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 I'm talking with Dr. Julio Aguirre, who is Faculty Director of the teacher certification programs and associate professor at the University of Washington Tacoma in the School of Education. We will be discussing an article she wrote with her colleagues Cynthia unhulled, Ricardo Cortez, Aaron Turner and Sonia Simic Mueller engaging in the powerful combination of mathematics modeling and social justice the Flint Water task, published in March 2019 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. Julio, thank you for joining us. So I'm going to start by asking if you can give us a brief summary of the article.
1:06
Well, thank you again for inviting us to be a part of this podcast. Our article describes this innovation that focuses on mathematical modeling, and the on to examine the ongoing water crisis in Flint, Michigan. The innovation is designed to introduce and extend mathematics teacher understanding of social justice context for mathematics exploration, and their understanding of mathematical modeling. The article provides a conceptual frame to think about social justice and mathematical modeling in synergistic ways, and includes accounts are illustrative accounts of how that this task was designed and enacted. With pre service and practicing teachers. The evidence of the innovation includes a close examination of the mathematical models produced by the teachers in one professional development setting. And the impact of the innovation is also evidenced by teacher survey data that supports a positive impact on how teachers perspectives on designing and implementing similar social justice modeling tasks with their own students. We provide guidance and tools for enacting this task, and to gain inspiration for other such modeling tasks to be used in the future by mathematics teacher educators.
2:18
Okay, so who should read this article?
2:20
I think all math educators interested in making mathematics more rich, rigorous and relevant to students, my co authors and I have enacted this task in multiple settings around the country and internationally. And the task helps math educators experience a mathematical activity that examines issues of social justice, environmental justice, and helps to clarify what mathematical modeling is,
2:43
okay. So usually, when we have these articles in a math teacher educator, there is one important problem or issue that the article addresses what was the important problem or issue that you guys are addressing in your article.
2:59
So there actually is a multiple that we've multiple problems that we were addressing, but the two I think that really stand out are the fact that social justice pedagogies and mathematical modeling are both under emphasized in mathematics, Teacher Education, and preparation. And because mathematical modeling is included in the standards in most states as a content standard, and as a practice standard, it's critical that our teachers become more familiar with it. And that hasn't been an integrated focus of mathematics, Teacher Education. So we, all of us, all of the co authors come from a cultural responsive approach to mathematics teaching. And we are interested in addressing mathematics teaching and learning from an equitable standpoint, and emphasizing social justice and mathematics in a meaningful and synergistic way. So it's very important that this type of problem, or this type of activity can accomplish multiple goals.
3:55
How does this article build on existing work in the field? And what particular theories or previous articles Did you ground your work in?
4:03
I would say that, you know, we had two relevant literature's that we drew from, which was called the responsive mathematics teaching, or math, x pedagogies. And also what we know about teaching and learning of mathematical modeling. So those were the two primary literature bases that we drew from. And then what was really helpful is an article written by Cyrillic Martel and wagar. And the 2016 apmp yearbook, in which they found they sort of articulated a really nice framework for thinking about social justice and mathematical modeling. And they identified three overlapping goals between those two areas. One, mathematical modeling and social justice teaching engaged students in ill defined problems for which they can have multiple valid approaches. To they both leverage the real world knowledge that students bring to the classroom, and three they raise students interest in mathematics by supporting them to better understand and To transform their world. So those three things that really helped us sort of think about what does this mean for mathematics teacher educators? And how can we develop a conceptual frame that explores these the sort of synergistic ways social justice, and mathematical modeling can impact one other interact with one another?
5:18
What research questions did you study to document the effectiveness of your innovation?
5:24
Well, I mean, our research questions was, how was this done? How does the Flint Water task influence or impact the ways teachers might experience and learn about mathematical modeling and social justice issues that can be analyzed with mathematics. And so we wanted to investigate the ways in which this might have happened. And we utilized data from one professional development setting in which we analyze the actual mathematical models that are produced with this task, and also teachers survey questions that were given after the teachers went through this activity.
6:00
So let's take a minute and talk a little bit about what the activity is.
