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 Anheuser and I'm talking with Lynette Guzman, who is an assistant professor of STEM education at California State University Fresno in the Kremlin School of Education and Human Development. We will be discussing the article complex and contradictory conversations, prospective teachers interrogating dominant narratives within mathematics education discourse, published in the September 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 Lynette shared in the article her successes and challenges and how these lessons relate to her other work. Lynette, thank you for joining us.

0:57  
Thank you for having me.

0:58  
So let's jump right in. Can you give us a brief summary of the article, including your results, this

1:04  
article is actually from my dissertation work at Michigan State University, I was working with a small group of prospective elementary teachers where we were meeting regularly. So this is a piece of that larger study, I was really interested in exploring and disrupting the kinds of ways that we talk about people in mathematics, and particularly children in mathematics in schools. So the kinds of larger stories that we tell about being a math person not being a math person, what that looks like, and in turn, what that means for future teachers as they approach their professional work, working with students in the future. So the article is a case study of a type of activity that I designed, where we were looking at the kinds of big points or discourses, stories that are told, using a an idea mapping activity, putting ideas together that seemed contradictory, or that could seem contradictory. And using that as a way to open up more in depth and philosophical conversations about what it is that we believe about teaching and learning, particularly with mathematics content. So that's the general idea is, this is me to sharing my experience of what I learned from designing that and implementing that with a small group to think about as a mathematics teacher educators, how can we provide opportunities for future teachers to tease out these discourses a little more to reflect and possibly come to other kinds of perspectives about teaching and learning mathematics?

2:42  
So when I read your paper, I had to look up what idea mapping was. We're gonna get to that throughout the questions, I think. But let's just keep that in mind that at some point, we want to get there. Who do you think should read this article or listen to this podcast,

3:01  
particularly, I wrote this in mind for other teacher educators. But I think that anyone who works with within mathematics education might find it valuable, or even in so I'm currently teaching in our single subject credential program. So I teach not just future math teachers, but across all subject areas, which is really exciting. But anyone who works with teachers, people who teach children, people who have an interest in education, and the kinds of stories that we tell about teachers and about students and how things fit together, how they don't, I would even say, people in administration, or anyone who is interested in these larger issues, when we're talking about education, the kinds of arguments that we make, and how these ideas fit together in a very complex system. And so there's bound to be some sorts of contradictions or at least tensions and the kinds of values that we're trying to advocate for, and how that works out or plays out might be challenging. But if we're able to, one, acknowledge and articulate what those tensions or contradictions are, then perhaps we'll be able to find nuanced ways to address the issues that we seek to mitigate in education.

4:17  
So that leads us nicely into the question of what is the problem or issue that you're addressing with your work.

4:24  
I'm trying to get people to slow down and think about the kinds of perspectives that we are sharing or re sharing in the work that we do. So working a lot with teachers, and having a critical perspective. I mean, as people who think about schools schooling a lot often as in my position, and the work that I do, I hear similar stories of like, these are the problems of education or we want to address I'm gonna use a specific example we want to address this issue of being a math person or not. And so that is As an issue of equity, so if some students see themselves as not being a math person, then that poses challenges to the mathematics education and the experiences that we might have in mathematics classrooms, and also the opportunities that might be available or that students might see as not available to them if they don't see themselves as math people. But for me, it's the issue is stopping at those like very recognizable phrasings or calling. So like being a math person, like we want to address that we want everyone to be a math person. But then if we take that approach, then these other challenges that maybe we didn't anticipate come out. So it's more about trying to, to think about ourselves in complex ways to be able to I don't know, I think that my goal right now, I mean, this has been a while since I had this specific, these are 2016 quotes in the article. But since I've been working with these ideas, more thinking about just acknowledging ourselves as people who grow, and it's okay to have these contradictory things, or think about I say, this idea in one context and this idea and another context, how does it fit together and to take that with that complexity of we're all complex as humans with care of taking that as teachers who are always trying to grow, always trying to learn, taking yourself as like that case of I'm complex and contradictory. My students are complex and contradictory. We each are. So I think more so my goal right now is to take that and bring it as a source of empathy. We're trying to be more empathetic as humans interacting with each other in the world. And so this is one way that I'm trying to approach that.

6:47  
So let's get a little bit more into this of it. Can you explain the idea of mapping activity a little bit?

