 Good morning, everyone. We'll go ahead and get started. I'm Cheryl Gann, the NCSSM Durham Math Department Chair. I want to add my welcome to you all and my sincere hope that in the near future I will be welcoming you to our campus for TCM conferences or other visits. I have the great privilege of introducing our keynote speaker, Dr. Rochelle Gutierrez. Dr. Gutierrez currently serves as a professor of Latina, Latino Studies and Mathematics Education at the University of Illinois at Urbana, Urbana-Champaign. Dr. Gutierrez has been recognized with numerous awards, including the 2016 Iris M. Carl Distinguished Leadership and Equity Award from Todos Mathematics for All. Dr. Gutierrez earned her MA and PhD in Curriculum and Instruction at the University of Chicago after completing her BA in Human Biology at Stanford University. In fact, it was an art history professor at Stanford who helped redirect Dr. Gutierrez from pre-med to a career in education. After discussions with him in which she raised questions and challenged him on issues, such as the low underrepresented minority population at Stanford University. Dr. Gutierrez claimed art professor and asked something along the lines of why not do something more challenging, like be a teacher? Fortunately for educators and for students, she took this advice to heart. Dr. Gutierrez teaches courses for education students, including a secondary mathematics message course for undergraduates, and the course in socio-political perspectives on mathematics and science education for graduate students. She also teaches an undergraduate seminar for all students on social justice, schooling, and society. Though now a college professor, Dr. Gutierrez identifies strongly with her roots as a middle and high school teacher. As such, her work is focused on advocating for teachers and for students, including challenging deficit views of students who are Black, Latinx, and Indigenous. Dr. Gutierrez's willingness to challenge throughout of her own experience as a member of an activist family. Her work has been inspired by her upbringing, by her desire to help others understand the perspective she gained through this upbringing, and by her dislike of following procedures without reason. Her life and education journey has led her to research in the areas of access, equity, identity, and what she has come to call the re-humanizing of mathematics. Dr. Gutierrez's work on this mindset was brought together with other scholars for the National Council of Teachers of Mathematics, 2018, Annual Perspectives in Mathematics Education, titled Re-humanizing Mathematics for Black, Indigenous, and Latinx students. As she explains in the introduction of that book, beyond being seen as a legitimate participant, a doer of mathematics, a student should be able to feel whole as a person to draw upon all of their cultural and linguistic resources while participating in school mathematics. Please join me now in welcoming Dr. Gutierrez as she speaks on restoring mathematics for our future. Dr. Gutierrez, please feel free to begin whenever you are ready. Thank you so much for having me here. It's an honor and a pleasure to be speaking with teachers. That's my old hat I wore and it's something that I really miss being in the classroom on a regular basis, though. I want to start by just acknowledging that I'm currently on the homelands and the unceded territories of the Peoria, the Kaskaskia, the Piankasha, the Peoria, Twitwi, Salk, Odawa, Maskutin, Kikapu, Barwadmik, Anishinaabe, and Chikasha nations. And I encourage you to think about, I say that we need to start by having truth and right relations because I encourage you to think about whose lands you're currently on. At the bottom there you see a website that's nativeland.canada and you can search to see whose lands you're currently on. I think it's important for us to think about the fact that the lands that we're on are past, present, and future, are the original stewards of this place. And so thinking about not just these kinds of land acknowledgments are important, not just for us to kind of recognize land as relative. But it's to think about what is our responsibility? What is the kind of reciprocity and the reparation that needs to happen for us to be able to move forward and to be in those right relations because historically we have not. And so how do we continue to care for these lands? How do we continue to honor those who have cared for these lands and think about how we can participate? So it's more than just becoming knowledgeable. I've placed a website down there at the bottom again that's the Alliance of Indian Mathematics Circles. And there's a place where you can find out the Indian Math Circle that is close to you, that you can contribute to, that you can participate in or that you can learn more about. But we are all in a crisis. We are dealing, I'm going to skip this. We are all, so let's start with the fact that I'm saying that we're going to start with an invitation. And the invitation is that not to go back to normal. The invitation is to say that we recognize that we're in the middle of a crisis that historically we've been in this place before, a version of this place before. In the upper left hand corner you see a picture of the 1974 Soweto Walkouts where students took over the schools and taught each other. At the bottom left corner is the Chicano Walkouts which is where the East LA 13 high school students, again both of those are groups of high school students who've chosen to say that the education that they're receiving is not a meaningful one. It's not one that prepares them or their communities to be able to thrive and to have meaning to understand where they've come from and where they're trying to go and also to maintain their languages and their cultures and their traditions. And we can see how this is not only something that's been in the past but it's something we're currently dealing with. When we think about the relationship between climate change, Black Lives Matter and COVID we can see that other than human relatives are giving us this invitation. They're saying pause and think about what is your role in society? So we should ask ourselves as mathematicians, as