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Episode Summary:

Are you struggling to help your students truly understand multiplication, beyond just memorizing math facts?

In this episode Brittany Hege from Mix and Math is here to share insights into how you can strengthen students’ multiplication skills. This episode dives deep into practical strategies for teaching multiplication in grades 3-6 using models that connect concrete and abstract thinking. Brittany will share the details of her upcoming Make Math Moments Summit session on multiplication. 

Whether you’re dealing with students’ struggles or aiming to strengthen your own approach, this discussion offers insights into creating “light bulb moments” in math.

Resources:

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

Attention District Math Leaders:

How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge?  

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

Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. 

Book a short conversation with our team now. 

Episode Summary:

Brittany, the creator of Mix and Math, shared her background and passion for helping teachers understand mathematical concepts. The team discussed the universality of mathematical algorithms, the value of multiplication for different grade levels, and the importance of using mathematical models to develop students’ understanding. They also addressed concerns about students not knowing their math facts and emphasized the foundational nature of multiplication and its potential for application in higher education.

Summary

Brittany’s Upcoming Virtual Summit Session Discussion

Jon, Brittany, and Kyle gathered to discuss Brittany’s upcoming virtual summit session. Brittany, the creator of Mix and Math, shared her background as a teacher, interventionist, and coach, and her passion for helping teachers have “light bulb moments.” She is based in North Carolina and has been a regular participant in the group’s digital forums. The team expressed their excitement for her to share a preview of her upcoming summit session.

Brittany and Jon’s Math Memories and Experiences

Kyle asked Brittany and Jon to share their memories and experiences with mathematics. Brittany shared that she had a difficult time understanding math in elementary school, particularly the algorithms. However, her experience changed when she started teaching math herself. She realized she didn’t fully understand the concepts she was teaching and spent a year learning and understanding the math she was teaching. This experience led her to develop a passion for mathematics and eventually become a math teacher. Jon also shared his experiences as a high school math teacher, admitting that he often felt unsure about his understanding of math despite teaching it. Brittany then explained that her early math education was vastly different from what she experienced in the US, with teachers from various countries teaching her in a French immersion program.

Discussing Mathematical Algorithms and Universality

Brittany, Kyle, and Jon discussed the differences and universality of mathematical algorithms. Brittany shared her experience of using a unique algorithm that her teachers didn’t understand, which led to a discussion about the various approaches to math. Kyle emphasized that while there is a standard algorithm in the US and Canada, there are many other procedures used globally. He highlighted the importance of understanding the conceptual aspects of math to appreciate the universality of the subject. Jon related this to the current situation of parents trying to teach their children at home, using different methods and models. The conversation then shifted to Brittany’s upcoming session on multiplication, with 

Kyle expressing his excitement about her approach.

Discussing Multiplication’s Value for Different Grade Levels

Kyle, Brittany, and Jon discussed the value of multiplication for different grade levels. Brittany emphasized that while 3rd through 6th grade teachers would gain the most value, middle and second grade teachers could also benefit from understanding the foundations and future connections of the concepts. Jon highlighted the importance of understanding the strategies and models used at different grade levels. They also discussed addressing concerns about students not knowing their math facts, with Brittany assuring that students can still learn grade-level content and build fluency simultaneously. The group agreed on the foundational nature of multiplication and its potential for application in higher education.

Using Mathematical Models Effectively in Teaching

Brittany, Jon, and Kyle discussed the use and misuse of mathematical models, specifically the area model, in teaching. Brittany emphasized the importance of using these models to develop students’ understanding, rather than just teaching them as algorithms. She suggested that teachers should encourage students to decompose numbers in ways that make sense to them, and to use concrete representations to help students grasp abstract concepts. Kyle agreed, adding that teachers should ask students how they want to decompose numbers, and show that students’ thinking is the basis for the model. Brittany concluded the session by expressing her hope that teachers would leave feeling inspired and curious about other concepts they teach.

