Eva 0:00
Hello and thank you for listening to the mathematics teacher educator journal podcast. The mathematics teacher educator journal is co sponsored by the Association of mathematics teacher educators and the National Council of Teachers of Mathematics. My name is Eva Sennheiser. And today I'm talking with Courtney Kessler, we will be discussing the article if the world were a village learning mathematics, why learning about the world, published in the June 2021, issue of the mathematics teacher educator journal, we will begin by summarizing the main points of the article and discuss in more depth the lessons they shared in the article, their successes and challenges and how to lessons relate to their work. The reason I emphasize day so much is because I'm actually part of the day because Courtney and I co author this article. So this is going to be a interesting interview question answering question, Courtney, thank you so much for joining me.
Courtney 0:55
Thank you for having me, Eva.
Eva 0:56
All right. So let's figure out how to do this by talking about our own article. So let's just start with a brief summary of the article, including the results. Do you want to get started, Courtney?
Courtney 1:09
Yeah, I can start well, so we decided to write an article about some work that we've been collaborating on for a while. It focuses on a lesson that we both taught in various countries around the book, and some websites called if the world were a village, where it takes the world's population and shrinks it down to a village of 100 people. And Eva, you detail your work in content courses, and I detail my work in methods courses a little bit, but it's really about your work in the content courses. And we've also done it in professional development contexts and in little kids classrooms.
Eva 1:48
Yeah. So I think that's good for a summary. And we'll get into details later. But I did want to point out that I learned about this task from you, initially. And I think initially, you used it with children, right. That's how it all started. And then,
Courtney 2:05
actually, I learned about it from my friend and colleague, Brian Flesner. And we actually did it in our math, math, math methods, courses, but I have done it as much with little kids as I have with teachers.
Eva 2:19
Okay, so and there's like a whole community now that does this task. So you and I have also co authored three levels of this task for early elementary elementary and middle school levels in the book series that's coming out next summer, which we'll reference in the show notes with co authors who've also done work on this task.
Courtney 2:44
Yeah. So part of the reason why we wanted to write this paper was to detail some of the back and forth work that we've done. It really you started writing this paper. And then I think if I remember correctly, you started writing. And then you asked me to co author. But we wanted to detail a bit about this back and forth, kind of push and pull that we have engaged in to talk about this lesson, and how it's kind of developed over the years. So which I think was kind of a cool idea to do.
Eva 3:16
Yeah, so I remember, like I learned from you. And then I was like, I'll do it. And then I did it. And then I came back and said, Here's what I did. And you said, Oh, what about this? And then I'm like, alright, I'll try that. And it kind of went just back and forth. And we did. One of the main goals of this lesson is critical literacy. Right? And I think well, let's get into that a little bit later. Let's tackle that question. First of who should read this article. If you want, I can go first on the sun. So I think the way this article is written, it's for teacher educators to implement the task and content as well as methods courses. One of the beauty of this task is that I always say you can do like any math concept with it, because it's so open. But it can also really focus on one or two specific math context. So if you look at the lessons we published, or there's this one lesson, we wrote up in this article that's really focused on fractions, decimals, percents, and understanding, like the notion that when we shrink the world down to 100, that each one person represents so many people in the real world and how that changes when we change the size of the village and those kinds of things. I do think and K 12. Teachers could read it and adapt it as well, but I think our primary audience was teacher educators.
Courtney 4:43
Right? I agree. When I look at it, what I like about the task is there are times when I have taught it, and I have focused more on the critical literacy piece within a Math Methods context or within a PD or or even an elementary school class. classroom context. And that's why I like talking to you. Because sometimes when we talk, you're really focused on the mathematics piece, while also thinking about the critical miss of the mathematics piece.
Eva 5:15
This is actually excellent, because you lead us into the next question, which is what is the important problem or problem of practice or issue that your article addresses? And I think we're trying to bring in the critical literacy into all of math at different levels. So do you want to share a little bit of what critical literacy is and why it is important in the math classroom?