math teachers what is our role? What should we be doing in mathematics? Should we be the ones who are coming up with predictive models that are helping us make decisions? Are we the ones who are supposed to be crunching statistics and giving people new algorithms to follow? What is it that we're supposed to be doing in our role here? And Sonya Renee Taylor when the pandemic first started had good language. This do not go back to normal. So I want to start with that. She says, we will not go back to normal. Normal never was. Our pre-coron existence was not normal other than as greed, inequity exhaustion depletion, extraction disconnection, confusion rage hoarding, hate, and lack. We should not long to return my friends. We are being given the opportunity to stitch a new garment one that fits all of humanity and nature. And so if we think about this from the perspective of mathematics what might it look like if we chose not to go back to normal in mathematics? That would require us having a radical dreaming. A radical dreaming towards a world that does not yet exist. And I say towards a world that does not yet exist because for the most part we've been doing mathematics and especially school mathematics in the same ways for decades and for about almost a century that we cannot reimagine something that we have not experienced. So it becomes a difficult task on the one hand and yet it's a necessary task because we cannot just continue to do what we're doing. We know in our hearts that it's not working. And yet when we're given this invitation when schools were given this invitation for the most part schools chose business as usual in other words instead of saying hey there's an invitation here for us to stop and think about what is mathematics what role do we want mathematics to play in our lives how do we want to how is this a window that's opened up for us to do things differently. And I would say that the one thing that we did do differently is our focus on socio-emotional learning. So I think many teachers now start their classes by checking in with students by asking how are you those kinds of things have become the new normal or a new kind of way that we interact and it's almost like students also expect that from us. And so when we go back to the first phase to face teaching on the one hand there is this emphasis on content but there's also that connection with students that may be a little bit different and I'm hoping that we that students will hold this accountable to that won't fall by the wayside. But for the most part when we look at policymakers and we look at the decisions that are being made about schools maybe not individual teachers are making these decisions there's a focus on this kind of learning recovery so when students there's this learning loss that students have had our role as math teachers is to catch them back up get them back into into the space of doing mathematics and not necessarily saying and do we want them to do the same kind of mathematics that we were doing before. I would argue that along with Bettina Love, Bettina Love's book is we want to do more than survive she says that we are trapped in an educational survival complex that our students are trapped in an educational survival complex and so you see on the left there's a plant that's surviving it's surviving it's it's eking its existence out there's you know it's lost a lot of its leaves but you know it's it you could say it's still alive and on the right there you see a plant that's fully thriving that has new shoots that's taking up that space and and so if we want to think about what are the things that are preventing thriving and mattering for students in learning mathematics we have to first start with that truth. So what is the truth about the experience for students and also what is the truth of ours in terms of math teachers what prevents us from thriving and mattering so I encourage you to put that into the chat box and as you're adding that I'm going to continue to move on but I think that what you'll find is you're looking at other people's writings is that many of the things that prevent students from thriving and mattering are the things that are preventing us as teachers from thriving and mattering so when you think about what is your when was the last time you felt pure joy in teaching mathematics what was that like how did that feel when was the last time you think your students had that kind of experience. We've had important advances in culture in mathematics we have known that in terms of ethnomathematics that there are many mathematics that are practiced throughout the world there's not one mathematics and that each forms of mathematics have come from the places and the cultures that people have developed in other words the local spaces that people have thought about the problems in their world and have thought about how to relate to others in their world have created the notion of pattern and if we think of mathematics is just the science or the study of pattern then we can see why it would be important to think about the particular place that you're in and so how would we navigate the stars and the sky how would we think about the aesthetics that we're developing how would we think about calendars and and even the number systems that we're coming up with. So that first part was the invitation it was to say here's this invitation what do we want to do about it the second part is to identify the current forms of mathematics that are untenable that are not part of our radical dreaming and so I have to ask myself how does mathematics collude with anti-blackness and settler colonialism what are the things that are present in on the forms of mathematics that we teach the forms of mathematics that we practice that that fail to challenge the relationship that we've had historically in terms of anti-blackness and settler colonialism and one of those is universalism so our emphasis on trying to get students to always come up with the general rule for coming up with the most abstract version for thinking about mathematics is always being universal you know we get these claims we'll have other people tell us well two plus two is four no matter where you go