 So, Rochelle is a professor of education at Champagne Urbana. She's done very important work on the role of intersectionality in teaching and learning of mathematics. And she has rechristened and led this workshop, which is now called Rehumanizing Mathematics for the past, this is her third year, yes, her third year. And we're very pleased to have her, and thank you very much for putting together this discussion. Wonderful. Thank you. I'm here with you today to welcome you in my ancestral language, Raramuri. And we start with truth and right relations. We've been doing this in our workshop well every time. And that is to first stop and honor and acknowledge that we are on the ancestral and unceded territories of the Northern Band of the Ute Nation. And these are nations that, although they have been forcefully removed from these lands at some point, they've continued to be the original peoples, the original stewards, and have connections to these lands and continue to have relations with these lands. And we owe our respect and our honor to them. The piece of art that you're seeing here is Wolf by Mak Koyote, who is a Ute Indian, a Ute Nation artist. And if you ever are wondering whose lands you are on when you go to give a talk, you can look at the site there that's nativeland.canada, because Canada has done a much better job than the U.S. in thinking about First Nations and the kinds of reparations and the truths that need to be told first before we even think about any kind of reconciliation or right relations. The lands that are here that we are honoring are Clayton Peak. This picture was taken while we were on hike. And again, we can think about how our more than human relatives are performing mathematics around us. Who are we? We are a group of excited and passionate people who range in backgrounds. We have people who are working with middle school and high school students. We have people who are working with colleges of education, doing teacher education. We have people who are consultants with school districts and with different cities. We have people who are mathematicians in universities and in colleges. We just come together all on this journey thinking about how can we think about the truths in mathematics and then getting ourselves into right relations. Good afternoon, everyone. So as you were entering, maybe you were able to get an index card. If not, if at any point during this presentation you have a question or you just want to make a little note, maybe come back to it. My fellow colleagues are in the program for me. We have some index cards that we can pass around. So at any point just raise your hand. You can get an index card and jot that down. We will have time at the end, some good chunk of time at the end to ask you questions. And we'll try to give a response. All right, great. I am Claudio Hocobo Gomez-Gonzales. I'm a mathematician at Carleton College. I just started. I've been there for a year. And first, we're going to kick us off with an individual reflection. You see the questions here, when has mathematics brought you joy and when has mathematics brought you pain? We're going to give you all a minute to individually reflect before we have some discussions together. And presumably, we're here because we've found joy in mathematics, presumably. But at least speaking from my own experience, I know you research mathematicians out there. I know you have some pain with mathematics. I want you to think about that too. Yeah, I know. Okay, let's do it. All right. So now I invite you to turn and talk with the people that, I mean, you hopefully know each other for at least a week. You're developing some trust, you know, some connections. I want you to share and I want you to see how your experiences relate to one another. So we want to give you all five minutes for this one. Please go right ahead and let's share these experiences we're thinking about. I need to, these are such vibrant conversations. I'm surprised how much they persisted. That was awesome. I hate to cut you short, but I want to hear back from like two or three, you know, just a few bounce backs from the audience will have, who's doing it? I can't see over there. Are you Chadwick? I can't see. So Chadwick, my, one of our illustrious colleagues will be zipping around. We want to get here from a couple folks, just share out what you discussed. Did anyone want to share anything? Oh, Willie has a mic too? Very good. There we go. Well, for the pain part in my group, it was somebody mentioned the pain of trying to, when you're teaching a mathematics and the students are experiencing the pain from not like if you see a student from whatever their background is and they're not getting it and then there tends to, there can be like a painful like teacher-student relationship thing that happens. Somebody else mentioned it and really resonated with me. Thank you very much. Let's get one more. Oh, I see one in the back. Thank you. Is it on? Okay. So our joy one was doing mathematics in community when you're able to go, you know, I mean, so I was talking to Mackenzie and like we went to ISM earlier this summer to work with a group of people and it was like really fun and joyful. And a pain thing, I thought that was interesting. I consider myself a research mathematician and you talked like our research, like giving us pain. And it's like, that's not at all my experience. Like even when my research goes badly, it's not as hurtful as the times when I have felt when I was not in community with people. So I've been, you know, at institutions where I felt like really out of place and like really not welcomed and like those, like when you said like pain, like it was like one specific time where I try to go to one seminar that got changed times without me being told like everybody else was told it was going to be at a different time. And I showed up to an empty room and I like literally walked back to my office to cry because like I just like felt so rejected. And so I thought that that was interesting. Like I was like, there's nowhere research could hurt me that bad. Wow. Thank you for sharing that. That's like snap, snap, snap. Thank you. Thank you. I'm going to pass back to Rachel. So part of what our group has been doing is been thinking about like, okay, universities are talking a lot about diversity and equity and inclusion and in what way is anything that we're doing in our workshop different from that or extending that or in conversation with that, right? So I think it's important to think about how we think and talk about our work because it's the language that we use that signals to other people who we are and what kind of