 So how do I challenge those aesthetics of math in a way that also honors the different ways that my students can represent their understanding? So it's, yes, I'm still teaching math, that's what's paying the bills, but as well, and how am I helping them to represent it in a way that they have, that they understand, that allows them to be kind of static with it, maybe representing patterns and braids, maybe through poetry, maybe through an art installation that they create, or podcasts, like ways that give them other ways to represent their understanding beyond just a paper test and then getting validation through high stakes testing. And where I am growing is trying to reflect on what has been my own training from my undergrad to my master's, and that was, oh, while you're training young mathematicians, call them scholars, but I've been reflecting more on what has been my own journey and my joys and pains, but really thinking about how I'm not training mathematicians, I'm encouraging my students to be confident in their mathematical know-ins, and in order for them to help highlight that, I have to get to know that and broaden my own understanding of mathematics. That's part of my project. That's Francis. Thank you. Thank you. Hi, everybody. I'm Cara M., and I think of myself as a teacher with teachers. I used to use the word teacher kind of, for teachers, louder, and I live in New York City. That's kind of my current home place. I moved to New York City in 1998 with a social studies degree, and through advisement and coaching, I also decided to pursue a second credential in mathematics. For many years, I taught middle school, and after several years of teaching middle school in New York City, I realized that I loved working with teachers as well, and so I became eventually the co-director of a space called Math in the City. Some of you might know that space at City College. I got to build mathematical communities of teachers from across the country and beyond, and we thought a lot about what that work looked like. I'm now gonna interrogate that work, but it was a really happy part of who I am as a person. I also started learning by becoming a researcher, kind of a reluctant researcher. I wasn't sure I wanted to be a tenured professor and to do research my whole life, but I was really wanting to participate in the work of mathematics education beyond the work I could do as a coach or as a kind of teacher educator. I wrote a dissertation that I defended during the pandemic that was the title of which is modeling where it matters, redesigning math education with adolescent girls of color. I was really concerned about and fixated with a paradigm in New York City and beyond that I would call repeaters algebra, the ways in which systems treat algebra as a gatekeeping device, and it's designed to keep some children out of higher mathematics. It's designed to keep and allow other children to pass through, and that gatekeeping effect is gendered. It's about class, it's about race, and I was really interested in trying to disrupt it through research. So I have a design study, and what that meant is I was simultaneously a teacher and a researcher at the same time. I didn't wanna contribute to that paradigm that has been solidified and is part of bigger structures, like white supremacy. I wanted to imagine something different. So my study is about what a classroom would look like and what role mathematical modeling might play in centering girls of color's stories and lives and mathematical identities. I'm still learning from that research, and I'm glad to be in this space. My project now, I work in partnership with schools across the country, specifically New York City and State, including some schools of colleagues in this room. So shout out to all of you. I think I'm intrigued and growing by this work. I find words like equity and inclusion and algebra for all. I find them kind of empty rhetoric, and it's very easy as a white woman trying to do good work to pat myself on the back for work that is not dismantling and not substantial and not transformative and doesn't interrogate my own privilege and power as a white woman. So I kind of needed a place that is here to really think about that work. I also have found that though I love mathematical community, it was another space where I didn't need to think about all the beautiful intersectional and unique mathematical identities that were in that community, including many that were devalued. And so I'm kind of holding in place the importance of acknowledging mathematical identities that are intersectional, that are racialized and gendered, but I'm also kind of thinking about how that plays into a space called mathematical community. And I guess finally I'm learning through Rochelle and through my friends and colleagues here how to be an accomplice and not just an ally. Rochelle wrote a beautiful paper in 2017 about backlash in math education and that has been speaking to me for a while. For me, that means kind of really interrogating all the ways that I benefit from a system and power and privilege, how I use language to give you a specific example. I think I used words previously, I would consider things like kids on the margins. And