FULL TRANSCRIPT

Jon Orr: Hey there, Britney. Welcome to the Making Mouth Moments That Matter podcast. We were excited to talk with you and and to dig in to your virtual summit session. That’s coming up. But before we get to all that, you know, give her give our listeners a kind of a snippet where it coming from, you know, what are you doing a math world these days?

Brittany Hege: Yeah. Well, first off, thank you so much for having me. It is such an honor to be here since I listen to your podcast. So it’s a treat to get to talk to y’all. But my name is Brittney Hege, and I am the creator behind Mixon and Math. I was a teacher. I did some work as an interventionist and a coach, and then I just fell in love with creating light bulb moments for teachers.

And I do it online and in person at conferences or doing in-person professional development. But yeah, I’m here in North Carolina. Sunny North Carolina, and it’s a treat to get to talk math with thousands of teachers across the world.

Kyle: That is awesome. Thank you for taking the time. The last time we had seen you in the flesh. John I’m trying to picture was that and CTAM last year where huh?

Jon Orr: Yeah, it was a year ago was a year.

Kyle: Yeah, it was very, very cool to see you in the concrete form because we usually see you in the digital form online. So thank you for taking some time to join us. And we’re really excited to not only chat with you here today, but also to give you an opportunity to kind of give a glimpse into that summit session that’s coming up.

So we’re super excited for that. But before we do, like we do on every episode with all of our guests, we like to put it to you and get you to think back to that math moment that sort of stuck with you throughout the years. When we say math, mathematics, math, class. What memory pops into your mind and do us a favor to let us know how it’s affected you.

Brittany Hege: Yeah. So funny enough, I knew y’all would ask this, and I have a terrible memory. Like, I truly do not have many memories of learning math, either positive or negative. It’s so expensive. I’m thinking through this and I was thinking back to so in elementary I went to an international school in Indiana, and so I was taught by teachers.

They were all in from all over the place Quebec, Zimbabwe, France, Belgium. In the way that I was taught, math was so different then when I went to like the public schools in Indiana, and I just remember having to like re learn all of these algorithms and I didn’t really understand why and I guess I was a good enough student to do it.

I relearned the algorithms. I don’t think I ever felt like I never understood math until I started teaching math. And this actually, I think, is probably the moment that was has shaped my career. My first year teaching, fifth grade math. I remember standing at the front of the classroom and we came across a math problem that was like or a multiplication fact is like 12 times seven and I remember standing there, I was like, All right, what’s 12, ten, seven?

And I remember looking to the student who I knew would likely know it, as I like, secretly pulled out my phone and was calculating it. And I was like, Oh, like that was like the first moment I realized, like, I don’t understand math. And so I spent that entire first year really learning the math that I was teaching. And it is when I fell in love with math. And it is why I do what I do today.

Jon Orr: Amazing, amazing. And, and I’m super I’m super curious about that school and like, what were you were doing before you had to like re re reshuffle and kind of like adapt to the way things were being done in the public schools. But, you know, like, I want to I want to hear that. But I also I also, you know, I guess identify with your, you know, your memory of standing in front and not really understanding math.

And, you know, I’m a high school math teacher, and I felt like that a lot of the times, too, even though it’s like I felt like I knew math, but it was like when I really didn’t really know the math. I knew the the one way and that was the algorithm way. And if you you challenged me on that, I probably didn’t have a great thing.

I just knew that I really like the algorithm stuff, and that’s probably why I went into it being a math teacher. But but fill me in. Give me give me a little snapshot of what was happening at that school before you went into the public system.

Brittany Hege: Yeah. So it was just so all of our teachers were from those countries. So we I was in a French immersion program in Indiana and it was just I don’t remember learning math, but I know that when I came out of that school, like the ways the algorithms looked different, like the way you set up long division was different than the way that we do long division in the US and the way even like regrouping for subtraction, they do that differently.

