 Happy to announce our today's activity. So this is a panel discussion and let me give you a little bit of the history. So as you all know, I hope that there is this week the workshop for equity in mathematics education, which has been taking place in one of the rooms down the corridor. And so this is a great event that's been happening at PCMI in one form or another for the past eight years or so. And every year now the leader of the program changes and so we were extremely fortunate to attract Rochelle Gutierrez, Professor Rochelle Gutierrez from the University of Illinois, Champaign Urbana, who is a renowned scholar in this subject and she's been leading her group wonderfully this week and I asked her to lead a panel discussion. This was an idea of having such a panel discussion for the past couple of years we've been doing this and this is a great way to share with all of the PCMI participants what the workshop has been doing. So joining her on stage are Brian Katz and Marielle Myers. So let me turn it over to them. Wonderful. Good afternoon. Buenas tardes. Buenas tardes. Okay. Oh, Mike. So I just wanted to start by acknowledging the land. I mean as a white settler nation we are standing here on stolen grounds. We are meeting on stolen grounds. These are the ancestral and unceded territories of the Shoshone, the Paiute, the Goshute and the Yute nations and I pay my respects to those who have struggled to live upon and nurture and save the land upon which we are currently meeting. We started this, we wanna have a conversation with you in three parts. The first part is that we wanna talk a little bit about why we've made this shift. Why have we shifted from talking about equity to talking about rehumanizing mathematics. Then we wanna spend a little bit of time and we'll introduce a framework. Then we wanna spend some time talking about what are we doing in these projects when we're in the other room over there, that room that sees the locked door that everyone says we can't seem to really get in. What is it that we're doing in that room? And then we're gonna move to some loving challenges and to some suggestions of how we hope we can all move this work forward and answer some questions that maybe are lingering in your mind. So we start with the fact that we've all been grappling with whether or not this word equity really captures the kinds of things that we wanna accomplish in our work. And for me, that word equity feels like it's been bogged down in history. It's something that even when we think, even when individually each of us wants to think about how our work is more complicated and more sophisticated than what that word typically captures. When we're in conversation with other people because we use that word equity or we use a word diversity or inclusion or any of those other kinds of words that are more mainstream, it stops us from being able to have dialogue and visioning because we don't stop in the conversation and say, well, wait a second, when you say equity, what do you mean by equity? When I say equity, I mean it this way. We just assume that we're talking about the same thing. And we actually really only know we're addressing equity when we're so far away from our target. So in other words, we might as a math department say, wow, the students that are in our math program don't really represent the people that are in society or the people even that are at this institution at this university. And so we wanna change that. But then as you get closer and closer towards who's actually in your program and how are they supported, maybe not everybody's on board with what's happening as you get closer. So again, it's this idea that we can all agree that we have this far off kind of direction that we wanna move to, but we may not all agree on the same destination. And also that word equity tends to privilege a kind of universal and a white stream way of viewing things that we really care mostly about getting, opening the door and having more people be part of this practice of mathematics and not that we actually expect mathematics to change. And the way I frame it is I often say, we say that people need mathematics in their lives. We say they need it because it will help them be good problem solvers. It will help them be engaged citizens and be able to be critical of graphs and other information that they're constantly getting. It will help them get better jobs and be part of STEM pipelines. And we never really ask, well, is this really just a one way thing? Is there, or is this thing two ways? Maybe it's not just that people need mathematics. Maybe it's that mathematics needs people and who those people are might ask different questions, might have different purposes for wanting to do mathematics. And so really kind of coming to this position of, well, maybe we need a new angle. Maybe we need a new angle on this very long-term problem and maybe that angle is more moral and humanistic than it is technical. So that's really kind of how we got to doing this work. We'd like to encourage you to think about. Oh, so we wanted to make sure this was active before the Q and A. And so we have a think-perish your activity for you. So we'd like you to take a minute to think about a specific mathematical experience that felt alienating, marginalizing, or dehumanizing to you or a peer or a student. You're just, you're trying to generate a concrete example and we're sort of intentionally asking you to brainstorm before we give a definition. And I know this is a very personal thing that we're asking you to think about and then share. So if you'd like to generalize it to this could happen or I