6:04
Sure, one of the things that was the inspiration for the activity was from a newspaper article that described corporations who were going to be donating a large amount of bottled water, like in the millions to Flint, to address the water needs of schoolchildren in Flint. And this was in response to, of course, the what we now know is the Flint water crisis. And at the time, this article came out in 2016, in January, and it seemed, you know, a really interesting article to explore about whether or not this donation by corporations like Coca Cola, or Nestle, Pepsi Cola, Walmart, if that was going to be enough to address the daily water needs of schoolchildren in Flint. And essentially, this is a claim, right? They claim that this would be enough water to meet these needs for the school children for the rest of the calendar year. That was what the newspaper article said. And so the question is, is that true? Is that really going to be enough? And so that was what inspired the activity. And what we do initially is we ask teachers, and I don't know if you want me to go through this whole thing, but we asked teachers to, or the students in front of us what they know about the Flint water crisis, just to generate background knowledge, what do people know? And then we have them investigate for themselves, well, how much water would it take for there to be enough water for schoolchildren in Flint for a calendar year? And so that's sort of their first engagement with the two components of our conceptual frame, which is the social justice, what do we know about this situation? And then entering into the modeling task of making sense of what what would we need to know in order to answer this first part of the question? And so once the teachers answer for themselves, well, we think that this would be enough water, we have them explore the activity and the examples of what the corporation said that they would do, and have them determine Is this true? Is this plan a good one, that the companies had suggested this is going to be enough water for the daily needs of schoolchildren in Flint for the rest of the calendar year. So it allows teachers that allows them to engage whether their own mathematical models that they produce originally, and look at the assumptions that and other kinds of decisions that the corporations might have made? in their claim that yes, this amount, this case, it's 6.5 million bottles of water would be enough.
8:48
So if one reads your article, this task is really a small little clip it I'm just gonna read that out quick, says Walmart, Coca Cola, Nestle and Pepsi co said that they will donate bottles of water for schoolchildren in Flint, Michigan, to help with the city's public health crisis over lead contaminated water on January 26. The company said that they are planning to collectively donate water to meet the daily needs of over 10,000 schoolchildren for the balance of the calendar year. And then you're citing the source. To do so to companies will send 176 truckloads of bottled water up to 6.5 million bottles to Flint. And then the questions under it is how do we know how much water will be enough to meet the daily needs of Flint schoolchildren until December 31? And is the company's plan a good one? So I read out this task really briefly because it is a little bit mind boggling to me that such a small little task can lead to such an amazing interaction and long engagement that you then describe further in the future. And I was wondering if we could quickly talk about the ill defined pneus of the task? Because this is something you come back to later, right? As a general principle, again,
10:10
sure. The first question, how do we know how much water will be enough to meet the daily needs of Flint schoolchildren until December 31? doesn't have any numbers, it raises the question about what what what do we know? And what do we need to know? And what kinds of assumptions or decisions are we going to have to make in order to answer that question? So it's very ill defined. And it requires people to talk about a generate, to make assumptions to find out information that they may not know. And then create some kind of mathematical model that helps them generate an answer to that question. And so depending on what they assume, or what kinds of information they get, which is what we detail actually, in the article, you're going to have very different and equally valid solutions. And that's also very, both important for teachers to experience. And also is part of the math modeling process.
11:07
Yeah. And I just have to be open here. I've also implemented this task already. And it was just phenomenal to see what kinds of questions come up and what students and some students decided that yes, it was enough. And some students decided that no, it wasn't, it was really interesting. I'm going to jump a little bit ahead, because there is this framework that you presents, in your paper. Do you want to talk a little bit about that framework?