So rather than like crossing out and then, you know, regrouping the numbers they kind of almost use, I didn’t understand it at the time. They almost use like a like subtraction as distance. So you would like write a one on the bottom number and then a one at the top. It’s really fascinating, but the algorithms are just different and my teachers had no idea what I was doing and they were like, No, you need to set up a division algorithm this way.

I need you to do the subtraction algorithm this way. And I didn’t really understand why when I was getting the right answers.

Kyle: Right? Right. There’s so many different like approaches, right? Just like anything in life, like you could, you know, I could cook tonight’s dinner in a different series of steps and still come out with a very similar outcome. And the same is true with a lot of math, you know, formulas that we use. There’s not just one procedure, but there is an accepted procedure, right?

When we say the standard algorithm for math, what we’re really saying is the American algorithm for math. Like, it’s not like standard everywhere. It’s like French is how we do it here. Right. And guess what? Canadians do it, too, you know, very similar. So that’s a really interesting math moment. We haven’t had one quite like that, but I think it’s worth everyone at home right now sort of reflecting on and thinking about this and going like, imagine a world where if we were to like math is supposed to be the universal language, right where it does, it doesn’t have borders.

But yet if you get teleported into a different part of the world and they do something very differently from a procedural standpoint, that you’re now talking almost a different language that really makes you think, Hmm. This is where conceptualizing the mathematics comes in. Such, you know, it comes in in handy for you to be able to kind of go and go, wait a second.

If I’m not making sense of this algorithm, if I back up and I go to the like the conceptual pieces and I go, why is that working? How does that work? I can now sort of go, okay, I now trust that the way that they’re doing it is actually going to come out with a very similar outcome, hopefully the same outcome as the way maybe I have been growing up doing it.So I think that’s a really interesting sort of sort of memory to share.

Jon Orr: Well, I think what you’re describing, Kyle, is what all parents are going through right now, right in in work is coming home. If you are trying to, you know, teaching in a way where using models, manipulative strategies in having your kids explore that in, in, in make sure that they feel comfortable in that fluid, you know, flexibility and fluency.

And they’re going home and trying to do that at home. And parents are like, this is not math, you know, like this is a different language.

Kyle: This isn’t multiple.

Jon Orr: Of a sudden we’re in a different country, you know, learning something else, like it’s completely foreign to them. And this is why everyone saying it’s new math, you know, and it’s not really new math. It’s just we’re representing it differently. But it’s is this is what parents are going through. Brittany, let’s let’s jump in, having talked about multiplication.

Let’s get let’s get into it, because I know your session for the summit is going to be on multiplication of poll numbers, fractions, decimals. Tell us, you know, tell us like what what are you going to get into? Like, tell us what what is like that? What’s the pebble that’s rattling around in a teacher’s shoe right now? Where, you know, attending your session is going to be like, pluck that thing out of there and they’re gonna be like, Man, I’m so glad I went.

Brittany Hege: Yeah. So we think that kind of like my inspiration for this session was the fact that a lot of times we can feel like when we start teaching a concept that we are teaching blank slates, like students come in and we feel like we’re starting from square one and we maybe I’m going speak for every teacher, but I can speak for myself.

In my previous experience, maybe even some of the teachers that I work with when we don’t really understand the concept ourselves, we don’t recognize that students have so much understanding that they bring to the table that allows them to be successful with the new concept that they’re learning, like we just don’t recognize. And so we are intentional to connect back to.

Oh what have you learned in previous grades that really sets you up for success to understand this concept? And so really my session is going through that progression of multiplication from third grade all the way through sixth grade and how what they learned in third grade really helps them multiply whole members fractions and decimals all the way through sixth grade and how we can use different representations to show students that, look, this is the same thinking that you were doing last year. It’s just maybe applied in a different way. So that’s really kind of the the basis of my session.

Kyle: I love that. I love that and that it really, you know, sort of rubber stamps this idea that, you know, if we want to teach students and meet them where they are, we have to be able to recognize what they’re bringing with them to the table. And maybe they aren’t bringing an algorithm memorized to the table. That’s where I think that blank slate idea comes from.