now I understand that those kids have been marginalized by systems, but that's not a neutral act. They didn't end up there by happenstance. And so the work is really much bigger, much heavier. And I'm really delighted to be here and to take something back with me to New York City. It's still in development and I look forward to kind of developing it throughout this week with my colleagues and friends. Thanks Kara. I'm Patrick Morris. I'm a math professor at Foothill College in Los Altos Hills, California. That's in Silicon Valley. We're an open access community college. Google and Facebook and Apple, they're all right there. I've been at Foothill for about 20 years, 21. I had about 10 years in teaching before that and I had a first career, about 12 years before that. Y'all can do the math. So I got to the classroom and I came in as, my first career was an actuary. I was building and using mathematical models of contingent financial events. So I came to teaching and I said, well I'll just make a mathematical model of student learning. How hard could it be? And I tried and I've got a lot of background with modeling and it took me about 15 years to realize that the mathematical model of points in grading is gets in the way of student learning. So in 2008 I abandoned points and percentages in my grading and I made qualitative assessment version 1.0. I have been challenged along the way most recently by some of the concepts in rehumanizing mathematics. In particular, the way that the body and the emotions impact student learning and its display. So I'm working now to move from version 7.4 which is the last version of assessment policies I used in the classroom right 8.0 and it's going to acknowledge the embodied nature of student learning and assessment. This final exam, that's a sea of desks in a final exam. What I realized right away in my teaching career is that the information that I got from situations like that was inaccurate. And I mean that and maybe you could even raise to see a show of hands if you've had the experience of having a conversation with a student who scores poorly on exams but in conversation displays incredible knowledge. Anyone had that experience? Yeah, yeah, I had that early and often. So what it told me was that with this kind of assessment I'm getting the wrong answer and I dug into that. I don't want to get the wrong answers. I'm had a lot of math schooling. I know what that feels like. So I dug into it and said, well, what's actually going on here? And I found that what I'm making is type two errors. I am, no, you're scaring me there, Charles. Yeah, all right, there we go. I'm making type two errors and what that means is that I'm deciding that a student is not qualified on the basis of information from this kind of a situation even though they are. So I've made a mistake and I don't want to make those mistakes. And it got, as I dug into it further I realized that those mistakes are absolutely racially predictable. So I imagine what is it that I'm actually assessing here besides student learning? And then I go to my college website and I look at the test taking skills. You can look up your own, right? And like how to take a high stakes test, right? We try to give students the tools that they need to succeed. And that to me is a key that we're assessing not just student learning, but also assimilation into the assessment structure, right? So the students that are not as well assimilated and I'll just say it right here who has not had access to the kind of assimilation training Brown and Black students, I'm assessing them on how well they've assimilated to my culture and not just their math knowledge. I wanted to stop doing that. I don't want to because that turns me into a racial filter. I'm the gatekeeper here and I want to stop that. So that's what drove me. That's part of what drove me into my rethinking assessment. So I just, in 90 seconds, I want to share an idea or a concept, a picture, maybe a proof of concept. This is a final exam in my discrete math class. These folks will be computer scientists in Silicon Valley. They'll transfer next year. I also teach differential equations. They'll all be electrical engineers. And I want to point out the two things that are going on here that I heard in your comments. I heard teacher-student relationship. I have a very different relationship with these students than I did when I was in a standardized test and it brings me joy. And the second thing is math in community that I heard. These are people that are doing math in community and it's a far more, the results I get, the artifacts that they generate are so revealing of their learning that I can reduce the number of type two errors that I make. So my challenge here in Park City is to, what does that look like? How can I rewrite my policies to embed the knowledge that mathematical knowings are embodied? And that will be a rewrite of my policies. In particular, I want to not only reduce the stress, the anxiety, that's an embodied expression, the anxiety of an assessment situation that blocks student access to their own ability. I want to acknowledge that as an embodiment dimension, but another one is that I want students to dial in to the wisdom