Eva 0:00
Hello and thank you for listening to the mathematics teacher educator journal podcast. The mathematic 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 Thanh highter. And today, I'm talking with Stephanie Casey and lighten up on the run. We're not talking this Andrew Ross, who is the co author on the paper but couldn't be here. Today, we are going to talk about the article engaging teachers in the combination of statistical investigation and social justice, fairness in school funding, published in the February 2023, a few of the mathematic teacher educator journal, we will begin by summarizing some of the main points and then discuss more what the author's learned, Stephanie and live, but can you briefly introduce yourself?
Stephanie Casey 0:53
Sure. I'm Stephanie Casey. I'm a mathematics teacher educator at Eastern Michigan University in Ypsilanti, Michigan. And I'm a principal investigator on the modules project that this article grew
Liza Bondurant 1:05
out of. And hello, everyone, I'm Liza bhandara. I'm an associate professor of math education. I've taught statistics at the secondary and post secondary levels. And then also as a scholar, I use statistics in my math, education research. And I'm really passionate about teaching and learning statistics, because statistics provides us with a framework for understanding and making sense of vast amount of data. And I really see that that is applicable to a variety of fields, some of the classes I teach are for gen ed majors. So and then also, it can also be like a valuable tool for engaging students in social justice advocacy, because it provides a way to analyze data, like about disparities, or that sort of social justice issues. And the work that we wrote about in this article kind of lies at the intersection of like statistics and social justice. So I was super passionate about this project. That is super
Eva 1:59
exciting. Thanks so much for sharing that. Let's jump in the article that you selected to write falls into that person perspectives on practice section of articles. Could you briefly explain what this mean?
Stephanie Casey 2:14
Sure. So the editors of the mathematics teacher, educator Journal did a really awesome thing, I think, with these perspectives on practice articles, which is the idea that we should be building on one another's work that we do in this field. And so perspectives on practice is meant to bring that out, they selected a couple of articles that have been previously published to the mathematics teacher educator, journal and asked for the field to say, Hey, have you done anything that builds on this work? If so, can you write about that, and we'll publish it in this new format perspectives on practice. So I think it's a fantastic idea. I'm really glad they came up with this because it is so helpful to the field to know like, how are people taking up ideas, making them their own? And I appreciate the opportunity to do that.
Eva 3:00
Excellent. So you've had they selected a few articles? Which particular one are you building on?
Liza Bondurant 3:07
So we're building on the article by Julio Garrett and colleagues from 2019. And it was entitled engaging teachers in the powerful combination of mathematical modeling, and social justice, the Flint Water task.
Eva 3:25
Okay, so why did you select that paper to build on?
Liza Bondurant 3:30
I had read that article previously. But as Stephanie alluded to, when I saw the perspectives on practice call, I reread it, and I was just astounded how similar their work within service teachers surrounding the social justice issue of the Flint Water task was aligned with what I was doing, which was piloting the modules, statistic materials and using the statistical investigation cycle with several lessons, but one lesson in particular having to do with fair funding of schools.
Eva 4:07
So would you say that when you read the Flint Water task paper, it reminded you of the work you do, but it was in a different context? or Yes, and you said it
Liza Bondurant 4:20
much more clearly and concisely than me, I guess, their model and I was like, Yes, this is like the statistical investigation model. And, oh, we also have social justice cycle going on.
Eva 4:33
Yeah. Excellent.