Right. As kids forget these procedures because they they’re not using them, you know, they haven’t used them in their daily lives in quite some time. And then they show up in our classrooms and we think, oh, shoot, we got to start all over. However, if we’re building on the same, you know, models, representations, using strategies, and we’re helping students to see that all we’re doing is just shifting, you know, the quantities that we’re working with, right?

Be it whole numbers, fractions, decimals, percentages, you can actually apply the same thinking without it just being a memorized procedure. So I’m really excited about that. I would say, you know, when you’re when you’re talking to this audience, I’m wondering who are you hoping will show up at this session, do you think is it only those 3 to 6 teachers or do you feel like there might be some value in there for some teachers outside of that grade band?

Brittany Hege: Yeah, I think obviously third through sixth grade teachers are to get the most value in it is they’re currently working with those concepts that middle school teachers. I think it’s important for them to recognize like what foundations their students should be coming in with. And if they do have some unfinished learning, then they have that perspective from elementary school that they can use to kind of support their students and I think also second grade teachers to see, okay, the work that I’m doing in second grade, where is it leading to?

Where is it connecting? So I think kind of on the fringes of that third through sixth grade, mark might really get some some benefit, some value from it. But really that third three sexes, the sweet spot.

Jon Orr: Yeah. Yeah. And I think I think I always I’m always a big fan of kind of stretching in opposite directions to really understand, you know, where students are coming from, where the students are going, what are the things that what are the strategies and the models are using down there or up here or side by side? We want to make sure that alignment is happening.

So so, you know, I would say, you know, beyond those grade levels, super important to also, you know, attend and kind of learn from this session. When I think about multiplication, I, I hear the words all the time. I don’t know about you guys, but I always hear like, what do you do when students don’t know their math backs?

You know, like what? Like when you hear that phrase as a teacher, like what? What are you like if a parent parent saying like, kids just don’t know their math facts lately or another teacher is saying that at the staff room or the staff team, what are you telling people these days? Like how do you address that concern?

Because I know your session is going to address that because that’s just the nature of of what you do in your sessions. But like, what do you how are you addressing that like lately right now when someone asks you that.

Brittany Hege: I think that we put a math. Facts are important, but I also think we put maybe an overemphasis on if they don’t know their math facts, they’re doomed. It’s like we can still do work to build fluency and they can still learn grade level content. And so in thinking about just even upper elementary where they’re supposed to be, a lot of teachers will say, Well, because they don’t know their multiplication facts, there’s absolutely no way we can talk about multiplying multi digit numbers.

And that’s just not the case. Right. Students still need to understand partial products. They still need to have exposure and experience with the area model. And there are a lot of things that we can do to support students as they’re still working and building that fluency, their supports that we can put in place to allow them to still work on grade level content while they are also developing fluency.

So I think it’s one of those things where they don’t know their math backs. We can work on that and they still have the ability to learn grade level content.

Kyle: I love it. I love it now, you know, being I think all three of us here are big fans of multiplication in terms of how powerful it can be to not only I mean month multiplication being so foundational, but also with we like to call it, you know, it has legs, right? Like we can take a lot of these strategies and stretch them all the way up and we use it in algebra and all of the wonderful things that we can do in high school with them.

What would you say is maybe a misstep that we that you maybe commonly see that we as educators take when we start to plan and teach multiplication?

Brittany Hege: I think maybe one of the biggest ones is and maybe this isn’t maybe it’s not the biggest one, but it’s the one that I think is just the most interesting to me is that we can take things that are models that are really strong models and really develop students understanding and procedural lines them. So like the area model for example I think is a very powerful model.

It’s one that extends all the way through high school. I mean, I’ve heard high school teachers, I’m not a high school teacher, but y’all are the high school experts. I believe, multiplying like polynomials. Is that what it is? Y’all use that?

