 1,012. I like that one. That was a tough one to work with, by the way. I’m not going to say the denominator. It was a tough one to say.

But you’ve mentioned, so this was a, it was a game changer for sure, this entry into thinking about unit fractions for us, for Shelly and Kathy and myself when we were doing the research. And as we continue to work with this idea, so first, I mean, I think we can all as math educators sort of acknowledge that

the importance of the unit, the importance of focusing on the unit with students. The unit is often something students might miss and can really throw off their reasoning or their working through of something. It’s something we do a lot of work around in many, many other contexts, not just measurement, most obviously maybe in measurement.

we also know in teachers too, right? Like I, I never, and this is the, think what Kyle was getting at about like how impactful it was because it like as a teacher and I’m high school teacher, you know, and I never really thought of fractions in terms of a unit, you know, like accounting unit. It’s like, it’s, it’s, not like one, one half. It’s not two. One, like it’s, it was just one half and then another half and two halves and three halves. You know what mean? Like it was, it wasn’t.

It wasn’t clear that that was a thing that we could do or, and that’s what math tends to be for us teachers too. It’s like, am I allowed to do that? You know, and, and, I think it is, it is mind blowing. It’s like kids don’t, kids are going to miss it. But I mean, like, I think there’s a lot of teachers out there that going to miss it too. Yeah, it’s, it is a new piece of, if not learning, attention, you know, a shift in your focus and your attention and

You know, one of the things when we dug into, we’ve written all kinds of literature reviews, and we’ve dug into the research out there on fractions learning, a lot of it is in the psychology world. But also, your lived experience, I’m sure, with students and fractions is they don’t understand fractions as a quantity.

they don’t understand fractions as a number and whether that’s because we have tended as was for sure the case in Sister Barbara’s class and other classes in my schooling. The early focus on procedures and sometimes that focus is because I know now my teachers then probably didn’t understand why we were doing what

we’re doing. So it was just the rule, you follow the procedure. And that essentially, you know, strips the meaning from it from, from working with fractions as quantities that you’re doing something to you enlarging them, you’re shrinking them, you’re much like you would when you’re performing operations with whole numbers. When we talk about fractions counting, and when we started to really explore that,

more and more in the research, you know, it just sort of dawned on us that when really young children at home or in school are learning about numbers, what are they doing? They’re learning to count. They’re counting and counting and counting. We don’t limit those experiences. We provide them in zillion different contexts. We sing our counting numbers. We read about them. We count steps. We count the trees. We count the cracks in the sidewalk.

And we never had given ourselves or students the chance to count by fractions. And through that counting, we build ordinality, we build cardinality, and we build that sense that a fraction is a quantity. It’s not just this weird symbol with one number, a line and another number. It’s a something. And we can name what that something is, we could put it together, we could take it apart. And we start

to enter into that through counting just like we do with wall numbers. Right, I love it. Go ahead there, Shelley. I could tell you’re about to add in, I was just going to say the other part to our research that I think is so exciting, and this sort of goes back to what I was trying to get at with my story as well, is that it’s small instructional moves that don’t require a whole bunch of prep or time.

But when teachers know more, they can do better. And so when teachers take these small strategies like counting, like using powerful representations like number lines, then they’ll see their students being more empowered to take risks in their thinking and to approach the questions from a more intuitive place rather than what’s the rule I need to know. So I feel like

Like when we meet, we just met with a group of teachers last week. And one of the things we heard was that they felt that the instructional strategies were easy to adopt and that they saw a really big impact on their students learning and also their students confidence around fractions. So I think that to me is what’s exciting about this is we’ve spent a lot of time doing

a lot of heavy lifting around the research end of things, but trying to make it so that teachers can take it and go because they are busy and they don’t have a lot of time. And also there are a lot of competing demands on their classroom practice. And so we wanted to make it user friendly for teachers. I must say as well, like the idea of easy to adopt, I think

is really important. It starts, in my opinion, with really small teacher moves, right? But, you know, sometimes as educators, we sort of want to solve like really big problems, like really fast, and that can be discouraging, right? So I think what I’m hearing you say, and I think I’m maybe extrapolating a little bit is, you know, for those who are listening, or maybe early in this journey is that you also have to give yourself as an educator grace, because you have to learn this progression, right? This continuum.

if you weren’t taught this way, which I’m going to argue that the vast majority of us did not, you know, I have a funny feeling Tara, that memory, like it wasn’t during a lesson where you were counting unit fractions where, you know, the wheels fell off. was, know, so there’s a lot of work to be done. And I must say, for those who are listening, those who utilize our make math moments, problem-based units that involve fractions, whether it’s counting fractions, adding, multiplying, or dividing actually

actually build in these concepts that we’ve learned along the way. So again, credit to you and your team for helping us to understand, but we can’t go to dividing fractions, utilizing this approach without kind of doing the journey, right? Counting by unit fractions and understanding, you know, how this works, because we have to become fluent and flexible, you know, before we’re going to feel confident to be able to allow our students to kind of come on that journey with us as well. So