Stephanie Casey 4:35
So that paper is available in on the MT website and also it as a podcast episode number eight, if anybody's interested. You're building on that article because you felt like you're doing something similar. So just explain our roles. So myself and Andrew Ross were co authors of the statistics materials written by the modules project which are meant to advance pre service, secondary math teachers understanding of how to teach statistics. And Liza was one of our rockstar pilot errs, who was in on the initial part of the project, and she got to use it, we use the materials. And so Liza kind of gave her perspective on how this gear at all article connected to what she was seeing as a user of the materials. But I go back a few years from that, because I was writing the materials. So what's really cool is that some of the co authors of the article, including Ricardo, Cortez, and Cynthia and halt are also on the modules project with me. And so I was really familiar with their work. And I knew about this article. And so when we were just first conceptualizing how to integrate issues of social justice, within our statistics, modules, materials, we went to this model that is in figure one of our paper that looks at the interaction between discussions of social justice and discussions of mathematical modeling, and said, Okay, this is a great framework for how to do this type of work, we're going to take that and adapt it, we're going to remove the mathematical modeling cycle and replace it with the statistical investigation cycle, and see how that works. And so that's how we designed our material. So that's why when it's so cool that Liza as a user who didn't even know we design our materials, necessarily using this as a reference, like she could see it as a user. So that's really cool to see. So that's my inspiration from this article as a writer. So
Eva 6:35
that's really fantastic. So you took the framework that they have that connects the context to mathematical modeling, and said, Okay, we're going to connect the context to the statistical inquiry cycle, correct? Statistical investigation cycle. Yeah. Thank you. How is your
Stephanie Casey 6:55
framework with the statistical investigation cycle different from the one that they had? Right? So basically, we've kind of swapped out what they had as the mathematical modeling cycle for the statistical investigation cycle, you might have asked yourself, well, why can't you just call statistical investigations doing a mathematical model? Why can't you just use that cycle, but there are some important differences. So in terms of like the mathematical modeling cycle, it talks about research information needed, and that may or may not involve data, but for statistical investigation that absolutely has to involve data. So that is a key difference that we wanted to bring out in the statistical investigation cycle. So like, you'll see that difference. When you compare the two models, where they say research information needed, we have a statement that you have to collect or consider pre collected data. Another big difference is at the end of the mathematical modeling cycle, they talk about computing a solution and interpreting the solution. And we never ever in statistics, use the word solution as what we produce from our work. And I won't go into get on my soapbox about that. But you can probably guess why, you know, I mean, that's just not what we do. If you know, statistics, that's not what you do. So we would never call what we're doing a solution. So that language and just the idea of that doesn't gel well with what we do in statistics. And so that was another impetus for replacing the modeling cycle from math with the investigation cycle that we use in statistics. That's really
Eva 8:24
cool. Thank you for sharing. And now in my brain, I'm thinking is there something that kind of combined both of them, but that may be a prospective article on the perspectives article? Yeah. So I think I understand why you chose and how you built on the article. Now let's talk a little bit about what you did that school funding investigation, we use this
Stephanie Casey 8:47
model that was an adaptation of a year and I was work throughout our materials. But in this perspective, is our practice article, as did a Gary at all, we chose to hone in on a particular task and our materials. And so that particular task that we illustrated in this article is the Pennsylvania school funding task. So the broader issue that it raises, like Liza mentioned earlier, is the idea of school funding, which was purposely selected as a context for many reasons, not the least of which is that as an issue of social justice, that should be really important to future teachers. So we wanted it grounded in the educational system, because that is the career they're choosing. And that is really important to develop their understanding of education through social justice issues. And so we dove in further to look at just Pennsylvania for a couple of reasons, not the least of which is that we could get raw data. Anybody who's tried to write activities like this knows how difficult it is to get actual raw data to get users to work with. But Pennsylvania was historically known to be a state with issues, school funding issues, and so a grassroots effort had pushed the government to examine the issue there by Back in the early, like 2015 ish. And so from that process, the there was a committee put together in Pennsylvania to create a fair method to distribute the state's educational funds. So that committee did their work. And they came back with a recommendation for what we call the the fair formula, fair funding formula. And that method took into account lots of factors that districts have that would be pertinent to what determines how much money they should get from the state things like how many students are in that, how spread out is the district because that impacts busing costs and things like that. But the reality then, as often happens in politics, is that instead of saying, Great, we'll use the fair funding formula now. But instead, the state decided to only apply the fair funding formula to 6% of their funding, which was the funding increase that year, and use the old formula to distribute the remaining 94% of the funds that the schools would get. So what this created was the opportunity for creation of a data set where we could say, well, what would the school districts have received, if all the money had been funneled through the fair funding formula? And what is the actual amount they received, which again, was 94% old just 6%, from the funding to increase new, and that's a very rich context to start investigating, do it in a data investigation. On top of that, we also could get, for every single district, some of these demographic variables at the fair funding formula wanted to take into account, what is the median household income of houses in this district? What is the poverty level? What is the race of the students in this district? And so one could look even deeper into the inequities using those additional demographic variables. So that's the context of this dataset. They're looking into the funding of school districts in Pennsylvania, comparing what they would have gotten through the fair funding formula with what what actually happened and looking at the impact of a third variable with all these demographics, in terms of could one use these to predict which schools we're going to get less than the fair funding formula would have gotten them to get.