Kyle: Yes, yes, yes. 100%. We do bonus for using the word polynomial, by the way. Happens. Okay. My favorite.

Brittany Hege: I was going to say I feel very smart right now, but I do not have high school experience. And but I’ll hear from high school teachers will be like, thank you so much for using this model in an elementary. But what I’ve learned is that a lot of times we will procedural is it like we will tell students yeah okay, we’re going to multiply a three digit number by two digit number.

So you need to draw two lines this way and one line this way. And it’s not getting at the heart of why we use an area.

Kyle: Why two lines like why? Why are we doing two, just.

Jon Orr: Teaching them another.

Kyle: Algorithm unjustly.

Brittany Hege: And I think even.

Kyle: Guilty as charged in my early going, by the way. For sure.

Brittany Hege: Yes. Yeah. And I’m a huge fan of math manipulatives and I think we can do the exact same thing in procedural as the use of math manipulatives. So I think it’s one of those things where I like to have teacher first off, recognize that a student can decompose the numbers in any way that makes sense to them. So it may not be by place value initially and that’s totally okay.

And so really just making sure that we’re using these tools that are meant for good in a way that develops understanding and not turning it into another thing to just use.

Jon Orr: So what do you what are you sharing with with teachers to say like instead of going like so there’s a teacher listening right now. I’m going like, oh my gosh, I’m doing that with the area model. When I thought I was doing, you know, I was doing more deeper learning with my students modification than the teacher next door.

And they’re just teaching the algorithm, but I’m just showing kids how to use the area model. And now I’m realizing there’s a that’s not any different because I’m just showing them how to draw a picture and then fill it out. Like what? What is your go to move to get a student to kind of like understand the like why the area model is the is a great model to use and not have it just be something that they have to now memorize.

Brittany Hege: Yeah. So first off, I just want to acknowledge like there’s no there’s no place for shame in math education. So if you are the teacher who’s like, oh my gosh, I’ve been using it in a really procedural way, this is just an opportunity for you to learn and grow instantly. Was that teacher so there’s, there’s no need to feel any shame about that.

But as far as I think how to use it in a way that develops understanding, I think it’s making those connections to the more concrete representations. So starting with whether it is good paper is a powerful tool because you see every single unit and talking about, okay, you’re modeling this multiplication fact on grid paper or even base ten blocks.

How does that connect to the work that you are doing in the area model? So yeah, that probably my best tip is, hey, bring it back down. I found that there’s kind of a progression, just like there’s a progression in the concepts that we teach. There’s also a progression in the models that we use, the representations that we use.

Some are more abstract than others. So if the area model feels abstract to a student, then what’s kind of the more concrete or less abstract way that we can show this concept?

Kyle: I love it. I love it. And, you know, I think to just to kind of add on to what you’re saying, I love the you had me thinking like when you talked about this idea that it’s really easy for us to procedurals, regardless of whether we’re doing things symbolically, whether we’re doing it, you know, by using visuals or drawings or whether we’re doing it concretely.

Because once again, it’s like, well, what’s missing if we procedure laser well, really what’s missing is not asking students to do the thinking. And so, you know, when I hear that and I go, you know, I’m like, if we can just ask the students how they want to do it, you know, and maybe even encourage students to, hey, let’s, let’s do this multiplication using if it’s the area model or maybe it’s arrays like you had mentioned, maybe it needs to be a little more concrete than the area model for some students as they’re getting started.

Kyle: But like, let’s see how many different ways we can decompose these two numbers and multiply. Now, we’re not talking about efficiency, obviously, because, you know, the student that breaks down seven into two, two, two in one. Right. Is going to have a different looking picture. But ironically, the same dimensions when we put it all together, a different looking picture than a student that goes five and two to break down the seven.

Right. So I really like that. And I think for those who are listening and John, like you had said, if you’re you’re trying to make these moves and you’re going shoot, maybe I’m procedural izing this again no shame, but it’s like how can I instead of going students, how can I ask students? You know, like instead of I if I instead of showing them how we’re going to decompose it, we say, how do how do you want to decompose it?