I really like that your session is a great, the way I read it. And when I look at the description, it sounds like it’s going to be a great, I don’t want to say introduction for those who might already be on this journey, but it’s going to be accessible. Knowing what I know about the work that you both do and also having been a part of your presentations in the past. So my wonder for you would be, you know, and I’ll start this time with, with Shelley. I’m wondering like when,

someone goes to your session and then they walk away, what would you say is something that you’re hoping that they’ll take with them? Be it an idea, maybe it’s a feeling, maybe it’s an action. What are you hoping when you deliver this session at our upcoming virtual summit? So first and foremost, always, always going for increased efficacy. We really want teachers to feel more confidence around going into their classroom and, and

working with their students and learning alongside their students. But also, you know, we’ll be doing activities that they can practice with us in a safe environment and then take back to their classroom, like the counting, but also some things around representations. I think I want, would want people to walk away with, as Shelly said, more efficacy, but even maybe before that or underneath that.

Less fear. Right. Less fear. I that. About fractions because we do, we do really think, I know that math anxiety is real, but we really, what our work has shown us anecdotally, I guess, is that there is a particular math anxiety around fraction. think very specific. teachers and students who.

love math, are comfortable with math, see themselves as great, you know, as mathematicians have that reaction when you say you’re doing fraction. God. Maybe Taryn I’ve had that reaction sometimes too. You know what? I think it’s important for us to be vulnerable. We talk about being vulnerable on, on our show a lot and that I know myself when I go into a land, in mathematics that

I know procedurally and I feel like it’s like I’ve, you know, sort of felt that I’m supposed to know as a former high school math teacher, like I’m supposed to know this, right? Cause I’m the teacher and you get put into that space where you don’t know, you can feel it, you know, and you, you, your tone changes the way you interact with the people around you. And this is what makes it so important for us as educators to engage in the mathematics with our colleagues to get past that feeling because

I’ll tell you, it still triggers. When John and I and Yvette on our team, when we do math, sometimes we get into this space where it’s like, I can’t control it. You just, boom, it just hits you. And you have to remind yourself that, wait a second, you’re doing something here new and you don’t have to know the answer yet. And I think that’s something that if we can at least notice and name it, then we can be better and do better for ourselves so that we can do better.

for our students in our classrooms. So I really appreciate those takeaways that you have for those who are going to join this summit. So I hope for those listening, you’re going, okay, I know there’s educators out there. We work with them all the time. We chat with them all the time. Math mentoring moment episodes where, you know what? You’re probably going, hey, this summit’s over a weekend. Like, do I really wanna feel this way? Right? And I’m gonna encourage people to do it, right? To try to prepare yourself ahead of time because here’s the crazy part is that

your session is going to be extremely accessible, but just want to make sure people coming into it don’t put too much pressure on themselves to think that they need to know all the answers right away, or that they need to fully, we’ll call it fully conceptualize it in one go, because we know that’s not really how we learn. So I want to thank both of you for coming on the show here. And even more, I want to thank you ahead of time for joining us in this coming virtual summit.

John and I get so much joy from being able to put this on. So educators from around the world, we have over 10,000 educators typically each year that join us. Today we’ve got a lofty goal for over 20,000 educators to join us from all over the world. So spread the word, those who are listening. And of course, both Shelley and Tara here spread the word to your network. And we’re hoping that we can spread some great math messages, including your session, which will be on

the unit fraction. thank you so much for joining us, my friends. Where can people find you if they’re curious and they’re like, I don’t want to wait for the summit. I want to learn more. Let’s start with Tara. Where can they find more about you? You can find more about me on LinkedIn. I also have to remember what is my Twitter handle.

Well, it’s nothing now because I think it’s not even like, yeah, my X handle. I don’t know if anyone’s still very active on there. I’m not, but I think I’m at Teracy Flynn. And we also have Kathy and I have a website for our research called the Trent Math Education Research Collaborative or at tmerce.ca

. And Shelly, where can people find about you? I think probably the best place to go is the fractions learningpathways.ca and they can see more about the research. There are tons of tasks on there. yeah, information about what we’ve done and supports to for professional learning facilitators that they can take and use. So that’s probably, you know,

Awesome. We’ll put all that in the show notes. if you are listening right now and you are looking to register for this session, head on over to makemathmoments.com forward slash summit, get yourself registered and you’ll be seeing Shelly and Tara live that weekend all for free. thanks again, Tara. Thanks again, Shelly. And we’ll talk soon. Thanks so much. It’s been lovely. a great day. See you soon. Take care. Bye-bye. Take care.

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