conversations we're interested in having. So when we say words like diversity, often we just mean like lots of different things, right? There's not really an attention to difference or when difference is used, it's used in a way that we don't necessarily think about power relations. In K to 12 schools, we can say, oh, yeah, that's a school with a really high level of diversity when what we really mean is almost 100% blacks pop student population. So when we say words like that, we have to ask ourselves, when we say diversity, are we getting at the difference between groups? Are we getting at the positionality between those groups? When we use words like equity, equity often is talking about kind of universalistic approaches like how do we get everybody on board? How do we do a math for all? How do we get a program that will make everybody feel good about mathematics? And it's often talking about those closing those achievement gaps and getting at the leaky pipelines. And again, from a perspective of critical scholars who think and talk about this work, who theorize this work all the time, we don't just want to have more in different kinds of people in the field. We don't just want to have more in different kinds of people getting awards in mathematics. We actually want to move beyond this notion of kind of including people. I like to give an example of when we talk about inclusion at a very minimal level, we kind of are talking about opening that door and like letting one more person kind of get in. But if you've ever attended a talk that's a really popular talk and you're one of the last people to get there and someone opens that door for you or you're kind of hanging from the outside and you're trying to see the front of the room, that doesn't really feel like inclusion. And I know that people feel like they're doing the best they can, right? But it's a different perspective to say, what if we centered the people who have most been harmed by school systems? And what does that look like to place those people, those ways of knowing, those communities at the core, where we dedicate our resources and our energy there and we focus on healing and not just including. And that part of that work is having political clarity. It means recognizing that a lot of the mathematical knowings, both historically or we would say are historically, they're historically, has been erased. And some of that means that certain people have gotten credit for contributions, whereas maybe these ideas were being discovered and performed and celebrated in many different cultures. So we just encourage you to think about when we use language, if you're in a math department meeting or you're somewhere in a space and somebody's talking to you about equity, is there a way for you to shift that language to say, and when you say equity, can you say a little bit more about what you mean, rather than just kind of assuming that the other person is in the same place that you are? We're using a term that's rehumanizing mathematics, not because I was really interested in creating new jargon and concepts in our field, because I tell you we have lots of them. But it was because when I was going around the country and I was meeting with students and meeting with teachers and even just meeting with mathematicians and talking about these ideas, the notion of equity didn't really get at it. It was this idea of there were things that people felt that were kind of these constant either microaggressions or structural aspects that didn't allow people to show up and feel whole, to bring all the parts of themselves to the space of doing mathematics. So again, you may feel like, well, as a math professor, I don't feel like I have microaggressions or I don't feel like the system is against me. But maybe there's a way in which you don't bring all of the parts of you to your mathematical spaces because that's kind of just not what's done. That Ruben Hirsch talks about a front and back of mathematics and we get to see the front, we don't get to see all the messiness of the back. So we just say here that rehumanizing mathematics is an act of love that seeks joy and belonging and not just problem solving. It's a choice to center those who have suffered most from a Eurocentric and dehumanizing system that erases brilliance. It's a recognition that there are many ways of knowing, which means that there are many knowers and many mathematics. It's a form of political clarity that asks us to follow a different rhythm and to recognize that we are part of a larger time scale than just humans. It's an active refusal to return to normal and it's a step towards restoring both restoring that which has come from the past, restoring that aspect and restoring as in building futures in ways that help us be in better relationships with our natural and spiritual worlds. And these are the eight dimensions and as they're talking about their projects, they're going to share how these play out in their work. But just to give an example, body and emotions is we think about what's the typical narrative that's written in mathematics and then what's the narrative that we're trying to talk about with restoring. So a typical example is well, you don't need your body, you don't need emotions to do mathematics. But what we're trying to get at is to recognize even more than just gestures and diagramming. There are things like intuition and other aspects that when we actually draw on all of our senses that we can have a fuller version of mathematics. And I think some of the terms there you can kind of get a sense of cultures and our stories, their stories has to do again with all of the different contributions around the world including the ways it's been documented through ethnomathematics. So you see four stars on this slide and that's because there's four people sitting up here who are amazing stars and doing this work. And there are eight other stars who are in the group who we need to name. And so after we get done talking about Francis, Kara, Patrick and Claudia, we're going to want to include the other people, stand up and please say something. But these are the four projects that you're going to listen to. So thank you. My name is Francis Pina. I teach in Boston public schools, middle and high school mathematics and my ninth year. So for me entering this program, I need to kind of reflect a little bit on where I've been and where I've started has been using the castle framework for social-emotional learning. So in my district, as on the slide, we've been given like a package to help us not only try to reflect and understand our own social-emotional learning needs, but a way to help our