Courtney 5:43
Well, for me, it's something that I started learning about critical literacy when I was a school teacher, and a math coach. There were a group of teachers working with Vivian Basquiat, Vasquez who's a scholar at American University, who does critical literacy work. And she was working with classroom teachers around critical literacy. And I was, so at that time, I was a math coach. And I was kind of on the outside of the circle, because I was wondering like, well, what are they doing in English language arts related to critical literacy? And how might that be related to my work as a math coach, so I would every once in a while, attend their meetings, but I still felt kind of on the outside. So I started wondering what how I might bring that work in. And so to me, critical literacy is this idea that when we're viewing the world, we bring our own experiences and our own lenses, to viewing the world. And it goes along with the work that I do with this, I getting kind of jumbled up, because it's such a big idea. And in some ways, it's really hard to kind of, and this is part of what we write about in the paper that we to do this work, we also kind of wanted or needed kind of a pithy kind of definition for it. So for me, it's this idea that everything is political, and everything is not neutral. So for me, critical literacy is this way to view the world and to think about who's writing, the texts that we're viewing and texts can be very broad. So do you want to take over cuz I feel like I'm kind of stumbling here.
Eva 7:18
So yeah, I think that what we did is, I remember us talking, this was one of our back and forth, where I was like, I need a definition of critical literacy for my students, because I want them to use critical literacy while analyzing and I couldn't find, like, usually when I need something like this, I go to, you know, the NCTM practitioner journals or something and try to find a concise article that they can read, and then they have it and I couldn't find anything. And so what we did is we found some definition on like in a, I think it was some kind of dictionary, and then you and I adapted it to work for us. And the idea was, I think we narrowed it down to three questions, who is in the stories and something else. But like, if we think about if the world were a village in, we shrink down to 100 people, the world population to 100 people, when I do this in my class, we always open up the world clock, which gives you a current, like how many people are in the world? And then we say so now if we shrink that down to 100, how much does each person represent? And then I we have I think both of us have our students predict a certain things like in teaching in the United, I usually asked my students, how many of these 100 people do you think would live in the United States? And they always over predict that because it's, it's hard to kind of figure out how many people are aware. But to get to the critical literacy in most resources that we saw the either the book or the Visually, the 100 people are broken down into men and women, right? Like it's usually 5050. And one of the things that we want our students to ask is like, why just these two categories? Why is there no more categories? Who is not represented here within this binary in similar for any of the other categories? Do you want to jump back in?
Courtney 9:19
So looking at the text and thinking about how we can start unpacking or uncovering different biases, whether intentional or unintentional. So another category we look at, in the book or on websites, when looking at different characteristics of the village, or the world is languages. And so students will look at the top, you know, the most spoken languages in our world or in the village. And then they start wondering questions like, you know, why are these if these are the languages that are most spoken, thinking about the kinds of languages that are offered at their high schools or at their university institution, and then thinking about it These are how the data are present. What about bilingual people or multilingual people? So even just those, those initial kinds of questions start bringing up how data are presented. And thinking about that no data are actually neutral, that people make decisions about data presentation and data representation. And then it goes beyond that when we ask students to represent the data using different kinds of conventional or unconventional representations, asking them to think about, okay, so, you know, some groups may pie charts, some groups may bar charts, how do those, how do those different representations communicate the date the same exact data differently. And so having those kinds of conversations bring this idea up that representations matter, that they're not neutral. And so I think those kinds of ideas are kind of the beginning of this idea of critical literacy.
Eva 10:58
So I remember one of the points you always make is that if we say represent either religions or languages, or like in my class, I have my students select the book, it has like one topic per page, and the websites have information. And so I have my students pick one topic they're interested in, and then represented in with, like, different ways. And the point, Courtney, that you always made is if we have the pie chart, it like represent the whole at the same time as the parts. Versus if we have a bar graph, it's much harder to see the whole, but it is a little bit easier to compare the pieces, right? So it's a question of what is it that we want to do, and just to kind of round out what the paper is about. So in my class, this is a two day lesson where on the first day, we, throughout the class, we distribute the characteristics, each group makes a poster with different representations, and then a summary sentence. And then we learn about the world by looking through all the different posters. And then on the second day, since I live in Portland, we kind of say, Okay, what if Portland was a village and shrink it down, and then compare, and this is where some questions come up, where it's like, for example, language is looks very, very different, right in the world versus in Portland. But then some things like my students are always because my students are always surprised because Portland has a very high rate of homelessness. But then if you compare with the world, and they go like, Oh, wait, homeless is different from without shelter? Yeah, just getting into into the categories of what does this mean? Where and those kinds of things is really interesting. And they're not just learning about the world, but they're also learning about their own community. And I know, Courtney, you've done it, like where the school is a village, right? Yeah. So
Courtney 12:55