so how can you say that mathematics is not universal we often hear this phrase that mathematics is the universal language and while that's true to a certain extent so we can say well two plus two is four depending on how you're constructing what your twos are we also can recognize that that over emphasis on universalism and abstraction highlights or kind of gets us into a spot of thinking that all mathematics is also objective because it's universal because it doesn't have anything that's tied to any particular people it's this thing that's kind of the equalizer right and that objectivism is what keeps people from thinking about context from thinking about their own intuition from thinking about their bodies their emotions other kinds of things that are important and so when we are taught that mathematics is universal it also encourages us to follow a kind of compliance that this is a set of rules that doesn't have an agenda doesn't have any morals doesn't have any power dynamics involved this is just you know universal stuff and so it removes us from the kind of ethics it removes us from thinking about more complete ways of knowing when we think about precision in mathematics you know the common core state standards the practice standard about precision is that you know we need to identify our units we need to think about being precise and accurate and that accuracy again can come at the expense of well who's deciding what these units why these variables are even here and are these the variables that we want in any given problem so again it's in that jump to kind of you know come up with the general rule to make it universal to make it abstract that abstract reasoning is the highest level of thinking often in a math classroom that we get away from more complete ways of knowing that again come from more holistic views and also that move away from this idea that somehow there's a set of rules that we have to follow rather see mathematics as a game that has its own axioms and so we can change those postulates we can change those axioms upon which they're based we can say we want to play a different kind of game in mathematics than we have currently in place in schools I one of the things that's been hard for me and thinking about all of this is you know what is it that's driving this system that we have if we think that there are things that are not working for teachers and not working for students why do we perpetuate it why are we continuing with it and one of the things that I feel like gets perpetuated one of the narratives that gets written in mathematics is that it's this idea that mathematics is useful that mathematics kind of you better learn mathematics or else you're going to be left behind you know it's so useful for your life and so we see here when I say that it needs a fuel source many of the reasons that people end up learning mathematics and persisting in these kind of educational survival complexes is because they have a fear of something there's a fear of losing maybe because we recognize that in a system where mathematics is the gatekeeper only so many people are going to be winners we know that mathematics because it's been used as a proxy for intelligence in society meaning like if you tell somebody you're a math teacher if you say somebody you're a mathematician right away you get that kind of adulation response you get people who say you know oh you must be really smart right so there's this kind of correlation and this kind of notion that somehow all people who do mathematics are smart and people who don't do mathematics are less smart and so you know if you don't learn mathematics you could be seen as dumb you could also lose out if you don't do if you don't study mathematics because you might not be able to obtain that job that stem job in particular that's going to give you a particular status in life and so again for many students it's not that like oh I see this as something that I want to do but this is rather something that I kind of better do or else I might lose out and we can see you know again how it relates to being left behind in a technological society maybe getting taken advantage of because you don't know how to read graphs or understand contracts you know whether those are with your credit card or your cell phone or something like that so I want you to think for yourself now you are as math teachers and as mainly as my high school math teachers and maybe math professors we're all winners of a system that I'm asking us to now dismantle so in many ways you may feel like fear really hasn't had that same feeling for you as it has maybe for some of your students but I would argue that fear has played into all of our stories and so I'm asking you to think what if any role has fear played in your story have you been motivated to learn mathematics out of fear have you been convinced to go get that master's degree in mathematics because otherwise you won't get that step up and ladder for your your salary have you been have you thought that like well I'll be more respected if I get another degree in mathematics as opposed to if I get a degree in in education and have you been prevented from learning mathematics out of fear so go ahead and type that into the chat box but what if we rejected fear and we replaced it with the desire for attachment so what you see here instead of the fire is you see sweet grass sweet grass that's been braided and is the is the strength of many indigenous communities in particular this this piece comes from there's braiding sweet grass she's scholar and so what if we rejected fear and we replaced it with attachment what would that mean why would attachment be an important thing for us to consider how we are connected to each other so if instead mathematics as the science of pattern and as the study of pattern became you should be learning the new narrative that we're trying to introduce would be that you that it's important to learn mathematics because this is how we see how we're all connected how we're all related how we can see joy and in that connection that we're part of something larger and so if we think about mathematics as being the means to helping us further attach to each other as