of their bodies and I'm going to try to write those up in my policies before I leave here. All right, is that working? Cool. In the spirit of everything we're discussing, I can't, I got to stand up. I'm really stressing out just sitting here and I think I will give you a better talk if you let me stand up. So, yeah, I'm Claudio Jacobo Gomez-Cotales, you've already met me. I'm a professor at Carleton College. This is like these icons in the top right sort of indicated journey of like beginning, I went to college sort of near where I grew up at New Mexico Tech in Socorro. I went to the University of Chicago for grad school, postdoc at UC Irvine, and these below them are some unions and other groups that I've been affiliated with along the way. You can see along the right some campaigns that I've been involved in. On the left, you can see some research. I do like arithmetic topology. This is a lovely rendering, totally original. I made every part of it. The relationship between topology and arithmetic that sort of motivates a lot of the things we think about. I've got some lovely pictures from student projects here and oh, this one's really fun. Ask me about that one, that one's a joy. And these are some pictures of mathematicians involved in fighting for their own rights and all these great sorts of things. So my project, go ahead and take it to the next one, Richard, thank you so much. My project is, I have a bit of freedom and I'm excited to sort of flex it. I'm teaching a class that's called argument and inquiry. It's a thing when you're a first year at Carlton in your first term, you take this A&I class, which is like a place where you're supposed to learn to like engage critically with your writing, your reading, your discussing, your argue, all these things. And any sort of tenure track faculty, oh, what happened? Well, I'll let you figure that out. Any tenure track faculty can offer one, well there hasn't been one offered in the math department in a while, so I was really excited to go ahead and do this. And I wanna mention this framework that Rachelle already mentioned, Hersh, the front and the back. This idea of like, I mean for those of you that have worked in, this is a metaphor from the article, those of you that have worked in food service, you know the front, like when you're like a waiter, you come out and you're like, oh yes, here's the food, you know, there's like this presentation. And then when you go to the back, you're like, oh my God, the guy at table six is, you know, there's this whole like change in the back, the messiness happens, the real work is happening, and then the front, there's this presentation. And so much of mathematics with students is about this front, right? This sort of idea that like, I mean, I think if you ask a lot of students, think that math is some sort of immutable rules that like have sort of existed forever, and there's no sort of connection between humans and the rules that we're using. Whereas one of the strategies that I really take in mind in rehumanizing mathematics, and it fits well with this A&I framework, is giving them a peek into the back, right? So in this class, which is specifically built around probabilities, statistics there, and the idea is I want students, well there's really nothing out there, huh? All right, well let's keep going. I don't have my bullets. But the idea is that I want students to think about not only that math is a human activity, but that human experiences are informed by mathematics, right? Like the mathematics that we develop in our institutions inform the ways that we as humans are supposed to interpret the world around us. So this example for us, probability and statistics, this is like a, I mean, it was sort of a metaphysical epistemic sort of all the words success story of like the 19th century that has totally changed how we think about the world. I want students to have a chance to interrogate that, yeah? And it's giving us this great framework. I'll mention, I don't know, how much time do I look? Okay, I gotta wrap up, I gotta wrap up. You don't get to see my bullets, sorry. They were so good, oh well. One of the ideas, I'll just give you an example to give you something concrete. People are familiar with PageRank, yeah? Google the internet, PageRank, yeah? We're ranking the internet, all that stuff. Oh, there, there it is. Next slide. I missed all that. Yeah, that's all right. And one of the things I wanna do here is I want them to think about PageRank as a artifact of math as a political activity, right? And one way that you can think about PageRank is a random walk on the internet, yeah? What better way to do this than to give students a bunch of chalk, my dice bag from Dungeons and Dragons, and tell them to start doing a random walk and to interrogate things, like what sort of topological features are like influencing which pages are important, yeah? According to this algorithm, really sort of sess it out and feel it in their movements around the space. Then you can push them further and say, hey, so what's going on with like, what features are interesting? Do you ever see this come up in your everyday life? Cause y'all are on the internet 24 seven. I know before you wake