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 thin Heiser, and today I'm talking with Stephanie Casey and Andrew Ross from Eastern Michigan University. We will be discussing the article Developing Equity literacy and critical statistical literacy in secondary mathematics pre service teachers published in the September 2022 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 these lessons relate to their other work. Stephanie and Andrew, can you briefly introduce yourselves? 

Stephanie Casey  0:50  
Sure. Hi, everybody. I'm Stephanie Casey. I'm a professor at Eastern Michigan University. I am a mathematics teacher educator primarily coming off of my 14 years of teaching high school math, and then switching to be a professor about 12 years ago. 

Andrew Ross  1:06  
And I'm Andrew Ross. My background is in statistics, operations research and data science most recently. And I also teach stats for teachers sometimes and math modeling class that future teachers take Well, welcome to the podcast and let's jump right in. 

Eva  1:22  
Can you give us a brief summary of the article including the results? 

Stephanie Casey  1:27  
All right, so this article was our opportunity to share with the math maths teacher educator community results of our work regarding writing teacher education, curriculum materials for secondary mathematics, pre service teachers in particular, to develop their statistical knowledge for teaching as well as their equity literacy. So Andrew and I are part of a modules project funded by the National Science Foundation where teacher education curriculum materials were written in algebra, geometry, mathematical modeling, and statistics. And Andrew and I were on the statistics writing team. In addition to ourselves, we had a K 12 Classroom Teachers of Mathematics and graduate student working with us named melody Wilson. And so the four of us spent years writing these materials in a very purposeful way to develop, you know, to try and meet the aspirational goals that a lot of the documents have come out in recent years, including the standards for preparing teachers of mathematics from a MTE, regarding what we should be doing in mathematics, teacher preparation. So in particular, thinking about the standards for preparing Teachers of Mathematics, there's assumption number one right up front is that equity needs to be front and center and integrated throughout our teacher education programs and mathematics. And in order to make that a reality, we need to integrate it into our content courses as well. And so we really were making effort to meet that need through the writing of these materials. So a good portion of this article is to help the reader understand our design of these materials, how we were purposely trying to develop students pre service teachers equity literacy, along with what we call critical statistical literacy, so that we're developing things that are content related and equity related in a synergistic way. So a good portion of the article is helping you understand the design of that and diving into one of the activities and then materials so that you can have a better sense of how this is all played out. I'll let Andrew talk a bit about the results. As part of enacting these in our classrooms. And with some pilot errors for our project. We asked our pre service teachers in the class as a pre survey and a post survey, how they are thinking about that, how confident they are that they can use to six in the class and a critical statistical literacy way, and about equity literacy questions. And overall, we saw improvement from pre to post, there's some interesting contrasts between their growth and critical statistical literacy and a growth and equity literacy that we can maybe talk about later. Overall, we were happy with the results. And the results also showed that just this one stats class isn't going to do it that we really do need an approach that that covers equity literacy in a wide variety of classes in the teacher prep program. 

Eva  4:16  
Thank you so much. I think that gives a nice overview. And I'm excited to dig more into the concepts that you have just introduced us to. But before we do that, who do you think should read this article? 

Andrew Ross  4:29  
Anyone who is considering teaching, obviously a statistics for future teachers sort of class, but also anyone who is working to revamp their teacher preparation program, whether they have a statistics background or not to be thinking about the importance of building a critical integrated focus on equity as the standard say, How can I go into the statistics preparation, how can I go into other aspects of the teacher preparation? It would also be nice if people who are sort of Just plain statistics teachers read this if they're teaching a class that future teachers take, but it isn't a designated statistics for teachers class, we know that's a reality in a lot of universities. Yeah, that's my reality. Right? I teach statistics, I actually taught statistics for middle school teachers too. And I don't have a solid background in being a stats educator. I know, I've used some of your earlier versions of the modules, and they were super helpful in my classes. So I highly recommend that down, let's jump into MTE articles are usually framed around an important problem, a problem of practice or some issue in math or science education, what is the problem that you were addressing in your paper, it's what I mentioned before, like, our primary problem of practice is that we are lacking teacher education curriculum materials for introductory statistics, content courses, that develop teachers statistical knowledge for teaching, as well as equity literacy. So, you know, again, there were these aspirational documents put out by organizations, but we here as mathematics, teacher, educators are having to figure out how to actually make this a reality. And so part of the work to make something a reality is to have curriculum materials that support this type of work. So that's the major problem or practice we're addressing. So let me see if I am going to try to rephrase it. And you let me know if I got it or not. Because I feel like it's similar to pieces that I've been working on. So the issue you're addressing is to have materials that address not only the stats, education standards, but pull in equity throughout the materials. Is that a fair restatement? Yeah, I think so. I was like, You're nodding your heads. That's not something people I know.