could imagine this rather than this did happen to me so that you feel safe talking about it with your partner, that's perfectly fine. So take a couple of them, maybe one minute, quiet. I think I have three, three minutes. Okay, at least one minute quietly and then at least two minutes with your partner. Go. So one minute to think quietly right now. Ready to start talking to your neighbor about your example? I might change to the next one, I'll present to her because I don't know what the next slide's on. And I feel like I'm kind of like, I'm forgetting where we are in the middle of, I didn't get to sleep last night. I'll leave it on the phone. I'm asking you to write your example on the note card. People are passing out note cards because there's gonna be other times when we're asking you to write something down. Going? Oh yeah, I feel like I'm definitely getting lost with the questions. All right, any note card to everyone or just people? Just when people want them? Because some people have started hanging around. Yeah, it's okay. It's okay, it's okay. Yeah, I need a lot of time to be where we are and if I don't know where we are in the hour. Yeah. I feel like. And that's so small, like I was trying to look there. Small. I think it was in 2016 and it was up in this stage and it was just black. I couldn't see anybody and there was just tons of people with bodies and it was a peanut yammer. Oh yeah. I was such a hot shock like to me. It was the most, it was the weirdest experience because I couldn't repeat those bodies. Oh yeah, yeah. I couldn't read expressions or anything. It was just really, and I was just talking to this. I was talking to this. It was like all about production. You know, like. I get a lot of talks though. That was different. That was different. Yeah, it was in some kind of special theater. Yeah, yeah. And so it was very, you were even just the stage, how far it was before the first set of seats. I think it's because normally there's like an orchestra or something else that's that space. Oh yeah. So you just felt like you were like, so far removed. I didn't set a top in three minutes, so. It's been two minutes of talking. Two minutes of hair talking. It's good. Okay. Let's come back together. So is somebody willing to share what you were talking about? Hello, hello. Testing, testing. Hello. Oh, oh great. Rochelle, you asked me to take a risk. So I'm gonna take a risk right now. This is about the parade. It was a high and a low experience yesterday. The high was the community. Of course we all love math and we have that spirit of camaraderie and we wanna share our love. And as we were walking halfway through, who were we serving? Who were we observing? Who were we seeing? We were seeing the wealthy and let's just call it out, white community, right? As we were walking down, we were seeing the demographics change. My heart hurts. Those of you who were maybe walking with me, I was chanting, viva las matemáticas. And who did we hear? We heard some of the people. Did we have any poster? Did we have anything reflect the demographics of the community that serves the population that lives here for maybe the summer? Are we representing math for all? My heart hurts. Are you guys hearing me? Am I, that parade was awesome because we share and reflect our passion for math. But are we sharing and reflecting our passion for the people of Park City? Some, but not all. Is there another person who'd be willing to share what you talked about? So in my senior year of college, my thesis advisor, who I'd come to admire a lot, used to jokingly abbreviate finite-a-billion groups as facts in our thesis work, not knowing that I was a gay guy. And so that kinda made it hard to feel like he was on my team. When I was in a differential equations class and I would work with another friend on homework a lot, and I got a test back and my score was significantly different than his and we answered a question very similarly. So we went to the professor and we showed them both our work and asked what went wrong. And he had told me that I had gotten it wrong on a previous homework and that I didn't deserve full credit. Let's just take one more. One more down here, in the front. So I wanna preface this by saying that I've had about as much mathematical privilege as one can have. I grew up in a family, you know, my mom's office is my dad's a mathematician, but my dad, oh, is this working? Okay, so this is a story about my dad who grew up in a small village in South India. His dad was an English teacher and when my dad wanted to take an extra math class in school, the math teacher said, I don't know why you're bothering. Your older brothers couldn't do math. Your dad can't do math. No one in your house, no one in your family can do math. Why are you bothering? And it wasn't until that teacher retired and a new teacher came in that anybody in my dad's family thought that math was something that was for them. So that was something that's always stuck in my head. So we've introduced a word, rehumanizing mathematics and we haven't really told you what it is. And we're gonna explain a little bit about the framework. But we wanna first just start with that idea of like why rehumanizing? Why are we using this word? And for me, that word re in rehumanizing really is honoring our history. It's honoring the fact that as humans we've been doing mathematics for centuries and that people continue to do mathematics. Thank you, sorry. And that people continue to do mathematics in outside of schools, outside of institutional settings that people are constantly doing this in everyday ways in life that are not necessarily