11:38
Sure. Well, this is also a conceptual frame that depicts the interaction between issues of social justice and sort of a discussion cycle that would occur when you present an idea like this, or an activity or a prompt this way. And then the engagement into the mathematical modeling process, which is in the lower left hand, or right hand side of the figure. And so again, there's these many opportunities where, in making sense of the prompt of the situation, there's going to be discussions around what does this mean in terms of social and environmental justice, with this specific situations in Flint, or in my own community? And then awareness and sense of action of what might need to be done, as one thinks about what information is needed? And what assumptions and choices are going to be made? And how this particular solution does or does not make sense in the context of the question, is it true or not true in terms of the claim, and the conceptual frame allows people to see that these things inform one another, the opportunity to engage in social justice discussions, informs the mathematical modeling process, and vice versa. The mathematical modeling process may generate more kinds of questions that engage teachers in thinking about well, does that assumption Make sense? Do we need to refine Why? what's reasonable? Why? Those kinds of things
13:06
so as I'm looking at your framework, it is like kind of two circles that are joined together. And so one is this social justice circle where you start with the issue, and then have a specific situation and then build awareness. And that's your circle that you kind of go around. And the other one is the mathematical modeling cycle, and then you go back and forth between those two. So I find this really useful for my work thinking about the interaction between the social justice and mathematical ideas. And there is some literature out there, right, that says, you focus on one or the other, and you are showing a little bit in the middle of the cycle of how those two interact through specific situations. Am I describing that correctly? Our work
13:59
starts with the idea that these two components mutually inform one another. And looking closely at teacher conversations and experiences implementing this, and then their models, you can see that there is this mutually informing interaction that's happening between those two cycles.
14:21
So one of the things that was interesting to me in acting this task, and that I also read in your paper is that there was a whole range of how much prior knowledge students had about the Flint water crisis from knowing quite a bit to having not really heard about it. You have this whole appendix in the back and I just want to make sure that everybody knows this that has the whole lesson laid out and has some videos and pictures that one could start with, to brainstorm and build some common understanding. So now the whole task is part of the article in the appendix,
14:57
right. It has a basically a brief Lesson overview or lesson plan that includes prompts that you can ask descriptions, videos that we have used that have we have found helpful and walks you through sort of how to launch it. What happens during the exploration? And then how do you engage in the summary and debriefing of the models where you compare and contrast models, when you sort of start to think about, okay, what were your assumptions being made here? How are they similar or different? What was the rationale or reasonings behind those assumptions? So it definitely generates those kinds of both mathematical modeling and social justice discussions within that last part. Yes.
15:34
So now I'm gonna jump back to my questions. After I did a little detour. What evidence do you present in your article to demonstrate the effectiveness of your research? And I think you already told us that you did some surveys and some other stuff. Do you want to talk a little bit about what you found in those?
15:52
Yeah. So in the surveys, what we were looking at, we picked up some sort of three main themes. And all the practicing teachers that were involved in this particular PD session, agreed that math modeling problems such as the Flint Water task had more benefits than drawbacks. And they could envision themselves doing such tasks with their students. And then later on, when we ask if they were asked, Well, what kinds of examples could they think that what might be similar from a local standpoint, or from their own community standpoint, they came up with many social and environmental justice types of things that they could think about that was similar to the Flint water test. So for example, public safety around the spread of disease, or Border Patrol and immigration, or the lack of running water or clean air. So they started to think about recycling, of course, came up quite a bit, they started to envision and could see other kinds of contexts that they could design modeling tasks that connect to real world community based concerns that would highlight social and environmental justice. And we were really pleased that that awareness was increased. So they saw benefits, and they could imagine themselves doing something similar with their own kids. Cool.
17:11
I think that's one of the things that we really have to work on, right is the notion of whether this is something that's possible to do with children in schools,
17:19
as someone who thinks about these ideas a lot, it's really important for me to vet a task like this with real, real young people. So for the audience out there, yes, this Flint Water task was given to middle school students, I would just want to say that it's both important for math, teacher educator preparation and education. And it's important for me that such a task would also pass muster with young people. And so while that is not written up, because it was a pilot, and I used a colleague who utilized a colleague, a math teacher, math, middle school teacher, in my own community, it was really important for me to see whether or not this would fly with youth. And it
18:03
did. That's cool. Yeah. And I think that's important to make sure that we don't just do this at the university level.
18:09
Right.
18:10
All right. The next question here is what evidence do you present in your article to demonstrate the effectiveness of your research? I think you already told us about the surveys.
18:21
Yeah. And also, I think it's important that the manager or the audience for this article also, we go through in detail different approaches that the teachers utilized at least two different approaches that the teachers utilize in their own math models to answer this question, I think it's helpful for math teacher educators to see the possible models, and the rationales behind the assumptions made and generalization and things like that, that that's helpful. So that when, if they try this with their own PD or teacher education settings, they will have some idea of what teachers might produce in terms of the models that help explain their solutions.