Eva  6:55  
Okay, all right. So let's talk a little bit about how this article builds on existing work in the field, particular theories prior work that you build on? 

Stephanie Casey  7:06  
Sure. So there's two major constructs that we are building on in our work. One is this equity literacy framework that we keep mentioning that comes out of Gorski his work. And the idea of this framework is to describe the key skills and dispositions that educators need in order to create and sustain equitable learning environments for students, as well as educating students about equity and enacting change in the educational system. So that had a really good fit with what we were trying to do, as well as the what the standards for preparing teachers of mathematics are asking us to do in math, teacher education, because it needs to go beyond just looking at the pedagogical practices that we're using and preparing our teachers to use. But they need to understand the social context of mathematics learning and the issues of equity in that and how to advocate for change in that system. And so this framework was really helpful for helping us understand what are the skills and dispositions that one needs to develop in educators in order to make them ready to do that work once they're out in the field. So let me see if I can rephrase. When we work with teaching math, for social justice, we often use the statement, it's both content and pedagogy is that kind of summarizing what you just said, we're trying to not only teach our future teachers, the content of statistics and how to teach statistics, but we're also trying to teach them how to use statistics to advocate for change in the educational system when they see inequities in that system. And that is the action component. Right? Right. So that's the action component Exactly. And that really links to this other construct that we use a lot which is called critical statistical literacy. So, you know, literacy, people are probably familiar with that term, like, can you read and write in that in that so right? So statistical literacy is a lot about can you read and write is statistical contexts, brass numbers, you know, any and all things that would involve statistics, data, etc. Critical statistical literacy, which is what we are trying to develop in our teachers is their ability to use their statistical literacy to inform action or change. And that's really important. That's that critical part. So we want them to be able to use statistics to make data driven arguments that can be powerful for informing an action or change in their world, and in particular, regarding socio political issues. I just loved your article because we've been wrestling with defining critical mathematical literacy. And so having you wrestling to define critical statistical adequacy has been really helpful. So I'm really cool. Reading that piece. Alright, so let's jump in.

Andrew Ross  10:00  
To the I think we understand the two constructs that you're building on that critical statistical literacy. And what was the other one, equity literacy, equity literacy. So those are the two in addition to the statistics. So let's talk a little bit about these modules that you developed. And in particular one you shared in the paper, I think it was about class participation, right in different math classes, not partisan. Yeah, enrollment. And I think you use a definition of equity that said something about predicting. So if you can just kind of talk us through that, because that's such a cool activity. And then that's just an example of many of the activities that you have right important to define what we mean by equity. And we use the definition that has a bit of a statistical sense to it that important demographic variables like race and gender and belief and proficiency in particular languages, would have no predictive power, to talk about student achievement. And of course, there's a bunch of ways you can talk about achievement, but you wouldn't see any statistical differences from one demographic group to another. So that's our overall definition of what it will mean to achieve equity, we hope. And so that leads directly into a statistical activity where we look at differences in enrollment in what in various math courses in high school, by race in particular. So this is part of an activity, where we've given the pre service teachers some definition, a framework for looking at having students think about a graph. So it's a crusius levels of understanding a graph. Are you just reading the data that's on the graph? Are you reading between the data like examining differences between this part of the data and that part of the data? Or are you reading Beyond the Data? asking, What does this data tell us about society? Where did this data come from? We're looking at a graph that shows a segmented bar chart of overall enrollment in high schools in the US. And then what was the racial breakdown of enrollment in what you might call advanced sort of algebra classes? And what about taking algebra one in grades 11, and 12, which is what you might call not advanced, and then also in precalculus, and then also in some sciences, biology and physics, I think. So we have our pre service teachers use the framework that they've just been learning about, to write questions as if they were writing the further future class that you know, examine the data as it is on the graph, just reading the data. And then it's the next step up, you know, comparing two categories maybe, and then getting into that equity literacy, reading beyond the data, and seeing what social conditions are going on that would lead to this graph. And then the critical statistical literacy of what can we do to inform action or change here, for example, write a letter to someone, a hypothetical person in a school district or a legislature making a data driven argument about this. And I think in the paper, you talk about supporting de tracking, which I think is a topic that is currently talked about everywhere. So it's a nice addition to that. Okay, so we get to see this graph. And then you have the framework for the graph reading, which was new to me. And I really enjoyed the three levels of reading a graph, and I'm gonna use this in my class tomorrow, because it's so cool. So it was like that just reading literally the data, right? And then between the data and then beyond the data, and then there's some descriptions of what that all means. And I'm excited to explore that with my students. The graph you shared really aligns well, with your definition of equity, which I think goes back to Rochelle Gutierrez is correct. Like we can predict. Yeah, that's right. And when you look at the stat graphs, you can see that the racial makeup in algebra classes that take algebra in grades 11, and 12, looks very different from either to general high school or the earlier algebra. And so I think that's kind of one of the things you wanted students to notice is my guess, and then talk about why that is. Am I correct there? Yes. That's a big part of the discussion of why are the getting toward the final level of reading beyond the graph? Why would the differences Why would there be differences in the number of the percent racial composition of white students versus not versus but along with other racial groups from algebra one and grades nine and 10 to algebra one