sanctioned as mathematics. So for me it's about rehumanizing mathematics because it's not something that we're trying to move to that we don't know or that we have to create but it's really bringing back that which has been erased by the institution of schooling. I think all of us know about the kinds of playful things that we did mathematically as kids and then when you get to school you're taught you no longer know mathematics unless you can show your work in this way or unless you produce it with this particular algorithm or if you stop using your fingers to count or any one of a number of things. The rehumanizing mathematics is also different from the humanistic mathematics movement of the 80s and 90s in that the rehumanizing mathematics is addressing the politics and the power dynamics and oppression that is happening in society. It's recognizing that mathematics has been a project that has supported white supremacist capitalist patriarchy and that means that there are ways in which mathematics has continued to operate in ways that are very masculine, that are very universal and take away from what individual people feel and especially people who've been historically oppressed. It's and the idea of rehumanizing is not just to stop with that what's dehumanizing that when we ask you that question what's dehumanizing we can stop there and we can say wow that feels awful for us to focus on that but rehumanizing is to say more than just wanting to be decoupled from kind of economics and warfare and oppression and dehumanization we want to actually couple with belonging and joy and other kinds of concepts that Francis Su has presented to us in terms of the mathematics for human flourishing. And I say rehumanizing mathematics is a verb because it's not an adjective, we could say rehumanized mathematics that we're moving towards a rehumanized mathematics but I say it's a verb because it's actually gonna require from us constant vigilance and constant reframing and constant asking of the very people that we say we're trying to rehumanize mathematics for that they actually feel that it's rehumanizing. In other words we alone as math professors, as math teachers, as math coaches we don't get to decide that our work is rehumanizing for other people. We need actually testimonials or documentation from the very people who say you know what this feels more meaningful for me. You know what this feels more humane for me. You know what this makes me feel like I belong to something and I want to be here. And I say we could rename it decolonizing mathematics but I don't take decolonizing as a metaphor or as a word that we would use lightly unless we're interrogating land sovereignty, mental sovereignty, recognizing the erasure of culture and language that has happened through boarding schools and other spaces in the United States and throughout North America then I wouldn't necessarily use that frame. So these are the eight dimensions of rehumanizing mathematics and I'll let you just look at them for a moment and then I'll unpack what those mean. So when I moved to presenter slide now the slides that are there are tiny and I can't read any of the text. So I'm gonna have to continue to look back up at the slide behind me. Okay, so here's the first four. We have across the top in blue those are each one of four dimensions and actually I wanna go back to one second. When I'm here, actually this should be a 3D kind of sphere and there should be ways in which there's lines that are projecting between words and that this is very synergistic. This is also not suggesting that when I say rehumanizing that this is some kind of universal experience for everybody, I'm talking about how do we center the experiences of people who have been historically oppressed, women, queer folk, people who are emergent bilinguals. And so when we look at this we wanna be thinking about what are all the ways in any one of these dimensions what are the things that are the typical narrative in mathematics and then what's the counter narrative that rehumanizing mathematics is actually creating. So let's go back to these dimensions. So in terms of positioning and participation so what those rows mean is the first row is kind of generally what the thing is about. That's kind of just the content of the nature of it. The second thing is like what would it look like if we were in a classroom and we were looking for this kind of thing and then the last thing is just what's some literature that actually is related because this didn't just kind of come on from nowhere. I'm building on the work of many other people and trying to bring it together. I think the thing for me that's useful about the circles and the framing is that it becomes a mapping space for us. So I'm not trying to tell people how to rehumanize mathematics. I'm saying these are the dimensions we need to pay attention to and we need to map onto our practice and say how am I doing with respect to positioning and participation? When do I address windows and mirrors? Do people leave my classroom or office hours or summer bridge programs feeling like mathematics is a living practice? What exactly would I see that would convince me of that or that would convince students of that? So again, each, I'm looking at the time. Yeah, I have a moment. So if we look at positioning and participation, again, that's just the status in classrooms. So that's the idea of like who gets credit for a problem? If somebody says something and then someone else is basically the same thing, does the instructor come back to the person and give credit to that person for what they said? Are there opportunities for