humans and then I would argue that we can take it a step further and say how do we learn to attach to land and to waters then that's also something that could be a different a different way that we're moving forward and so again if mathematics can help us see and create patterns that connect us then our role as teachers might be instead to instill this longing for lifelong learning and wondering about each other and how we are the same and different from each other how the patterns that we live are connected to the patterns that others live elsewhere I've talked about these eight dimensions of rehumanizing mathematics and again the reason that at the center of that circle is the indigenous black and people of color women who are queer folks is because when we when we get to the point where and in particular school mathematics but I would say mathematics in society as well when we get to the point when mathematics for queer and black indigenous women are free then we know that everyone else has been freed and so I'm borrowing that from the Combahee River Collective and these different dimensions are basically saying these are the kinds of spaces that have been spaces of dehumanization and so these are the ones that can be shifted into a new way of thinking so for each of those dimensions I find it a useful practice to think about what are the typical narratives that are written in each of those dimensions and then what are the counter narratives that we might want to write and so if we think about what is the typical narrative that's been normalized in mathematics we could think about like if we flip back and we look at okay let's say body and emotions well one of the current narratives that's written about body and emotions is that you don't need your body you don't need emotions in fact if you bring emotions to the classroom sometimes that's not exactly a helpful thing to be doing and so that idea that we should ignore our body you don't need your body to do mathematics you only need your brain and computer or a calculator or paper pencil or something like that and kind of in some ways it's almost this sense that you know you should leave your body outside of the mathematics classroom that the body is only needed to like carry the head it walks into the math classroom but you don't necessarily you're not going to attend to your body and yet when we think about other forms of mathematics that have been developed and the ways that we actually are really mathematical before school so much of that comes through our body so much of that comes through our emotions we are ingrained as humans to be mathematical and to search for patterns to search for joy and so I think again about one of the things the greatest forms of dehumanization at such an early age and that is counting when people when young children are learning to count and I would say you know we've seen in mathematical studies with children as young as like four years old they learn pretty early that you know we were born with this with this set of manipulatives at the ends of our fingers right we have ten manipulatives right here and if we can use our toes we've got twenty and but people are taught very early in age that that's seen as a primitive way of counting so you actually using your fingers like that to think about how you would count or to add on that's not seen as very intelligent and so at a very early age young children will put their hands under the table we see adults do this right so people will put their hands under the table because there's a form of shame that says you shouldn't be using your body you should this should all be mental math you should be able to do all of this in your head right and so again we can take each one of these dimensions and we can think about what are the narratives that we write for people and I don't mean it in the sense that like we stand in front of our students in classrooms and say you don't need your body you shouldn't bring your emotions but it's it's in the way that we frame the tasks and activities it's the ways that we especially frame our evaluations our assessments those are the things that tell students what we value and so if we say we value cultures and histories if we say we value students having windows and mirrors in their lives if we say we value students actually creating mathematics then all of those things have to come through in our practices in our in our evaluation systems so I say that we first identify the kind of narratives that have been normalized in mathematics and then we think about what's the counter narrative that we want to write because again the purpose is not just critique and to complain about you know there's things that aren't right in mathematics but it's to say why are we trying to move towards what is this other possible future that we could be participating in that we could actually not only envision but embody and enact and so when we think about that counter narrative I think well what part of this is that school mathematics erases all the forms of mathematics or many of the forms of mathematics that we have before we get to school right so you know young people find patterns in all kinds of things they come up with their own ways of representing pattern they come up with their own systems of counting and and representing groups and things like that and then you get to school and school teaches you you're no longer mathematical unless you present them in these specific ways you show your work in these sanctioned ways that mathematicians do it and again at such an early age we jump to that kind of generalization the abstraction which again are important tools are important notions for mathematicians but when we do that so early by the time we get students in high school they kind of have been taught that like you don't need to really understand and think about this stuff in a way that feels whole for you for you to be able to bring your whole self you just need to be able to replicate the patterns that previous mathematicians before you have done and so again how do we bring back that which is erased through schooling and part of that is to recognize that many people continue to do forms of mathematics outside