early on, when I started developing this lesson, I did it in a classroom with second and third graders. And they were really interested to look at their school data and their school district data. And it was such a phenomenal experience, in part because they got very passionate about the way the labels that the school district used. So they really became interested in why the school district would, for example, use black and not African American. So we had lots of conversations around, you know, different labels for racial and ethnic groups. So we talked about Latino and Hispanic and Mexican and why you know why a kid might say, I'm Mexican, why does that not show up on this graph? We also talked about I might have alluded to this example earlier, but we talked about how the school that I was teaching in had a Spanish bilingual resource teacher, I think that's what the title of the teachers position was. But there was not a Chinese bilingual resource teacher, even though there are almost as many Chinese speaking kids and families in that school is Spanish speaking. And so the kids second and third graders, were asking these very critical kinds of questions based on the data that they were seeing. And so it was a very, very powerful experience for them to take the world where a village asked for these data that were related to their school and school district community, and start asking really powerful questions and starting to write, you know, letters to their principal and to their school board to say, Why is this not happening? Why don't we have a Chinese resource teacher? Why don't we have Why aren't there other categories to include people like me, so but it was also hard for me. So I was a guest teacher. I was teaching every day when a cooperating teachers classroom, it was during my graduate work. And so it was it was also hard for me to say, you are included in this data your parents and family members had to you know, check box when you were enrolled in kindergarten, and it's unfair that they had to do that, but it was just a very, there was just a lot of tension there to have to say this is the system that we have to participate in. But and it's unfair. So what can we do about it?
Eva 15:15
So I think this is a really nice description of the critical literacy aspect of the task. And I wanted to add a little bit of the math piece because as soon as you compare later, it's the world and your hometown, or the world and your school or even your hometown and your school, whatever two comparisons you want to make, you can get into fairly high level mathematics, like we did fraction comparisons, right, or decimal comparisons, when we did that, to just kind of understand how many times more or less something occurs in one context versus the other. And then for people who are interested to take the math, even at a higher level, the very end of the book looks historically about how many people if the village was 100 people today, how many people would have been in the village 100 years ago, 500 years ago, 1000 years ago, and it goes back. And so one of the activities we've done is predicting what the village would look like in the following years, which gets you into, you know, beyond linear functions modeling. So what I love about this test, too, is that you can really dig into both right into the critical literacy where you can also dig into really deep mathematics and back and forth, and you can show how you need that mathematics to actually make sense. So let me jump into the next question. How does this article build on existing work in the field? Do you want to take a first stab? Or shall I either way, so to me, I think this task really builds on the Flint Water task that is also an MTE, a few years ago, that was a or is a math modeling task. And I think it adds to the different kinds of maths modeling tasks that we can use in mathematics education, I have done multiple podcasts with math modeling tasks, where there was no context at all. And so I think just this idea of what do we think when we think about math modeling? And do we start with a context like I think and then mathematize it? Or do we start with a math idea and then contextualize it, those are the things that kind of swirl around in my head. When I think about this, what comes to mind for you, Courtney,
Courtney 17:40
I recently went to one of my friends talks, she has a new book out with her colleague Nori, her name is Katie Swalwell. And she has a new book out with Maureen Rodriguez called Social Studies for a better world. And I think about like in elementary school as a former elementary school teacher, my work was not, you know, teach language arts, teach math, teach social studies, it was so much more integrated, I did work at a very unique school and that we were really pushed to think very interdisciplinary. And, and I do know that there are there are people who think in very, you know, black kind of ways, but I just like I think about the potential to really connect to critical literacy work, right. And like, there are people doing critical literacy work in math, but not a lot. I just see the potential and the need to do more of this work, in elementary in elementary spaces, and in middle school and high school spaces. But when I went, I bring up Katie and oriens work because when I went to their talk showing their new book, I was like, this is exactly the kind of work that math educators are doing. When we're talking about teaching math for social justice, but not know, it doesn't seem like math, teacher educators are talking to social studies, teacher educators in systemic ways, right? Like, we might talk to people in faculty meetings. But we're not going to each other's conferences, we're not talking about to each other in really systemic ways about our scholarly work. And so I just thought about the need to really think about what can you know, literacy folks, tell us and inform us about our work? And what can we tell them? How can we use social studies, scholars work to inform our work and so I just really see, you know, how we can bring in this critical literacy work to really push kind of the social justice work that's already there and all this momentum that's there, to push it forward. And just
Eva 19:44
to kind of self promote a little bit you and I co authored a paper with a bunch of other people about critical literacy and math education, a book chapter, right that coming out at some point, so Well, link that to this podcast when it comes out. So the next question is tell us a little bit more about the innovation. I think we already talked quite a bit about that. But anything else you want to share about that, or how it addresses our problem of practice,
Courtney 20:17
I think maybe you also mentioned this, but what I like about this task is really, really being able to take kind of this seed of an idea that, you know, thinking about the world's population, that's a really, really huge number and taking it down to a village of 100 people and then being able to take these different angles to it, right, like we can take the critical view of, you know, what the data mean, and what how we can kind of unpack the messages in the data, or we can think about data representation, or we can take think about percentages and fractions. And the thing about equivalencies there. I just think there's so many different ways to come at the lesson and push it forward. And that's why I think, the real power of this lesson, and in terms of math, teacher education, I think, future teachers and practicing teachers really need to be able to think innovatively about tasks like that. Because when they're in front of students being able to push or pull a task, I think is a really important skill.