6:54  
Yeah, so in this idea mapping activity, I had a one giant chart paper that we were all contributing onto. And the idea of mapping, it's kind of similar to a concept map, if people are familiar with that, so you have a main idea. And then you might have a connection to another idea. And there's like a link between it. And so you might have related ideas to a central concept. But those related ideas might also be related to each other or branch out and create sort of a web of ideas that are related to a particular topic. So being a math person, you might go into other conversations about identity, or you might be specific of if I'm going to think about what math person means in the context of, I am a brown woman. And I've been seen as good at math. And like those sorts of storylines or stereotypes or so you're creating this web of ideas. And so it's similar to that. But we were using with paper, sticky notes. So each person had a pad of sticky notes, and was able to we were create co constructing this idea map together. So I might put my idea of like, oh, something that's important from the conversations we've been having is being a math person, because it keeps coming up over and over and someone else might contribute. Okay, well, I think anyone can be successful with mathematics. And so like that they would contribute that to this, like chart paper idea. And the reason that I chose sticky notes is that we could easily move ideas around and be more fluid with it, rather than drawing it out or even using a whiteboard and having to erase and rewrite. So having the physical product for this specific activity was useful. But of course, there are digital resources where you can do a similar idea where you're contributing ideas and adding to this larger collection. And so the idea mapping as the facilitator, my job, well, I was fully participating in the activity myself, so I had my own pad of paper, or sticky notes. Each person I'll also note had a different color pad of sticky notes. And that for me, as a facilitator was to be able to look at the different colors, the distribution, who is participating, or adding the ideas and use that as a way to make particular moves, inviting people to contribute to the conversation if necessary, but as the facilitator My job is to really it's it's actually a lot of mental labor to pay attention to what is on the chart paper. What are the ideas there? And are there possible tensions or contradictions that come up within this like I mean with it across the group of people maybe but like, even within a person, a single person who is contributing an idea and contributing another idea that might not seem to fit? So the goal for me in the facilitation is to look at the math and see are there sticky notes that I might want to place together? And bring that pose that to the group as some conversation to explore. Are there contradictions here? Is there more nuance that we could further explore and come to some sort of discussion, it doesn't necessarily need to come to a nice conclusion of, we've resolved the contradiction, because from my perspective, the activity itself, the experience itself, of just going through and thinking through ideas put together that maybe you didn't have an opportunity to put those ideas together before is the valuable experience, it's not necessarily the goal to have everything be resolved. It's an ongoing conversation.

10:40  
So in your case, you described that you met with this group of pre service teachers once a month over the year, what was the goal of those meetings,

10:49  
so we the broad goal was just to explore different research areas, different kinds of tools of how we can see children engaged with mathematics in our school context. So that was the larger project. So we went to site visits, such as we went to a science museum, they also went on a math nature walk. And so there were different outside of school spaces where the goal was we're going to observe children, not in classrooms, to see if we could make connections to mathematical practices, or ideas in what children were doing in the everyday. So it wasn't surprising actually, that the the conversations that kept coming up as being a math person, or that everyone can do math, because that was basically the focus of what we were trying to look for. So if you're looking for something, and that's your focus, yet, we did find a lot of it. And it was it was really exciting and powerful, because moving outside of the classroom context, provides some sort of space for possibly different kinds of conversations about children and math and what that looks like. So that was the goal of these monthly meetings. But with that said, even though we were having these experiences, and out of school spaces, those dominant discourses about what math is, and what that looks like, still came up, because it's still part of the larger kinds of ways that we talk about mathematics and who is successful with mathematics. So that was part of the goal is to try to challenge those ideas a little bit and open up, broaden the ways that we see basically how the brilliance of children and how they not only engage with mathematical ideas outside of the school, but how it's Messier. It's not clean. It's not simple. It's connected to other ideas, other subjects, other disciplines. And so that messiness is where we like to play around and kind of challenge what it means to do mathematics. So I think you just jumped ahead to where what my question is going to be, but I wonder if you could just restate how this idea map fits in with those meetings