students develop that. But what I felt was missing was a way of being proactive about that or proactive about not only the relationships I'm building with students, but the relationships I'm helping my students build with math in my classroom. The social-emotional learning has felt like it was an add-on. So even with my training, it wasn't through my math department. It wasn't through a math PD by the district. It was something that was an add-on or separate. So I'd even feel the pressure to truly incorporate it and give it its due. And then when I did, it was because of potential harm that I had presented to a student or because of, as something I was mentioned earlier, a student not getting it. And then I am using that, trying to use that toolkit to help them process it, but not in a way that I am thinking about not those deficits or them developing that, but what are the assets that my students are bringing and not just the assets of their knowledge, but their experience. So for where I'm going with this and thinking about re-humanizing mathematics, I'm trying to think about how do I help my students not only develop metacognition of their mathematical understanding, but to refine it. And what would that look like in the math classroom? How do I have that not only through discussions, but through that community that we are building and the discussions that happen with each other that is also highlighting their assets. So my project is about building a year-long portfolio that not only captures the artifacts of their mathematical understanding, reflections and discussions, but also incorporates some art. And art that is not just, oh, here's the, you know, the Fibonacci sequence in squares or the Golden Ratio, and they're just coloring it in, like not a paint by numbers type of approach, but in a way that challenges aesthetics. I don't want to just highlight, oh, the Pythagorean theorem when there were cultures for centuries already there, representing it in their own understanding. 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 masters. And that was, oh, well, 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 the mathematical know-ins. And in order to help highlight that, I have to get to know that and broaden my own understanding of mathematics. That's part of my project. Thank you. Hi, everybody. I'm Karim. And I think of myself as a teacher with teachers. I used to use the word teacher 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 going to interrogate that work. But it was a really happy part of who I am as a 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 as a coach or as an 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 want to 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 what a classroom would look like and what role mathematical modeling might play in centering girls of color 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'm I find words like empty 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 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. 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 I got to the classroom. And I was 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 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 is gets in the way of student learning. So in 2008, I abandoned points and percentages of my grading and I made qualitative assessment version 1.0. I've been challenged along the way most recently by some of the concepts and re humanizing 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 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 the sea 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, just a lot of math schooling, I know, I know what that feels like. So I dug into it and said, Well, what's actually going on here? And I found that I'm, I'm what I'm making is type two errors. I am No, you're scaring me there, Charles. Yeah, there we go. I'm making I'm making type two errors. And what that means is that I'm, 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 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 try to give students the tools that they need to succeed. And that to me is a key that we're at 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, not just their math knowledge. I wanted to stop doing that. I don't want to because that turns me into a racial filter on the gatekeeper here. And I want to stop that. So that's what drove me that's part of what drove me into my my rethinking assessment. So I just in 90 seconds. I want to share an idea or a concept of picture, maybe a proof of concept. This is a final exam in my discrete math class. These folks will be elected 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 wanted 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's it brings me joy. And the second thing is math in community that I heard, right? These are people that are doing math in community. And it's a far more the results I get the, the artifacts that they generate are so revealing of their learning that I can I can reduce the number of type two errors that I make. So my challenge here at at in Park City is to how what does that look like? What how can I rewrite my policies to 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 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 like everything we're discussing, I can't I gotta stand up. I'm like really, 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 glad you're talking about this. You've already met me. I'm a professor at Carlton 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 in 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 some unions and other groups that I've been affiliated with along the way. You can see along the right some 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. I'll ask me about that one. That one's a joy. And you know, 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 a second. 