Eva 21:22
Yeah. My next question is, what were the research questions that we asked? And I don't know, if you have the paper open? I just opened it.
Courtney 21:34
The question was how to integrate social justice issues in the math content courses that allow prospective teachers to learn math through the context, to see math is relevant to the real world, and to uncover and address their understandings that do not align with the world.
Eva 21:50
That's a mouthful. So it says, what were the questions? And what evidence did we provide? So can we take up? Can you like, give me the first piece of that again?
Courtney 22:02
Yeah, well, I am. There's something that I don't think we've actually talked about that you do that something that's really embedded in your work that I think might be part of this question, too, is the tension of integrating social justice into math content courses, while staying true to social justice, content, and mathematics content? So do you want to talk? So I'll turn the question on to you are,
Eva 22:28
to me, also, I don't know if that came out of the questions. But it might not be justice tasks. But to me, one of the main goals of my content courses, and remember, I teach content courses, before teachers get into the teacher education programs. So these are prerequisites. They're not with kids yet. And often, they come in thinking math is this like abstract set of rules that somebody made up, and they just have to kind of master they don't really want to teach math often. And so one of my goals in my courses is I want my students to understand that you can make sense of math and shift their image of what math is. And I think we open and close the paper with asking them, you know, what do you think math is? Or what do you used to think math is? And what do you think math is now and same for math teaching. And so their views really shift from this abstract notion of rules that I have to remember and teach to? It's a tool that I can use to make sense of the world, which is how, you know, I would interpret what math is. That's one of the evidences, that's not one of the particularly smaller questions that we asked, but that, like the larger evidence that we're presenting, is this notion of how did their view of mass shift, but also, how did their understanding of the world shift? And I think that's what you alluded to, it's like to do both right, not just the math, and not just the social justice, but both in combination. And so as I said earlier, I think every single one of my students overestimated how many of the 100 people would come from the United States. And then when they dug into the data, they realigned their view of where, how people are distributed around the world. And so they're learning about that, while they're also learning about data representation and data it like fractions, decimals, percents, and so they're learning about the math in a context that they're interested in, and that makes sense. And to me, those are the pieces that are really important.
Courtney 24:48
Did you want to Yeah, I just, I wonder how many methods faculty think very similarly. Like, I feel I mean, obviously perspective, teachers aren't going to have many perspective, teachers aren't going to have huge shifts in 15 weeks or nine weeks, right? Some will write, I had a huge shift in my undergrad. When I had an amazing faculty members, something went off. And I was like, Oh, my gosh, what I like, well, I also had an interesting experience in undergrad. But I thought, like all the math that I knew was not the kind of math that I needed to be a good math teacher, right, like, and so I had that aha moment that I needed to kind of relearn the kind of math that I needed. But so I just like because I, I have always felt like the work of what I do in methods is a lot of content still. Yes.