Stephanie Casey  15:00  
I'm in grades 11 and 12. And then we also have our pre service teachers do some pre work before they come to class, thinking about perhaps their own experiences with tracking or being shuffled into one class or another. And even before that, we have a part of a lesson that's about ways to have courageous conversations about difficult topics. So we're all communicating respectfully, and doing important things like that. And there's a lot of research and stories on counter stories out in books that talk about these experiences of parents of black children who are not being advised into the higher level of math even, you know, with math education, parents, who then had to fight battles just because of their race, or because the teacher had some bias. And so I think exploring what you have with in combination with Sam's experiences, which I think you say you do with videos and stuff is really powerful to to also make sure we don't like take wrong conclusions from the data. Another powerful aspect of this graph I wanted to bring up which helps in the discussions is that the breakdown of the high school science classes biology, chemistry, and physics are extremely similar to the overall high school enrollment, or looking at breakdown by race. Then if you compare that to the what's happening in the various math classes at the high school level, in terms of their breakdown, by race, they are substantially different from the overall enrollment. So that really is trying to bring out differences. You know, what is going on here. And I think what I like about that is it helps us hone in on issues in mathematics, teacher education, which is really important and often doesn't happen if you are taking just a general social foundations class in the College of Education, for example. Yeah, notice is good. And math is used as an indicator on level of smartness. Right? So this really has a huge impact. Alright, so let's move on to your research question. What was the research question or the question that you looked at for the effectiveness of your innovation, if you can share a little bit of that? Sure. So we have one question with two subparts. So our research question was, does the use of our statistics, teacher education, curriculum materials, improve secondary math pre service teachers competence, value and likelihood of applying both their equity literacy and their critical statistical literacy? So again, those two big constructs that I talked about earlier are the two sub points that that research question. So regarding the idea of value and likelihood, I just want to make sure people are familiar with where that's coming from. So there's something called the expectancy value theory of achievement motivation, which talks about the idea that somebody is more likely to make choices that promote success at achieving a target, when they value that target. That's the value part. And they feel likely that they can Spry that if they try to achieve that target, they will succeed. That's the likelihood part. And so the goals that we have for our study, were applying critical statistical literacy and applying equity literacy. And so we're wanting to know, are these pre service teachers expectancy in value, and increasing from the beginning of the course to the end of the course. And so we did pre post surveys. And in this survey, there were a number of survey items that were on Likert scales where they went from zero, not at all to five very much in terms of how well does this statement describe you, for example, it is important to me to use critical statistical literary literacy skills when considering claims made regarding socio political issues. That's an example of one of the types of questions that we asked. So we had a total of four critical statistical literacy items, and six equity literacy items that were on these Likert scales. In addition, there was a open ended portion of the survey at the end, asking them questions like, what did you learn about equity and social justice in this class? What was helpful for your learning about teaching statistics in the future that involves issues of equity and things like that? So we have some results in our paper that are coming from both parts, the survey items and the open ended in one of the things that I really loved about your results is how you present them so as you share the results, maybe you can share how you represented them as well. I'd like to jump in and point out I don't think it's been said in the podcast yet. So we do. In the article we feature this activity about tracking and

Andrew Ross  20:00  
racial percentages. But that's only one part of a much larger strand in the in the statistics modules. We have three modules exploratory data analysis and study designed statistical inference like confidence intervals and hypothesis tests, and statistical association, like linear regression, and two way tables, chi squared stuff. And each of those modules has a few central themes that use an equity related data set. So the results we're going to be talking about here aren't just to the one activity about tracking it's integrated throughout the whole semester. And I believe that your article lists the topics in one of the appendices, right, so people can go and see.