Eva 12:19
So one of the things that you have in the article is some images from using the software code up, could you talk a little bit about how that is used and how the visualizations help make sense of the social justice issue
Liza Bondurant 12:37
code app if the listener isn't familiar, common online data analysis platform. So from the article that we have in our list of references by David most Cenex, systemic racial bias in latest Pennsylvania school funding, there's a link to the dataset. And then we uploaded the dataset into Kodak. And we, as Stephanie said, our x variable was how much money they would have gotten with the fair funding formula. And the y variable is how much they actually got with was it 4% or 6%, with a fair funding 94, you know, with how much they actually got. So that's your x variable, your Y variable. And so each.on the graph represents one school district. So they have like, this graph with all these dots, all these data points, and then we added the line y equals x. And we talked to students who are pre service secondary math teachers about what does a point on the line represent? Well, that represents a school district that got the same amount with the actual formula as they would have gotten with a fair formula. Okay, what does a point above the line represent? They got more with the actual formula than they would have gotten with the fair funding below the line. Okay, they would have gotten more with a fair formula, and they got what the actual formula. So then, as Stephanie said, we have all these demographic variables. So we start experimenting with okay, what do you think would be a predictor of a point being above the line on the line or below the line? And a lot of my pre service teachers and myself thought that it was like socio economic status of the area, like, okay, property taxes, fund schools, I thought, so I thought, okay, if you're in an area that has higher socioeconomic status, property values, lower percent poverty, I thought that would be a predictor variable, of whether they got more or less funding. And so the image on the left in our article, I chose the shading of that third predictor variable. It's equally distributed, distributed above and below The line, the darkness and or the lightness of the shading. So that's not a good predictor. So then we looked at the percent of white students in the school district as a predictor variable. And lo and behold, the school districts with predominantly a higher percentage of white students are getting more with the actual formula than they would have gotten, they were above that line y equals x. And then the ones with lower percentage of white students were below the line. So they were getting less with the actual formula than they would have gotten with the fair formula. So I mean, that just shook me. And it really, it shook my students to as an injustice.
Thanks for sharing that. So this task, really, in that sense, helped you understand the real world better through using the statistical investigation cycle. In the article, there's a link that takes you straight to code up. And so yesterday, when I read the paper, I was also playing around with the data. And that was really fun. So if we're nothing else, then people should pull up the article to get there and be able to play with that. So you and your pre service teachers, it sounds like Lauren's about the world, and about statistics through doing this engaging with this task? Absolutely. It definitely had that dual emphasis, like a nice synergy between the social justice advocacy and learning about the statistical investigation cycle, which is from the gaze framework that I learned about another project that Holly Lin did with Stephanie. So yeah, there's the statistical investigation. So they're learning. I think Michelle Gutierrez calls it like the dominant axis achievement and axis, you're you're playing the game, but they're also learning the critical axis, how to change the game, we're empowering them for advocacy, because the last step is taking action, where we ask them to write a letter to their legislatures, about what they learned, and some of the quotes that we obtained. They realize they had that lightbulb aha moment where, okay, now, I'm not just making an argument, I can support my argument with data. This is, these are the facts. This is wrong. Yeah. And that's
Stephanie Casey 17:25
one of the big themes throughout our modules, materials is creating data driven arguments and equitable and social justice issues, you know, so in those contexts, the in the, the empowerment of that, like you're saying, to enact action, or change through advocacy efforts, and it's just a great way to actually make their lead their learning of these topics more meaningful or powerful to them. And, you know, like you said, that synergy really deepens their understanding of both in a way that you couldn't if you're doing one alone,
Eva 17:58
all right, so let's kind of think through wrapping up, if you think back about this project, and this paper project is so cute. But the paper, what would you say, in a brief summary, is your contribution to the method community with this paper?