students to be authors in our classroom, to co-author the classroom with us? Or does it feel like this is kind of a dictatorial experience and I don't really have any say because mathematics is kind of just the way it's being presented? So I say here that the authority shifts from the text or the teacher to other students and to students as meeting makers. And so oftentimes you might see a student who's raising their hand or waiting for you somehow to come over and to tell them that either doing well or they're approaching their problem where there's people that are sitting around them. And so that feels like the positioning and the participation is not a rehumanizing experience. And we can look through each one of these and look at how those are playing out. If you don't know things like ethnomathematics or funds of knowledge, ethnomathematics has been around since 1985. Ubi de Ambrosio has talked about the mathematics that are being practiced throughout the world and all of the mathematics that many times are not sanctioned by school, by institutions, by the West. People in ethnomathematics also point out that math departments in North America and through much of the West that those people who it's not an ethnomathematics is in, there's cultures like, I think many people could think of, oh yeah, there's the Mayan Vigestimal System base 20 and oh yeah, there's the concept of zero that was created in India or there's, but it's really recognizing that every culture has a culture of mathematics. So that means math departments at universities are also operating with an ethnomathematics. There's a particular mathematics that's being shared among people in terms of the culture, how we practice it and what we do. And you can think about it from the point of view of your work too, like what's the culture of how somebody would represent and talk about number theory different from, say, topology, say from something else. So we're all operating with these kinds of cultures. And thinking about when does mathematics actually help us reconnect students with their own histories and their ancestors and roots? And again, not just thinking about it from the point of view of it being ancestral as in pointing back that there were people a long time ago who did this, but who are the people today that are still doing this? Some people have been doing this through the work of having their students doing biographies on mathematicians after 1950 so that people recognize that it's not just the old dead people that we can point to. And again, you can look through, who you're pointing at, who's in the audience? In terms of windows and mirrors, the reason that I like this term windows and mirrors instead of something like, it includes things like culturally relevant pedagogy. Some of you, how many of you heard of that word, culturally relevant pedagogy? So a whole bunch of people at the back. Wow, what does that mean? A whole bunch of people at the back and then some people up here in the front. Culturally relevant pedagogy or these kinds of social justice pedagogies or curriculum, oftentimes those to us sound like they signal there's something for other people, but they're not something for everybody. So culturally relevant sounds like, oh yeah, that's for the black students or the Latinx students or for the, but it's not for everybody to be doing. So again, it windows and mirrors recognizes that we actually all need ways to see ourselves in the curriculum, that's the mirror, and ways to extend ourselves and to grow and to see a world that maybe is not necessarily us and that's the window. And so asking ourselves, when are we providing windows and mirrors to students where that doesn't create the kind of binary that like this is for these people, this is for those people. Any given example could be both a window and a mirror. So I'll give you an example. If we think about a social justice mathematics project, we might say, well, we would assign high school students the opportunity to think about the probability of you being harassed because you're standing on a corner near your high school and you're all black students. What's the likelihood of you being pulled over by the police because you're gathering there? Even when you can see across the street, there's three other groups of students who are gathering and nobody's bothering them, right? So you might use mathematics as an analytic tool to look into that situation and then prescribe, well, what should the school do differently through mathematics, right? So that thing we could think of as social justice mathematics, but we can also frame it as, well, that very problem can feel like that is a mirror to a student of color who is constantly pulled over by police or is constantly harassed when they're gathering with friends because they stand out, but that very experience of that for a student who's maybe white and has never even thought about the fact that I stand on corners all the time and have never been hassled, that then for them becomes a window, right? So it moves us away from thinking about there's those people and then there's us or there's some kind of like normal that is white and then there's everything else that's compared to it. The living practice is recognizing that we are currently working with a modern mathematics, a very young mathematics, and that there's ways in which it is changing and that we are breaking rules or adding new postulates and that's really changing what we're coming up with and making that visible to students. The other four dimensions are broadening mathematics, creation, body emotions and ownership, and under broadening