Thanks for adding that to talk about the way that we're presenting the research results, or the results of the pre and post survey. So it's like your data. And we have two ways to look at it. One is movement from pre to post. So we're using something called a river diagram. It's also called a Sankey diagram, sometimes. So it shows the distribution of people's answers zero through five on the PRI, and then in a parallel way on the post. And it shows signs and bars going from, let's say, people who responded a four on the PRI to responded a five on the post, or someone responded, more rarely would be like a four on the PRI and a three on the post. But that happened every now and then. But it was pretty rare. Most people either moved up a category or two, or just stayed where they were. So when we look at this graph, we can kind of see the movement by how the lines are slanted to the mostly to the right is an increase. And that's correct. The last Yeah. And then this is paired data of pre to post. So we also compute the difference pre to post how many categories they moved. And then we make segmented bar chart of that showing how many people change zero categories on this question, how many people change by plus one? How many change by plus two? There were some minus ones. And we do that for each of the four critical statistical literacy related questions and each of the six equity literacy questions. So overall, we saw a great positive movement, you know, as an overall trend, it was interesting, the scores are that the readings that people gave themselves on the PRI, were much higher for equity literacy, there were a lot of people who are answering five, they're very comfortable or have a lot of place a lot of value on equity literacy related questions. So there wasn't much room for them to show improvement. Where I think people were a lot less confident in their ability, and perhaps even how much they value using up statistics, critical statistical literacy, which might be an effect of how the US educational system has perhaps not done as good a job as it shouldn't be doing with statistics, knowledge and statistics affects you could say. So we saw better larger improvements for critical statistical literacy, perhaps because people came in with that more negative image of statistics. But these being pre service teachers, perhaps they already have a strong value on equity literacy topics. Okay. My next question is, what evidence do you provide? But I think we already touched on that. So I'm going to move to the next one, which is I kind of our last question before we bow out. So what is the new contribution to our field of mass teacher education that your article or larger your modules set makes? So in terms of materials, we are, you know, and have finally created some teacher education curriculum materials that are allowing teacher educators to have something in their hands to support the type of work we've been saying we want to do in our classrooms. And I wanted to mention also that the modules project in addition to just giving you Teacher Education, curriculum materials, we also have expansive support for instructors that use these materials. So we've created open canvas sites with all kinds of resources to help instructors know how these materials work videos of professors using these and things to attend to regarding that teaching to support the enactment of you know, what we're wanting these materials to do and their implementation. So I think there's just a lot to be you know, we've got a lot of supports now that weren't there before. So that's definitely a major focus, but I think you know, in terms of the article and thinking about ways that it can support mathematics, teacher education in general and like some bigger things, like Andrew mentioned, like one of you know, when you think about how do you address equity literacy and development of teachers understandings of issues of equity, what we have found from pre

Stephanie Casey  25:00  
serious research in our field is that most secondary math teacher education programs, if they do address it never get to issues that address systemic racism. And so that was a major goal of our materials was to address systemic racism. And that also, you know, are just issues of equity and systems. And so that's something that AMT standards emphasize is something that we found a way to do through this idea of a strand of a common topic that goes throughout all of our materials. The major focus of our strand is on income inequality. And what are some different things that are related to income inequality, and the ones that we focus on a lot in our materials are education related factors, because we are working with future teachers. So we feel that they are not only should care a lot about the education as a system, but also that's the system they're going to be working with. So that's the one they can most likely enact change. And so you know, just this idea of how do you have a common theme that's running throughout your course that you keep visiting again, and again, to deepen pre service teachers understanding of this systemic issue about equity is something that can be carried over into lots of different applications and experiences that we are designing for our future teacher. So I think that's another contribution that our work has for the field. And I don't know if we've mentioned this before, but the modules are free to use. And if somebody wanted to use them, what do you think how much time commitment is needed to get started on using them? I'd say it's about as much as switching a textbook. There's no you can sign up to access the materials that our website modules to.com. Once you get the materials, you can see the student version and the instructor version. And you can also watch videos written by or filmed by the writing team and engage with other people. So it's about as much work as switching textbooks in general. All right, is there anything else that you would like to add or promote before we close out now? Okay, thank you this modules. Sounds amazing. And for our I should thank you for joining us. So thank you for joining us. You're welcome. This has been fun. Thanks for the opportunity. It is totally fun for me. I've got so many ideas of what to pull for my classes. I'm always excited luxury to get to do these interviews. Okay, for further information on this topic, you can find the article on the mathematics teacher educator website, as well as the link to the modules project. This has been your host Eva and Heiser, thank you for listening and goodbye.

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