Eva 25:51
Same. And I taught methods, you don't feel like, I don't feel the difference is that big between how we teach methods and how we teach content? Potentially, there's a little bit less emphasis on lesson planning in content. And you know, more prescriptive, you have to cover these math ideas. So I think it's different in that way. But I don't know that we can pull apart, like, what is the math? And how do we communicate with math? So I agree, I think that like, that's why I think you and I collaborate and why we published us together, because it works for both settings. And often people enter methods courses not having content experience that shifted their view of math. Yeah. And so then, then that is, you still have to do that. Right, I do
Courtney 26:42
something they have some shift. It's just not all the you know, I
Eva 26:46
do think that with focusing your course, whether it's content or methods, on making sense of mathematics, through understanding issues about our world, will have an impact. Like if that's how you teach that in students haven't seen that before, that will shift the way how they think absolutely about math. And, you know, like, if you're not really sure how to do that, luckily, there's a set of books coming out this summer, that will be a good starting point for people that have a bunch of lessons in them. And we we are happy to share the various lessons if people want to email us about the if the world were a village. So we're going to get everybody teaching this past. So my next question is about challenges. What challenges did we encounter when we developed this innovation? I know one of the challenges that I also learned from you was, how do you avoid when you have people make predictions about the world? How do you avoid them feeling bad if their predictions weren't accurate? And I think that's a problem we have in maths in general, how do you avoid feeling bad when you have an answer? That's not the one that or one of the ones that people were looking for?
Courtney 28:13
Yeah, that's a really great point. Yeah, it can't feel like a gotcha. When you reveal the answer. I try to be really transparent when I, you know, had misconceptions. There's always when we talk about the world's most populated countries, we talk a lot about those countries, the six most populated countries are the five most populated countries, like I tell them about my knowledge about those countries, and one of them is Indonesia. And I say that, you know, I've been doing this lesson for quite a few years now. And I, you know, previously knew very, very little about Indonesia. And it's bizarre to me that I went through life not knowing anything, or little to know nothing about Indonesia, when it's one of the largest countries in our entire world. And I talk about when I did it in a classroom here in Athens. And there were there were kids from Indonesia, and how, how exciting it was, for me how exciting it was for the children, how it really enhanced the lesson. And, you know, I say, I'm sure there's people in here that know nothing about Indonesia, and then everybody raises their hand. And so it's, it's more like, you know, I was there are two and I only know about Indonesia, because I have made an effort to learn about it. Right. And so we talk about other countries, and we look at it, you know, we look at a bigger list of, you know, the 20 most populated countries and we think about like, why don't we know about where our world comes from and where you know, where the most populated where the most people come from? And so just sharing those stories, I think helps that, you know, I think
Eva 29:55
I agree and then I think another task that I got from you is asking the students how many continents there are. And there are actually three different answers to that, right? Some countries teach five, some countries teach six, and some countries teach seven. And then when I usually share with my students that it blows my mind having grown up in Europe, that I learned that Europe was a continent where there is no visible reason for Europe to be a continent, other than socially constructed, right? There's no like natural, like, it's its own land, my ass or whatever. And I actually remember being confused as a child. A lot about So Europe stops in Turkey, right? And then there's turkey, there's Israel, there's all those countries there. What continent? Are they Asia? Because that's the other side, right? So and we refer to them as the Middle East, but we don't say that the continent. And so technically, are they Asia? And how does it make sense? And so I remember asking myself all these questions. What I don't remember asking myself is should Europe be a continent? That was just a given? Right? Because that's what I was taught? Yeah, that's a prime critical literacy example, right? Why do we just believe this? And so I think we have the pictures, potentially, in the task, if not a link about, you know, like, there's an argument for five or six or seven, so you're not wrong. And you say one of them, right? It's just a matter of, whose interpretation are you answering to?
Courtney 31:39
Yeah, that's such a nice, neat exhibit little example of a critical literacy task that can explode, right? Because kids would be and undergraduates and, you know, teachers can be really interested in the research behind that, right, that it's not, or that they could do some research on their own to say, you know, there's not one definitive answer, right, somebody with power gets to decide who learns what and that there isn't one, you know, there's not a book that says there's seven continents, right, that gets to be the sole arbiter. So I
Eva 32:13
have to say to me, like, every time I implement this task, I feel like I'm learning something new about the world. So just continents piece wasn't part of the task when I when you and I started working on it. And we've made it part of the task recently because of some conversation, right? And that's another one of those back and forth. Yes, to me, this is also a very clean, like you said example of arbitrariness and, and this when you grew up as a child, you just believe and so if we don't teach critical literacy, then it makes sense that our kids wouldn't know how to question the things they see in the newspapers and in other places. Right. Okay. Last question. Before I asked about promotion, though, we already promoted throughout what new contributions to our field does our article make? How does it inform or influence teacher education? How do you see people using it? And let's start there?