of what's sanctioned by school we can think about you know when people are putting away their leftovers in the evening and they're taking around pot and they're looking at a square rectangular prism and they're thinking how do I get this into this space nobody's taking out a measuring tape and saying okay first I need to calculate the area of this circle of my pot and then I need to think about the height of the pot and then I need to that's not happening we haven't embedded this kind of natural reasoning well again it's that it's that formalization that comes early and it's that focus on getting the correct the accurate the precise answer before making our meaning and what I refer to this kind of new form of story or this new narrative that we're trying to put into place is restoring mathematics and what I mean by restoring is two things restoring without the why restoring means going back we inherently know and feel and experience in our bodies and in our spirits and in our and in our minds as humans so restoring that which gets erased by school and then restoring in the sense that we are telling a new story and so it's that idea of we're pointing to a new future and so what I love about restoring mathematics is that it's consistent with our indigenous perspectives in the sense that we have past present and future all all together at the same time and so for me rehumanizing mathematics is bringing forward particular principles it's an act of love that seeks joy and belonging and not just problem solving so again this goes back to the like is our main message about mathematics that it's useful that this is this kind of utilitarian narrative brings us joy and it helps to see how we're connected to each other rehumanizing mathematics is also 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 many knowers and many mathematics so again some of you may be involved in bringing in biographies of black women mathematicians, you might be trying to get students to even think about their own mathematical journeys and in doing that how do we position different people as mathematical knowers and doing different kinds of mathematics and how and rehumanizing mathematics is also a form of clarity it's a form of clarity that asks us to follow a different rhythm so on the one hand rehumanizing mathematics has at its basis the concept of Nepantla and Nepantla means basically kind of neither and both at the same time so we can think of this form of clarity asking us to follow a different rhythm and there's this push right now for everybody to get the kids back into classrooms and to get people back into learning and so I'm arguing that we do need that but we also need to slow down and if we think about how trees function their timeframes can be centuries rather than you know this day the next day so Nepantla helps us think about how we need to both slow down and have that sense of urgency so it's not a choosing of one or the other but it's recognizing that those rhythms require us to not follow a set of rules but rather to think about the complexity that's involved and it's an active refusal to return to normal I think that's the main part of it and I said it's helping us restore and restore our relationship to each other and to the natural and spiritual worlds so I've been talking about trees I've been talking about you know ways that we connect to the natural and spiritual worlds and this is the third piece that I think it requires from us if we're going to do this restoring and that is the shift the shift is to say we recognize in our herstory their story our story that we are the younger brothers and sisters on this planet that humans came after animals and plants and land and waters and so if we shift our lens to de center humans what forms of mathematics might we get what forms of mathematical learning and teaching might we get and so if we think of pattern and joy in relation to animal plant water and land nations and we center land and water as our teachers how might that move us forward so I want you to take a look at these pictures this notice and wonder stuff is what many people are doing these days in their classrooms and so I feel like this maps perfectly onto ways that we can encourage students to notice and wonder things in the natural world and in those notices and wonderings thinking about thinking about those patterns how do we search for acknowledge and affirm the patterns that we belong to so rather than seeing patterns as kind of outside of us as something that we kind of identify and then we generalize how do we first be in that moment of belonging of recognizing how we are part of something larger and when we are part of something larger that comes the sense of feeling like you have something to contribute feeling like you have a sense of responsibility to others and in particular in doing this work thinking about how you are in relation to land and waters and plants and how we are dependent interdependent on our other than human relatives so you might have looked at that rope and you might have thought you know okay what kind of a spiral is that maybe how many times is it spiraling maybe how long is the total rope you might have thought about what is rope made from what kind of plant is in that rope where is this, how is this rope being used and on the right you know you might have recognized okay that's some kind of plant thing but I'm not sure what it is and I'm not sure what it's doing but again you might have focused on the spiral itself and there's many things you could have thought about so that picture that I showed you is a maso and masos are otherwise referred to as fiddle heads masos are not a species of fern but they're a growth strategy and they follow a logarithmic spiral and so they you know in terms of that logarithmic spiral we just know that it cuts all of the lines at a constant angle and but when we look at the way that masos grow they grow, they come up out of the kind of dead leaf in with their heads down and they can grow all the way up to two feet out of the ground like this and and when we so masos are a food they're a food, they're maso is the malacite nation word for fiddle head it's used in medicinal tonics it helps