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. It's called argument inquiry. It's a thing when you're a first year at Carlton. In your first term, you take this AI 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, well, I'll let you throw that out. Any tenure track faculty can offer one that 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 want to mention this framework that Rachelle already mentioned. Hersh, yeah, 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 was, you know, there's this whole like, change in the back, the messiness happens, the real work is happening. And in the front, there's this presentation. And so much of mathematics with students is about this front, right, the 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 re humanizing mathematics, and it fits well with this AI framework is giving them a peek into the back, right. So in this class, which is specifically built around probabilities, statistics there in the, the idea is, I want students while 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 like 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 I look. Okay, I got to wrap up. You don't get to see my bullets. Sorry. They were so good. One of the ideas, I'll just give you an example to give you something concrete. People are familiar with pay drink. Yeah. Google the internet pay drink. Yeah, we're ranking the internet all that stuff. Next slide. Missed all that. That's right. One of the things I want to do here is I want them to think about page rank as a artifact of math as a political activity. Right. And one way that you can think about page rank as 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 suss 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 what what features are interesting? Do you ever see this come up in your everyday life because 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 that we're so good. Thanks, everyone. Yeah. So before we jump into Q and A, it will be 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 will start on the left while my left sorry directions, right vectors. Hello, my name is Chadwick Johnson, math teacher, high school math teacher in Boston. 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 north northern Wisconsin. Good afternoon. My name is Wilfred Ollangi 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 people's education. Thank you. Hello, everyone. I'm Illa Varma. I'm a professor in number theory, assistant professor at University of Toronto. I'm Adriana Mejia. I'm from Columbia. I have Adriana Mejia. I'm from Columbia. I am a math professor and I research in theory of categories. Right. Yeah. So at this point, 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 going to pass them to the people? Oh, yes. Yes. You're going to pass your index cards after you write your questions down to the 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 that's it. Again, the question's coming up. If you want to learn more about our individual projects and our action plans and what we're doing with more depth, we can invite you to our showcase that will be this Friday from 12 to 1. 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. I'll start with the first one. As a graduate student who is well down the food chain, 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? 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 a 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 this 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 that can bring to bear or bring to light sort of the necessity for this type of work. 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. This is to me. When passing from quantitative to qualitative 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. And I hide the grades and I show the names. And then that and I do the same thing. And then that brings in all of the my relationship understanding of the conversations I've heard. And I do the same grades having 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 B plus. I go with the higher grade of the two. Most of those that are that that are different. The second draft is higher. And I credit that to the fuller knowledge I have of the individual. And if there's ever any grade on the list that is more than one click different, I start over. So it's a it's a bias check. That's a really excellent question. So I do it once without the grade, without the names, once with the names, I take the higher of the two. I hope I answered that. So we have a couple of questions here that I think can be answered a little bit briefly. One is what is meant by more than human? More than human is our animal plant, land, skies, waterways as our relatives. It's recognizing that in this world we are the humans are the younger brothers and sisters and that for millennia, our more than human relatives have been performing patterns and performing forms of logic and other things that we would consider mathematical and have actually been our teachers. And we do a disservice when we go and take students out into nature and say, oh, see, look, here's a Fibonacci sequence or here's a whatever and we stop there because that's not really asking that's not really showing respect to our more than human relatives and asking what else can you teach me? It's basically saying I already know what I know. I just need you to be a prop. I just need you to I just need to show your your image so I can tell students this is what it is and now we're going to go back to doing everything that we did before. So that's one way of thinking about more than human relatives is kind of recognizing our place in the world as humans. On one of the slides you wrote how the current system erases brilliance. What do you mean? The question is on one of the slides you wrote how the current system erases brilliance. What do you mean? I go back to the example I gave that many of you have experienced is that that of having a conversation with a student who demonstrates brilliance that has been erased by the assessment experience. One way to think about it is even if I am trying to create a diagnostic. So it's not even a summative thing. It's a formative assessment for my students. The questions that I'm asking could have bias in themselves or even in the format of the question that may not be creating space or multiple representations of what the answers are what I'm looking for or entry points. So the student has it up here. They do have a way of representing it but I'm that I'm not fishing for that. I'm fishing for a specific thing that will show up on a later assessment. So even that is like limiting the space that should be opening up for that creative representation of what they're understanding this. I also want you to think about like what ways of knowing or are or are advantaged or reflected in your curriculum or what you value as mathematical knowledge right and what ways are either devalued or pushed to the side. Who gets credit? What are the mathematicians names that are used to give credit for work and whether they are the actual entities that actually created that knowledge or was it stolen or curated from other places right and where does that enter the conversation with students? How are we honoring that other communities other civilizations curated the same knowledge independent of Eurocentric knowledge and where does that enter the conversation? And so who is actually reflected as mathematicians