Right. And then maybe we asked two or three students to decompose it different ways. And we can show that that this is their thinking, that they’re the ones breaking this down and they’re actually showing us, hey, that I actually understand why we’re doing that, because it shouldn’t just be two lines, you know, two vertical lines in one horizontal line because of this particular, you know, two digit by one digit or whatever it might be.

We want to make sure students are understanding it because, again, when we’re not there, we want them to be able to rely on this tool to kind of guide them through the process. Right. So I love that. That’s fantastic. This has been an awesome overview of what people are to expect coming into this session with you. Brittany I’m wondering the sessions over, we’re going to wave a magic wand.

It just happened. We’re in the summit. You’re about to wrap up. You’re like 2 minutes before the time is up, which never happens for any of us. It’s always like 4 minutes after. That’s okay. No shame in that either. But you’re ready to wrap up and you think to yourself, I am, I feel or I hope that these educators took away this big idea.

If there’s one big thing that they could take away from your session, what are you hoping that they’ll get as they walk out that virtual door?

Brittany Hege: You know, this is probably not the answer that you were expecting and it doesn’t have too much to do with multiplication. You know, I think that yes, I think that’s the thing that I want to leave teachers with is just either a light bulb moment about multiplication, because I truly believe that our light bulb moments fuel our teaching.

When you are inspired, it it changes how you show up in the classroom. And I hope teachers are left a little bit more curious about the other concepts I teach. Like, what else have I not thought about or what? How could I? What other concept in my teaching that maybe I am procedural, izing it a little bit, or maybe I need to dove deeper into, I think that curiosity and that inspiration, like if I’ve done my job of teachers, leave my session feeling that way, it’s.

Kyle: It’s like a, it’s like a good Netflix ending, you know, where you’re just, I can’t wait to do the next episode, right? There’s got to be more.

Jon Orr: Right. But what I love is, is, is you call them light bulb moments. We always use the term epiphany moments, you know, and it’s like actually a really big part of, you know, the work that Kyle and I are doing with with districts across North America right now is is how do you how do you build more epiphany moments into your PD programing across a district for for system wide change.

And you know and the thing that I think and that we get passionate about those epiphany moments because you’re right, like, you know, a lot of times districts are saying, like, let’s let’s make change, let’s make pedagogical change. But when you focus on the pedagogical change, sometimes teachers might be like, I got to learn the math a little bit deeper, you know, and then they go off and maybe have an epiphany moment.

But if you focus on epiphany moments first for a teacher, guess what happens every single time a teacher has an epiphany moment, they say, How do I teach this better, right? They always causes a change in a pedagogical change. So it’s like if you want pedagogical changes in your in your district or your school or with yourself, you know, focus on the epiphany moment.

Like what other light bulb moment are we not having in mathematics that will inspire you to go and figure out how to teach that better? And now you don’t have to worry about are you are you making sure that we’re changing our effective teaching practices.

Kyle: And to recreate that epiphany moment for the students? Right. Right. And I think that’s the part like it like gives you that fuel to go like, whoa, if I felt like I do now, like, when you have an epiphany moment, a light bulb moment, you go, Oh, that was cool. And you’re like, I want to do that with my kids, you know?

Yeah, I don’t want to just do what I had on the, you know, on the slide or on the, you know, the transparency that’s stained yellow.

Brittany Hege: That’s yeah. Anyway.

Jon Orr: Yeah. We want to thank you for joining us here today and sharing your insights around your session. Coming up, we can’t wait for your session in the in the summit, folks. If you have not yet register for the summit, get on over to make math moments. Decomp works off summit and get yourself registered. It’s free. Get in there.

You know you’re going to hear Brittany’s big takeaway among many others. So, Brittany, thanks so much for joining us. And we can’t wait. See you there. Yeah.

Brittany Hege: Thank you for having me.

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