clean the body of impurities and toxins and when people, this is a ritual that people go into into the forest or go into the fields and harvest and forage for this, this is a springtime tradition in many native communities and in this one in particular is that St. John River Valley in Canada well it's part of the connection to Connecticut these fiddle heads are eaten as a vegetable and so when we think about what we would study in this if we were to study masos we could say well what do masos teach us well on the one hand you know they can teach us about spirals and but they also if you harvest masos you have to harvest them at just the right time if you harvest them too late they're bitter they open up their fronds kind of papery and when they're soft and still firm you can cook these in a pan but if you try to harvest more than half of the masos that are growing there they'll actually die, the whole plants will die because they're in some ways connected to each other and so again we can say oh yes I've done things like this look at pine cones and you know find Fiminacci sequences or oh I've had students look at you know something in nature but what happens often time is that when we think about this it gets reduced to this notion that fiddle heads are showing us mathematical properties that we already know right so again we come back to the like okay and as we're constructing this with my students I'm making sure that they're understanding that all the radio lines are at a constant angle and what does this produce for us but we think about masos is as teachers we have to be able to think about pattern in a larger definition and not just this kind of geometric one or this algebraic one and so what are the kinds of non-numerical things that masos can teach us what are the other forms of pattern and can they help us broaden our notion of what mathematics is who it's by and who it's for so again I think a lot of times in the math classrooms we jump ourselves to first you know kind of formalizing the patterns that we see without sitting and thinking about where we can go and so again this is an example using bull from that is helping students see how this logarithmic pattern is functioning but again if we want to learn about how to be in the world and not just about numbers what might that look like so I have here two poems and each is about masos and you can think about what might it feel like for students to have this emphasis on looking at having fiddleheads or having masos be our teachers and thinking about what else do they teach us I'm going to read a piece of the poem that's to the right and this is Aileen Chong and she says the fern in infinite slowness uncurls each frond each frond a sister to another so many fingers and hands learning to flourish on the underside of things the fern is steady unafraid of the dark pushing through stem bark spring dew and winter rain mists gather to watch the reels incise themselves and ripen with spores ready for release the beginnings of another sprung from moss fragile made in light translucent in the light and I say is there inlaquech so inlaquech is the Mayan principle that is windows and mirrors you can think of it in that way inlaquech says I see recognizes that we are all just vibrations in this cosmos and that we are all our pattern that we are all related to each other and so inlaquech is recognizing that I see a version of you in me and a version of me in you and so we can think about if we had our students looking at poems like this maybe inventing their own poems what would be the kinds of things they might come up with and how might that help them think about pattern differently the journal of humanistic mathematics has a section where there's mathematical poems so mathematicians write these poems and some of the emphasis on the poems is the mathematical analysis of the structure of a poem and other ones are poems like these that are about things in the world that feel mathematical and here's another one again I'm not going to read it but we can see how again the ways that the poem is said so if we say compared with Euclid's elementary forms nature loosening her hair exhibits patterns sweetly disarray a float uncombed not simply of a higher degree and but rather of an altogether different level of complexity the number of the scales of distances describing her is almost infinite so again we can think about what are the ways that we are bringing mathematics into the classroom that that allow us to have our other than human relatives as teachers this was something that I did with my students and that was that we said what if we just created art based on this experience and so for me as somebody who does a lot of activist work I was really interested in in our fists and what is what is the mathematical pattern in the way that our fingers are shaped and it's a kind of an approximation of the Fibonacci sequence and so for me I produced this piece of art that had the fist and has the Fibonacci sequence and for me it represents more than just those numbers as a Fibonacci sequence it represents strength in numbers and so that concept of strength in numbers is something that is a larger pattern for activists so we can ask ourselves what else can we learn from our relations so what do we learn from Falcons and how they approach their prey well by keeping to that constant angle in approaching their prey they never lose sight of prey right so we can think about what is the purpose for our other than human relatives to be living these patterns to be showing us these patterns and to be showing us other patterns that maybe we miss if we're only looking for kind of numerical relations and so again we can launch this kind of activity with our students what do students notice and wonder if we put them into groups and they go into a room and they start seeing what kinds of pattern do we see what kinds of things do we want to know more about and how does what you're seeing in the picture is it a form of you and not a form of you so what are the things that we see that are creating that attachment to each other and then that attachment to land and waters we can think about the role of the mathematical practices when we say