mathematics, we have at least in the K to 12 curriculum and many of you probably feel like this is true at the college level curriculum as well. We have a very prescribed notion of what counts as mathematics. We give people this idea that there's this really strong focus on the kind of algebra to calculus pathway and when we bring that even lower grade levels we can say well, that's a lot about numeracy, number sense and not necessarily things like spatial reasoning or other kinds of mathematics that we could value. And under creation, not just reproducing what has come before you but thinking about like, well, how do we present to students an opportunity for them to create mathematics? So some of this comes from what maybe people know of as discovery mathematics or constructivist mathematics where we might say you're going to discover that pi is the relationship between the radius and this object but you're not necessarily, even in those experiments or in those ideas, maybe this is something that the students that they're creating and it's new for themselves but it's not necessarily new to our field but I'm saying like, how do we even get students to start thinking about things that would be new to our field? So in history pointing out the kinds of ways that people have broken with rules, we might think of okay, when students that are in elementary grade are presented with addition, subtraction, multiplication and division, those are four operations, what if we said to them what if you came up with a fifth operation? What would that look like? Why would that be necessary? How could it be helpful? How could you be internally consistent in your system? When would it stop being useful? Those kinds of exercises I think get us to the point where I think many of you know that when you're in higher levels of mathematics, you're not just following what other people have been giving you but you're constantly thinking about what if I started with this conjecture? What if I ignored this postulate? What if I added this postulate? So again, thinking about where can we get that kind of creation to come into play? Body and emotions is really recognizing that for many, many students, the idea of mathematics is that it's really about a brain and then some kind of form of representing. So whether that's paper pencil or whether that's a calculator or that's a computer, it's never really asking do I need my body, my full body, my senses, my physical body to do mathematics? And so thinking about when can we actually invite the senses into the classroom? When can we invite the body? When can we invite students to not be able to do math problems unless we literally have another body? And so that might mean that we need like walking scale geometry problems or we might need graph theory problems where you actually are on the graph and you are part of the problem. In terms of ownership, again, recognizing that mathematics can be something that is not just something that other people give you but that it's something that you would do for yourself that you would want to do because it's joyful, because it's playful, because it's a form of expression for you. So again, where are we looking for opportunities to do that in our spaces? So I'm bringing you back here to the eight dimensions and giving you a second to look at that. Oh, okay. So we're gonna skip this. We were gonna ask you what we thought in terms which of those, so maybe you're just processing this in the back of your head. Maybe you're writing it down on a note card if you had a question for us and we're moving on. I can't see what the slide's saying. So what have we been doing for this week that we've been here? So what have we been doing? We have been taking that framework and we've been taking that framework and we've been saying, when we have guest presenters, so we have had mathematicians who have either zoomed in with us or who physically come and presented how they're taking a course and how their students are all creating a wiki and they're actually writing the textbook for the course or somebody has radically changed their assessments and how they're using group exams and how they're having students reflect on their emotions as they're taking exams and things like that. We've had all different kinds of presenters for us and we've been analyzing what they present to us through this frame and then we've been thinking about our own action project. So everybody that's in the group is presenting, it came with an idea of I wanna go do something when I go back home and then thinking, okay, how do these dimensions relate to it? Hello, everybody. I'm just gonna talk a little bit about my journey. My name is Mario Myers. I'm an associate professor of mathematics education at Kennesaw State, just north of Atlanta, Georgia. And so I've been thinking about these issues for quite some time and I remember when I first came into the profession and I was really kind of gung-ho about culturally relevant pedagogy and I felt like that's not really working for me and I started really thinking about equity and I was like, oh, this isn't really working for me and I kept having to have these debates about equity versus equality and why aren't those things the same? And I just felt like it wasn't getting me the mileage that I wanted and so then when I started thinking about what does it mean to rehumanize mathematics, that seemed like it gave me a framework to really think about structuring my course. So much of what I do is to prepare elementary mathematics teachers. Yay! So excited to have elementary people in the room with me or that love elementary mathematics. And so,