up, you're on TikTok, thinking about that algorithm. I want them to make some connection between this mathematical activity they're doing in their class, the math that they see around them. And then I want them to complicate that with research from say like, Sophia Nobles, other black feminist scholars, thinking about the ways that Google and the search epistemology shapes the way that we like think about truth, and think about the world. This is an example for humanizing mathematics. I'll stop now, I'm out of time. Yeah, you see this, but we're so good. Oh, thanks everyone. Adios. Do you want to introduce the other people? Yeah, so before we jump into Q and A, it will be, it gives chance to introduce the rest of our colleagues, and we have mics on the left and mics on the right. So feel free to introduce. We'll start on the left, while my left, sorry, directions, all right? Vectors. Hello, my name is Chadwick Johnson, math teacher, high school math teacher in Boston. You, yeah, I can't believe it. Hi, my name's Octavia Beckles. I'm a math educator and consultant from Canada, the greater Toronto area. Good afternoon, everybody. My name is Charles Wilkes. I'm a postdoc researcher at San Diego State University. Hello, everyone. My name is Richard Velasco. I'm an assistant professor of math education at the University of Oklahoma. Hello, good afternoon. I'm Amy Vickers, and I teach at a technical college in the rural northern Wisconsin. Good afternoon. My name is Wilfred O'Langi from the University of the Philippines Baguio. So I'm from the Philippines. I'm an indigenous person and a mathematician. I work in the area of indigenous peoples' education. Thank you. Hello, everyone. I'm Ila Varma. I'm a professor in number theory, assistant professor at University of Toronto. I am Adriana Mejia. I'm from Columbia. I have... Adriana Mejia. I am from Columbia. I am a math professor and I research in theory of categories. All right, yeah. So at this point, the good reason to introduce ourselves is that we will be doing presentations later, but we'll wrap that up and talk about that. But for now, we would love to open it up to any questions that you may have already written on your index card or that you have. You're gonna pass them to the people... Oh, yes, sorry. Yes, you're gonna pass your index cards after you write your questions down to my colleagues on your right or your left, depending on where you are sitting. So we can get a whole stack. Thank you for passing those questions along. Yeah, it does say low battery too. We'll make it. Low battery. Okay, so as we're getting the questions coming up, if you wanna learn more about our individual projects and our action plans and what we're doing with more depth, we can... We'll invite you to our showcase that will be this Friday from 12 to one. It will be a work in, well, a presentation lunch. So you'll get a chance to hear from anyone that you would want to hear from, or all of us. And that'll be over in the smaller lunch tent. We'll have it set up for that. So thank you. And now we have a few questions. Good, start with the first one. As a graduate student, who is well down the food chain, oh, oh, oh. Influence or suggest to faculty to change their approaches are, do you have any influence or suggestions to faculty to change their approaches to math education? Woo-hoo. Shot it. Why would you nominate me? That's a really good question. Because it's hard, right? I mean, especially at these institutions that we're in, there's this sort of systemic issue where like doing that is not in your interests, right? You're supposed to do research. You're supposed to do all these things, yeah? And I think, I mean, I have answers for you, but I don't want to get super lost. I think you're right that sort of the positionality of the graduate student is a really difficult one to overcome. And I think there's a bigger picture with a bigger community of people that can bring to bear or bring to light sort of the necessity for this type of work. And it can be like in your relationship to the advisor or relationship of other graduate students, many graduate students together in relation to this professor. I have a lot of thoughts. I don't want to get us lost. But yeah, I think there are ways to communicate the necessity of this work. Like it's not just a sort of frivolous thing. It's not just for fun. And I want to find you and talk to you. Let's talk more, yeah. This is to me, when passing from quantitative exams, how do you mitigate the effects of personal bias? Excellent question. I have a bias check built into my procedures. And that is that I look at my grade book first with the names hidden and just looking at the lines of data. And I come up with a grade that way. Then I hide the grades and I show the names. And then that, then I do the same thing. And then that brings in all of my relationship understanding of the conversations that I've heard. And I do the same grades, not having a look at what the first draft was. So then I put the two drafts side by side. And 70% of the time, it's the same grade that goes on the transcript. Most of the rest of them, the grades differ by one click, like an A minus or a B plus. I go with the higher grade.