construct a viable argument and critique the reasoning of others we might insert before critique the reasoning of others appreciate the reasoning of others see how the reasoning of others is connected to your reasoning make that attachment first before we critique somebody else so again there are so many examples of things that we can learn from you know why is it that murmurations of starlings fly in the particular patterns that they do well keeping track of only six other birds is going to be an efficient way for me to be part of something larger so again you can think of this murmuration of starlings that's at the top center and say that's a pattern that they follow they all are following a kind of social algorithm that is saying here's the thing we're all going to do together right and I learned recently that you know that when we see these pictures of starlings doing this we should not just say oh that's really beautiful we also have to acknowledge the resistance and the resilience of these birds because when we see these kinds of patterns when they're all grouped together like that and they're making these different forms it's because they're under attack it's because they're trying to escape a predator and so we don't want to just look out and say how beautiful we also want to say how resilient how important that they stay together in those ways to protect each other so I want to kind of leave us thinking about can we imagine our classroom being a place where our students learn from other than human teachers and if so how and why and if not why not so be thinking about that for yourself what would that look like for me in my classroom what would it take for me what kind of things would I need to prepare myself for what kinds of things would I need to learn what kinds of partnerships might I need to come into I'm being in right relations I'm not encouraging people to simply use muscles or pine cones or murmurations or starlings as kind of props to say here's this thing that we get to learn from they're like a representation of the thing we already know to learn but we're literally saying we're open to learning something new for me that we don't even know what we could learn and in doing so what's our sense of responsibility if I decide to have my students grow plants in my classroom and we want to study something about them and we want to think about the patterns that they're offering to us whether it's about growth rate or whether it's about other kinds of things then what is our responsibility after we finish that project is part of our sense of reciprocity to those plants to go plant them back in the ground should our classroom maybe have some kind of space where we say if we're learning from if we're learning from a particular kind of butterfly or a particular kind of bug or an animal should we be trying to create and support the habitats for those as a kind of thank you for teaching us and that's the role of reciprocity that's saying more than just saying we want land and waters to be our teachers it's saying what's our role then in reciprocating and saying thank you for teaching and we have something to give as well so what is needed at this time from my perspective is a mathematics that's for problem solving and joy it's to thrive it's not just to solve problems and it's to underscore a broader notion of pattern again are we open to thinking about things like we put a lot of emphasis on symmetry in mathematics and yet in the biological world asymmetry is really important for protein folding for other kinds of things and so what is it about asymmetry that we either haven't studied or don't emphasize that could be a way of opening up for students new avenues for thinking through mathematics and again we need a mathematics that's going to reconnect us with each other and with these lands and waters this form of mathematics I'm talking about is in response to the crisis that we find ourselves in and so I say in terms of looking to the future we're ready for change let us link hands and hearts this is borrowing from Gloria Anzaldua who's a Chicana scholar she says we're ready for change let us link hands and hearts together find a path through the dark woods step through the doorways between worlds leaving huellas or foot steps footprints for others to follow build bridges, cross them with grace and claim these puentes these bridges are home si se puede, que asi sea so be it, estamos listas we're ready vámanos, so now let us shift so I ask us to think about if we are interested in this kind of radical dreaming how do we accept the invitation and part of the first part of accepting the invitation is to think about how we take it all in I ask us to breathe in and think about what does it look like when no one is hoarding in mathematics what does it look like when consent is asked for and given what does it look like when we are grateful for our relations to the whole what does it look like when past, present and future are all within us in teaching mathematics and in learning mathematics can you imagine a mathematics that is healing that supports us to thrive and matter and not for recognition but for our people and for our connection to this planet and what would that mathematics look like what would it feel like what would it smell like so take a deep breath in and exhale and think about what are you long for in mathematics I feel like in so many ways we have been taught to deny our belongings and yet we have this invitation in front of us and so again take a deep breath in and think of what a new future in mathematics feels like and breathe out and release all of the ways in which you and your students have been harmed by mathematics breathe in again and imagine us building a future together and breathe out and let go of your attachments to the forms of mathematics that have been dehumanizing and that have kept us from connecting deeply with one another thank you thank you so much this is a powerful and inspiring inspiring let's give her a round of applause we do have a little bit of time for Q&A here so if you want to type questions into the chat I'll read them out to Dr. Gutierrez as we get started on that NCSSM facilitators if you could go