Courtney 33:14
Well, I feel like you've talked a lot about critical literacy. But I do hope that I mean, we know in teacher education, if we want students to think about equity, and justice and have a critical progressive frame that it has to be a coherent thread throughout courses, right? Like it can't just be in one course it has to be a coherent thread. And so I think that if we work with colleagues across disciplines, across courses, that this critical literacy idea can be something that we do across courses and across lessons, right. Like a lesson isn't just a critical literacy lesson. It's a it's a frame that people can use to look at all lessons in their course, in all readings, right. So I think to me, that's a really powerful view that this article brings. So if
Eva 34:09
I understood what you said, it's like an example of how to use critical literacy in a lesson that then you could potentially use across various lessons. I also think that the less nine we have a lesson plan with the lesson in the article, I also think that this is an amazing beginners lesson. If you have never done something like this, you know, as we said, you can tackle different math pieces that we have one in this article, but you could see if there's something else you want to do decimals, percents, graphing all of these come out and it's just if you've never done something, this is a lesson you could do. It's going to be well received by the students. The students always love learning about the world. And and it could give you an idea of how that plays out. So I think in that sense It's also a nice
Courtney 35:02
next lesson. Absolutely, yeah, definitely you can take it as it is one lesson. And then I really appreciate how you always take it back to the local context, right, like looking at Portland data looking at community data. And I think that that's really something that students would be really interested in thinking about. And I know a little, I mean, I've done it with little kids, I don't do it as much. And under my undergraduate work, often because it serves the purpose as kind of an entree into critical literacy. And so I just, I haven't done it as much. But I really appreciate that you, you do it in different ways, I think, to bring out the mathematics and to think about different ways to doing it. But then that really grounds it in student experiences, which I really appreciate.
Eva 35:50
And the other thing that we haven't talked about yet, but that is a big part of what I'm doing is connecting across different representations. So I always have my students use unifix cubes. And they can like use different colors to represent the different things, then you can see how if you use different colors for, say, different religions, or languages or something, you could build a bar graph out of the unifix cubes, then you can have a bar graph with the different colors, then you can have a pie chart where you use the same colors. So you can really like see the connections, you can have the table. So we're also learning about how to connect across representations, physical written graphs with color. And I usually do this task very early in the term because it offers a lot of how to do these kinds of things. And so I think when the pictures in the article, you'll see that there's some unifix tape to the unifix cubes taped to the whiteboard, which then we re constructed those into, like the one hundreds chart to really connect how, how does it look into one hundreds chart. And so to me, that's another piece that I think like you mentioned earlier, coordinate this interconnectedness of ideas, you can do really well with this task. Closing thoughts,
Courtney 37:11
I have just really appreciated how we have used this task as a way to go back and forth. To me, it feels like kind of practitioner inquiry in practice, right? Like we've done this task, we've talked back and forth, we revise it, we improve it, we go back and forth. Like it's just a really nice living example of that work in practice. And I've just really appreciated working
Eva 37:38
so work, work with somebody. And if you have questions, email, Courtney. I'm just kidding. So I want to shift topics before I close us out, because something happened when we published this article that I think we wanted to tackle really briefly. So do you want to talk about it? Sure. Talk about it. Sure. Yeah.
Courtney 37:58
So after we submitted the article, we, you know, went through the process, we got our page proofs back, we, you know, check those off, we submitted those. And then when we saw the article published, we realized that they changed my pronouns. So that was really disappointing. And so it was just disappointing to see that the journal decided to
Eva 38:22
do that. Yeah. And the reason we wanted to bring this out is not in particular to shame MTE. But this idea of not respecting who the authors are, even we we do not think this happened intentionally we do. That's not what we're saying. What we're thinking is some somebody fixed this incorrect quotation marks and didn't pay attention. But I think the impact that that had on just not respecting a person's identity was huge. And I think we wanted to bring this out in this podcast, just as a message to everybody like, just be careful and accept the people. You know, maybe if you want to change it, reach out and ask, don't just change it, you know, because I think that that just hit really hard. And as we're moving forward, hopefully, this can be avoided. So on that lovely note, let me close out the podcast by saying if you want any further information on this topic, you can find the article on the math teacher educator website. This has been your host, Ava Sennheiser, talking to myself and Courtney today. Thank you so much for listening and goodbye.
Unknown Speaker 39:43
Thanks.
Transcribed by https://otter.ai