Stephanie Casey 18:18
Well, I think a big thing for the method community is trying to bring the AMT e standards for preparing Teachers of Mathematics, to actualization. So when they came out in 2017, they, you know, were very aspirational. They were presenting a vision of what mathematics teacher education could be, and should be, but it was very much left up to the field to figure out how to make it actually happen. So, you know, there was, you know, assumption number one in the standards for preparing Teachers of Mathematics document is about how equity needs to be first and foremost in our math, math, teacher education programs. And so how were we going to actualize that, in our mathematics content courses has always been a question for the field, like, there's always been something that's been done somewhere else, by somebody else. But that's, you know, AMT standards really challenged us to change that. So I think we've presented the field with a way in which we can productively integrate development of equity literacy, with also an understanding of content areas. We're doing it in statistics I Gary at all are doing it and, and modeling, and there just needs to continue to be attention to how to develop both of these together in content courses that we're offering in our teacher preparation programs. And I think that we've gotten some great ideas and actual curriculum materials that support that.
Eva 19:46
This is such a lovely wrap up. So
Stephanie Casey 19:48
let me ask you, if other people wanted to use some of this, like this particular task, they had the link to put up but what about other tasks in your modules? How People go about that. Yeah, we've got a website for the modules project, www dot modules two.com. It's got all kinds of great information about the project. It's got sample lessons, it's got videos to let you know more about it. And it's also got a tab that says use our modules materials, and you fill out a short request form. And then you can get access to our materials which are free, not only to you as mathematics, teacher educators, but the student versions are also free, because we felt it was very important to not increase textbook costs for college students. So everything is freely available. And we also have a open Canvas support page, which provides instructional support to those wanting to use the modules materials. So we've got a lot of videos there a lot of information to help support your use of these modules, materials, which may be quite different than materials you've used in content courses in the past.
Liza Bondurant 20:56
And I think to just a plug, Stephanie did modules grow out of M tap, which were both a part of. So M tap has a lot of different racks, Research Action clusters and different teams and programs, a lot of good work. But Stephanie and I both are both plugged into that network Math Teacher Education Partnership, so we would encourage you to check out and tap as well. And modules in case you teach a methods course, there are full courses for content courses, like if you were doing statistics, or geometry or algebra or modeling, but I was doing a methods course. So you can pick and choose some of the lessons from a variety of secondary content areas, even if you are a methods teacher, you know, if you weren't teaching a content course,
Eva 21:40
thank you so much for sharing all of these valuable resources. Is there anything else that you would like to promote? While we're at it,
Liza Bondurant 21:49
I was just gonna say a little thing to encourage others to read these calls that come out and to not be afraid to reach out to maybe more accomplished math teacher educators and ask them if they're interested in collaborating with you. As someone more novice, that's been a big lesson learned for me is say yes. And ask the question.
Eva 22:13
Thank you. And in addition, you can also always reach out to the editors, they're always happy to talk to you and support you. Well, thank you both so much for joining me today.
Stephanie Casey 22:24
This has been really fun. Thanks for having us.
Liza Bondurant 22:27
Yes, thank you so much for the opportunity.
Eva 22:29
For further information on this topic. You can find the article on the mathematics teacher educator website. This has been your host, Ava Sennheiser. Thank you for listening and goodbye.
Transcribed by https://otter.ai