ahead and get meetings started for the 11 o'clock so that they're ready to go that would be fabulous as well so any questions for Dr. Gutierrez and maybe it doesn't have to be questions maybe it can also be comments what is going through your mind right now thank you also for everyone's active participation in the chat Dr. Gutierrez it was on fire during your session so very thought provoking points there we do have one question here where would you want teachers to begin the journal of humanistic mathematics perhaps I think you should begin whatever makes sense for you whatever feels like is a connection if you're way into this was wow the poetry really spoke to me then that is the way in for you if the way in for you was wow I really need to think about my participation in terms of like reparations for Indigenous people maybe I should be reaching out to local community and finding out how can I learn to think about how to be in relation to land if it was so I think whatever feels right to you is the space that you should move towards and again I think the main thing is to is to have the patience well to have the patience and the urgency to move this work forward and not feel like you have to be the sole arbiter of the truth that you bring to your students but rather to think about how can you be in partnership with other teachers with community members and not do the work alone any advice for bringing colleagues along on this journey I think one of the things that's just very that's just very visceral is the feeling of dehumanization that many students experience that many people the trauma that's so prescient when you as a math teacher talk to other people and you hear the ways that they have been either convinced that they're not mathematical or that they that they can't learn this at a later point in life and this for me is different than the whole kind of growth mindset stuff I feel like this idea of you know how do we bring forward this notion of attachment and joy and belonging as part of mathematics and not as a tacked on thing so I think one place to start is to kind of start with that trauma like what is the trauma that you either know of that other people experience and or that you've experienced I've been teaching math methods for 25 years at the University of Illinois and my students are mathematics majors and they are education minors and they are they are very strong in mathematics but when they get to college level mathematics and those courses are courses with 200 people in them or more and where the professor is going so fast and there's a focus on theory before students have really even been able to understand how to do theoretical work in mathematics because so much of what they've done in high school has been more kind of procedural and conceptual but it's more applied then there's even a sense of trauma for them and a questioning that like am I really that good I think one of the narratives mathematics is that if you're a mathematician you need to be good at mathematics all the time in all topics and that's actually just not true when you think about mathematicians if somebody is an algebraic topologist or if somebody is a geometry they don't know how to talk about all the other mathematics that their colleagues do but we have this impression in society and I think in classrooms because teachers feel the sense of showing students all the mathematics that they know and so I think it's maybe starting what is the trauma that people know of from others and also again potentially your own and thinking about how does that open the door for us to say we don't just want everyone to be good at the forms of mathematics that we had historically in classrooms Thank you One more question here Do you have any suggestions for how to make this a cross-curricular school-wide conversation Oh I think this is an easier kind of cross-curricular conversation because I think mathematicians math teachers are often the ones who are less interested in doing things that are whole school we're often the ones who want to be the exception to the rule and so these kind of interdisciplinary units that people do in schools it's often harder to feel like you fit into that because you've got a kind of rigid curriculum that you're trying to march through I think if it came from somebody in the math department and said we what I'm really interested in thinking about how could the students in science be actually studying some of the biology and chemistry of these other than human teachers that we're learning from we could be thinking about what are the kinds of patterns and what ways does this do these new teachers both show us patterns that have been sanctioned by human mathematicians but also maybe are showing patterns that are not so obvious how can the English teachers be writing about helping the students write the poems and the art teachers coming up with representations of some kind of gallery showing that might be something that would be presented in the community or to parents or to another grade level so that it would be like a gallery walk kind of thing or if it was online it could be the same kind of so I think that this is right for an interdisciplinary unit in a whole school kind of getting on board with the idea of attachment and connection because again it's very much reflective of the moment that we're in with COVID and Black Lives Matter and climate change. Well, thank you so much. I'll just share real quick that there is the last question is is there a book that you have written about rehumanizing mathematics and and yes, yes there is and and papers so maybe we can drop that information into the files for you all. I do want to give a little bit of transition time for our 11 o'clock sessions so thank you again so much Dr. Gutierrez for joining us today and for sharing those again inspiring and powerful words and thanks you everyone for your engagement in this session and I think this is just such a great note to start our conference off on so enjoy the rest of your time here the session should be started for 11 o'clock keep the conversation going we've got lots of chats you guys can keep discussing sharing ideas with and thank you all have a great day