12:54  
that you've had. Yeah, so

12:55  
the idea mapping was the last meeting that we had as a group. So this wasn't something that we started with, it was more of an exercise of, let's reflect over the course of our year of meetings, and try to come up with something meaningful from like, look at all of the things that we've done all of the ideas we've explored. And let's try to make sense of them. And we had already done a couple activities where so they had reflective journals, where they are keeping logs of their thinking at different, like different snapshots over the course of the year. And so we had already done an exercise where we were looking at our previous journal entries, and we were reflecting on our own words. So it's not the first time that we've done a reflective exercise where we were analyzing what we had said in the past. But it was something new in that we were creating this map together. And it wasn't it wasn't just an individual reflection type exercise, it was something a collective like, we're trying to explore these ideas. And with an explicit focus, if we're trying to find contradictions, contradictions are okay. It's not necessarily bad, because we all have them. And that was, that was something that was very important for me to communicate. Not only that, we have contradictions in our ideas, but I even have contradiction in my ideas. I don't know all the answers. It's okay. Like this is part of why we have this learning community, we're trying to help each other as colleagues, and we might not have all the answers, but we can have this experience where we're still continuing to question what we see, I think that was fits in with a larger purpose of this group is we're trying to question what we see. And so going in these out of school spaces was one way and then looking inward at ourselves and our beliefs philosophies was another way that we did that

14:53  
in the paper. There's a really nice picture of your ideal map if anybody wants to go and look at that and you also Provide an appendix for people who want to do some of this. So there's some helpful ideas in there. You started a little bit, but I would like to explore a little bit more in and let's put these two questions together. How does the work you do fit in the larger work that you do? And how does the work you did in this article fit in? within the method research? Yeah.

15:24  
So the work that I do, I want to first point out that fired by a lot of ideas, but one in particular was an exercise that I had to do in graduate school. So at Michigan State, I was with Dr. Beth herbal Eisenman, and she had us do this willing to be disturbed activity every single week. And so this comes from Margaret Wheatley. And this idea of either making the familiar strange or the strange familiar. And so basically, the the exercise of willing to be disturbed is to listen and analyze and critique basically, your thoughts or other's thoughts, with an openness to understand, I guess it's like the best way that I would put it. And so part of why we would want to do that is maybe we're not so different, or our ideas aren't so different, as we might think, or maybe our labelings of who is on our side or not, is not what we think. And just having this again, focusing on empathy, trying to understand people have rationales for believing what they believe, or perspectives or experiences. And so what is it that we can learn from other people. And the other piece of it of why I like to think about willing to be disturbed is this urgency or not urgency, but like this desire to not be complacent with where you are, I might not know at all. So I'm going to be open to the idea that I could be wrong or that I might need to adjust what it is that I believe. And so that's kind of, in the larger scope of things. That's where a lot of this comes from. I've used some of this in my current teachings, I mentioned the single subject of thinking about. So an example would be thinking about wanting students to express creativity. But then also an idea that we might believe is that students need to first learn the basics or fundamentals. And so those might conflict because we have this desire to have students be open and creative and do all these wonderful things. Yet, we're also holding up you but they need to learn things first, before we can get to that maybe at the detriment of this creative thing. And so that's kind of how I've been using that in my current work of trying to explore these broader I mean, it's not just specific to mathematics education, which is why going across the subject areas is interesting, because we can get at these big ideas about teaching and learning and those philosophies. And of course, within a subject area, there are possibly those more specific discourses that could be explored. So I'm very familiar with the math education ones, but I might not be as familiar with some of my other colleagues, like in history or art. But there are discourses that are common that we can explore a little bit more. And then the mathematics education literature, I mean, this I really am an advocate for equity and justice and mathematics education. And so fitting this in of particularly this question of what is it that we are meant to do in mathematics education? Is the goal for everyone to be to see themselves as a math person? That is a tricky question to explore. It is something that I mean, in terms of equity efforts, like that sounds great. It's wonderful. But at the same time, there's a lot of questions and nuance and hesitations there. And there's the prospective features I worked with, in this article started to get at some of those really deep questions that and one of the things that I really appreciate about this, and something a point that I wanted to make with this article is that through this exercise, and this openness, and this exploration, particularly with a goal of not necessarily needing to get to a perfect resolve is that the prospect of teachers I was working with, were able to work as philosophers and as knowledge producers. And this was an opportunity that wasn't like, I'm the teacher educator with all the knowledge you learn from me, but we're exploring kind of really deep questions that even professionals in the field don't have consensus on. And so that to me was really important in the context of mathematics. Teacher Education thinks

19:35  
I'm trying to slide into the next question, and I'm not sure if this is appropriate. So just let me know if you feel that it isn't. So one of the questions we typically ask is what new contribution to our field does your article make? How would you respond to that?