18:59
So to wrap up, let's kind of illustrate again, what are the new contributions that your article makes? And how does it inform other math teacher educators,
19:12
this article really does two things. One, it provides a conceptual frame for people to see the relationship and interaction between mathematical modeling cycle and social justice discussions, and how they can mutually inform each other. When you have a very rich, very relevant task or social context, community context that can generate those kinds of discussions. And so I think that the conceptual frame is very helpful. I also think that our detailing of how we implemented this with pre service and in service teachers plus the lesson overview provide some guidance for math teacher educators to have the confidence to include in a consistent manner, so social justice issues in their mathematics teaching methods courses or their professional development, as well as emphasizing mathematical modeling, since it's so emphasized in the standards of different states, I also would want to make sure that people take a look at the implications section of the article, in which we talk very carefully about how you can also develop such tasks. And part of it is, you know, being aware of articles and newspapers or images, photographs that would generate math modeling context for your teachers to explore. And to realize that it's it's important to think about when you decide that maybe this context has a lot of potential, that you think about the dignities, and complexities of the communities who live in those in those communities. So the example we give is that when we first decided to implement this task, we invited a teacher, educator colleague of ours, who was working in working and living in Flint to see if she would like to try this activity out with her teacher candidates. And she declined, because it was too real, too raw, they were too much in the moment to be able to engage in something like that. But two years later, we had some colleagues who were working with teachers, elementary teachers in Flint, and they did the activity with the teachers in Flint. And it spawned some really nice examples of teachers now deciding they would create similar tasks for their kids. And one of the tasks was with a second grade teacher who created a task in which students explored how many bottles would their class need for a day, and their lived reality was having to go and get water bottles every day for their class. And so two years was, in this case, enough time to get a little distance from the situation and be able to engage in social justice and, and mathematical modeling discussions. Whereas if, when we tried it earlier, people weren't ready. And I think that that's something that Matthew educators when they are thinking about the relevant context and exploring social justice issues need to really examine and make sure they take into account with sensitivity, the communities in which all situations may be happening, we give some pretty good advice and tools and resources for people to think about and create such activities.
22:37
I agree, let me summarize, I think the three points you mentioned, one is that you are presenting this Flint Water task in a way that really allows somebody to go ahead and implement it and get some background from what it was like when it was implemented somewhere else. So it's a nice first step, if one hasn't done this, or hasn't done it a lot. And it's also a very concise task, that is doable in a one three hour lesson or something like that. The second thing that you're contributing is the framework with the circles. And it's a little bit hard to describe without the picture, but it's definitely worth downloading the paper and reading it. And then the third thing that was really useful to me as more noise in this area, is exactly what you just talked about that the end is implication section. So how do I take this Flint Water task in kind of create other tasks that are similar? And the way you're talking through this, the notion of something being ill defined and looking at the paper and seeing if there's something similar? makes it feel more doable to me? Because often, I think when we opened a paper, we go like, Whoa, there's missing information yet, right? That's the way how we read the paper. And so now we could say, Oh, that's ill defined, that could be a good task.
24:09
Right? We need to define the quantities Yes, or make assumptions and reading and try to figure it out. I was also going to say that one of the things that I think is also very powerful, that math teacher educators as a community we need to do better, is to really think about ways in which we can normalize conversations around social justice in mathematics, teaching and learning contexts. And the more we do that, the more natural it will become. So we'll be coming. We're going to normalize it and then by the fact that we're engaging in these rich conversations in which kids can bring their kids and teachers bring their experiences to the activity and they're trying to make sense of it. We essentially start to humanize again, mathematics learning. And as we know, we need to do better at that both normalizing and humanizing mathematics. And its connection to the world we live in. And so I would say that if this is a great starting point, and people see themselves as that they could do something like this. This shouldn't be something that is just a one time thing. This is something for you to consider as part of your approach to teaching mathematics. And the more you do it, the more you engage in thinking around mathematics and social justice at the same time. And math modeling is a way as an entry point into those conversations. I think we would do better as a community to make mathematics more which rigorous and relevant to the teachers and the students that we work with.
25:43
I agree with us, and I think that's a really nice summary statement. So I'm gonna wrap us up by thanking you for talking with me. For further information on this topic, you can find the article on the mathematics teacher educator website. This has been your host, Eva Sennheiser. Thanks for listening and good buddy.