and who is not? So that is erasure of brilliance and it does impact the youth that we teach. And I think I would I would add to that that the other aspects of brilliance that get erased is when we are taught that the only thing that you need to do mathematics is your brain. So you're already you're already disengaging all other parts of yourself and so the brilliance of your body, the brilliance of your connections to to other places to lands and waterways that are already informing you on a regular basis the kind of felt-knowings that you carry within you you just have these gut feelings you don't even know how to explain them. Those are also all forms of brilliance that we carry that we don't always acknowledge. Yeah I just want to add I think maybe echoing off of Octavia and I'm not saying any of my wonderful colleagues are doing this but I think it's an easy pitfall to to well whatever easy trap when thinking about this is a the consequence like I don't want you to care about this because like the world is like a smidge and less productive right like like erasure of brilliance and Octavia you said it right it's like who like you're like destroy you're like you're like the person the human consequence of that is this person right like it's it's not about optimizing something you know and also I just want to re-emphasize that graduate students I really want to talk to you I feel really bad my bad answer earlier. I think maybe the last question that we have time for is um how do we prepare students for both the world we dream about and the one we live in now in particular is there a way to help them learn how to assimilate slash code switch slash play the game when it can help them in the world we live in now while still progressing to the world we dream about I'll try to keep it short so everyone else can chime in because there's a lot to say about this one um it well first I would what I would want us to think about is I want us to I want to challenge the the binary that it has to be one or the other right it could be both because when we think about even the percentage of our brain capacity that we are even using we're not using all of it so there's a lot of space for us to still push the truth like if we lead with truth in that honesty in those discussions and how we build those relationships as as either like student to student or as professors or teachers to our students we could provide that true information and we don't have to be the gatekeepers of that of those action steps but how do we develop those steps as a community how do we want to address that so even having that question that's something I would present directly to my students like what does it mean even for like them to see me in the classroom and and how am I am I do you feel I'm even bringing my full authentic self so I I'm a positive that's so much I could say but I'm positive they want to add yeah I appreciate this idea that like our realities in our dreams are not two different spaces and I think for me it's like holding on to the vision of what we want and I'm realizing that we don't go away that edit alone this work has been about being in community and solidarity and for me as a white woman listening really really deeply making sure that I'm not positioning other people to do the work of teaching me about what I need to do to enact that vision and to dismantle systems that are harming children so that's part of the journey too I think I think it also means that we need to provide spaces to radically dream we need to normalize those spaces and then we also need to recognize that there's much work that we will do in our lifetimes that we will never see the results of and then from an indigenous perspective that notion that we honor our relatives and that our entire lives are about how do we become a good ancestor means that we're always thinking about our everyday actions are affecting the next seven generations and so I just encourage you that even when you feel like things are futile like there's no way that what I'm doing right now is going to even make a dent to just know but will you be a good ancestor are you helping pave the path towards futures that we want that you want for your children for your grandchildren for their grandchildren and it's it can feel daunting but at the same time we can't think of waiting for these things to happen we have to start living those futures now yeah wow that was that was really great and and I want to really echo um Francis as well around this point of like can I see that the question again I want to make sure I'm not misrepresenting it but first I very much agree that there's like there's a there's a tension here right um rather than a duality right like yeah yeah um and and I think like I would like to challenge I think the uh it's tough because it's about like this question is about individuals is in particular is there a way to help them learn right it's about like individual people and I think the the tough part of this is is the next bit which is like when it can help them in the world we live in right this is the first part and then while still progressing to the world we dream about and that part we can't do alone right like we can't do that part by ourselves and and I think um creating that space as you say Michelle right um for this like collective reimagining for for like the reshaping of worlds is is a that's part of the job and that's that's that's that's what gets me out of bed and we think peace in the question I just want to challenge the them and I want you to think of the them as us so how are we helping us freedom dream reach our desires that we want seven generations into the future thank you there is no ground and one of the ways we do this is by having opportunities to gather like we are here at PCMI to be able to engage with those of you that are mathematicians or doing other kinds of research to have opportunities to be in dialogue to have time to be supported to take our radical dreaming and think about what does that look like within school systems that we're working within and against and outside of so we thank also PCMI for the opportunity to be in this space to gather and to radically dream together wait before you leave we want to acknowledge that everyone had amazing questions that we weren't able to get to all of them there's a link though Michelle's going to open up her laptop and you're going to see a QR you're going to see a QR code on there and there's just a link to a survey to for us to kind of know a little bit more and we hope that this would be the beginning of a lot of conversations going to happen while we're here and after we leave