19:51  
So this was actually a question in my dissertation defense about this particular article, because I personally am hesitant on this Like, this is what it contributes. So all I'm doing with this article is I'm just trying to offer an example of something that I do as a math teacher educator. And I'm not telling everyone this is the way that we should all be going. But this is an option if people want to take up these ideas in their own practical work working with teachers. And so that is the contribution I'm trying to offer is it's okay to be messy, it's okay to explore these conversations. I think that from what was said in these conversations, I mean, again, they experienced to me is what was worthwhile, rather than, like, I have evidence that every single one of these teachers is has this sort of perspective or can do these things. But that's also for me, I think that I, at this point in my career, I value philosophy a lot. And having these philosophical conversations is important for thinking about how is it that we're even framing how we see teaching and learning mathematics in schools. So I would say that's probably the contribution, this is just something that if you do want to take up some aspects, sure, that's great. If not, that's fine, too. But this is just one approach. I mean, I tried to also articulate through the revision of this article, the challenges, there are trade offs to if you want to do this sort of work. One is that it does take a lot of, it does take a lot of mental labor, it takes a lot of vulnerability, it takes a lot of you know, that relationship building to be able to even facilitate this activity. And in this example, it was with five students. And that's not the size of any methods class, you know. So there are trade offs to or limitations to the kinds of things to be directly applicable to math methods, classes. But I do think that there is potential to at least take up some ideas and make adjustments and figure out how it could fit in a mathematics course.

21:57  
So I read this article this week. And I'm thrilled, and I created a Padlet, which is what you suggest in the article for larger groups. And I'm going to actually use it in a class that we're talking about learning theories, and how we all view learning, and there's very different views across people in the class. And so I actually thought this is a really good way of allowing people to put ideas out, and then potentially taking those up. I also loved the fact that you use color to kind of made me think a little bit of the equip tool that measures participation, right? Because you can kind of have a view of who participates, and so on Padlet, I couldn't figure it out the colors, but you can attach names to sticky notes. So you have kind of an overview of who participates how much. But you can choose not to do that if you prefer people to do it that way. Anyway, so I can see many ways that people could apply this idea in, I could even apply it in a content course I teach content courses, not methods, but we come up with contradictory ideas like, you know, should kids be allowed to like to creativity? You mentioned, Rachel, Debbie allowed to develop their own way of doing math? Or is it really important, they use the standard algorithm, and there's arguments to be made on both sides. And I was really intrigued by your notion of putting contradictory statements together. Because in a class that's often difficult, you know, it's like, who is right and who is wrong and making peace with the fact that maybe we're all right and wrong song. I just think it's like, I think everybody should read this paper. And I think everybody can use it in some way, not necessarily the way that you used it. But it inspired me to do some stuff. And I'll let you know how it goes. Yeah, I'd

23:51  
love to. That's great.

23:52  
Yeah, I was really thrilled reading that. So let me close out by just asking, Is there anything else that you want to add? Before I do? My little spiel,

24:02  
I've tried an adaptation of this sort of idea in my current class. And I think that, I mean, I need to try it in more sections. But one thing that I have been thinking about a lot is, many of my students are what we might label as Generation Z.

24:21  
And it's

24:22  
something that I have been thinking about but haven't studied, but I'm sure other people who study Gen Z might be able to give more insight on his thinking about a generation growing up with social media with that has canceled culture or people digging up like ideas from a long time ago and critiquing them and holding out. I have personally noticed anecdotally hesitation to share some of these like ideas that might go counter or this You know, shutting down shutting off. And so that's something that I'm currently trying to think through as a teacher educator, as someone who designs instructional activities of having what is it that we do with that sort of dynamic as well, that's not in the article. But it is something that I've been thinking about more in my work of being sensitive to the vulnerability aspect of it. If you're putting your ideas out there, even though we're in this learning context, even though it's very unlikely that someone's going to blast you, but still recognizing that that is possibly a dynamic that is that might impede this sort of rich conversation. And I mean, it's not specific to Generation Z. But the reason I'm bringing it up is because I'm trying to acknowledge the contextual aspects of I don't know what it's like to grow up with social media. I mean, I I'm all millennials, I grew up with the internet. I understand that perspective, but it is something that I've been trying to think more carefully about in my work.

26:05  
Yeah, I think that's gonna be so interesting to see as we move forward. Right? What, what's happening? Well, thank you so much for joining us. For further information on this topic, you can find the article on the mathematics teacher educator website. This has been your host, Eva Sennheiser. Thank you for listening and goodbye.