# Rehumanizing Mathematics: A Call for Social Justice in Education

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## Introduction

Mathematics is not just a set of abstract concepts; it is interwoven with our identities, cultures, and societies. As educators, practitioners, and learners, we have a responsibility to explore how mathematics intersects with social justice. In this article, we will delve into the notion of rehumanizing mathematics—a framework that emphasizes inclusivity, equity, and the re-examination of our teaching practices in the context of social justice. We will discuss the implications of this approach both at the classroom level and within the broader discipline of mathematics.

## Acknowledging Our Historical Context

### Understanding Settler Colonialism

As we embark on this journey, it is crucial to acknowledge the historical context of our actions. Standing on stolen land, particularly in a settler nation, calls for a reckoning with our past. Recognizing the contributions and histories of marginalized communities, particularly those whose legacies we have often erased, is foundational in redefining our relationship with mathematics.

### The Limits of Traditional Equity

For too long, conversations around equity in mathematics have been defined narrowly, focusing primarily on access and achievement. While these are critical, they fail to capture the more profound aspects of mathematics—specifically, the identities and experiences that learners bring to the table. TRUE equity involves creating an environment where mathematics feels like a space to express one’s whole self, free from the pressures of conforming to preconceived notions of success.

## Framework of Rehumanizing Mathematics

### Moving from Theory to Practice

**Reconceptualizing Classrooms**: Rehumanizing practices begin in the classroom. It is essential to dismantle traditional hierarchies that stifle student voice and promote compliance over creativity. This involves redefining power dynamics so that students feel empowered to share their unique perspectives and experiences in mathematics.**Interactions Between Students and Teachers**: The classroom dynamic should facilitate open dialogues. When educators engage students in conversations about their mathematical experiences, it opens the opportunity to address dehumanizing practices, such as microaggressions and a one-size-fits-all curriculum.

### The Dimensions of Rehumanization

The idea of rehumanizing mathematics can be broken into several dimensions that educators should reflect on:

**Participation and Positioning**: Consider how students are positioned within the classroom dynamics and what role they play in discussions.**Authority and Authenticity**: Shift authority from simply residing with the instructor, encouraging collaboration and peer-led discussions.**Windows and Mirrors**: Curriculum should serve as both a window into new worlds and a mirror reflecting the identities of all students involved.**Creativity and Emotion**: Embrace the idea that emotion belongs in mathematics and allow room for creativity in problem-solving.**Broadening the Curriculum**: Moving beyond calculus and traditional pathways to ensure diverse mathematical backgrounds are present in the curriculum.

## The Challenge of Diversity and Inclusion in Mathematics

### Critiquing the Current Model

In many educational settings, mathematics has been upheld as a universal language—often in a way that inherently excludes diverse cultural perspectives. This single-narrative approach perpetuates a cycle of marginalization, where students from underrepresented backgrounds may feel that their contributions to mathematics are less valued.

### Bridging the Gap between Theory and Practice

Transitioning from traditional practices to rehumanizing frameworks requires more than mere acknowledgment. It necessitates:

**Engagement of Diverse Perspectives**: Foster environments where the contributions of historically marginalized groups in mathematics are celebrated and integrated into the curriculum.**Expanding Access to Mathematical Conversations**: Encouraging students to bring their cultural and linguistic identities into mathematics can redefine what it means to perform competence in this subject.**Challenging Traditional Assessments**: Tests often measure rote memorization rather than genuine understanding or creativity. Shifting to assessments that value unique approaches and process over mere correctness can create a more inclusive atmosphere.

## Conclusion

Rehumanizing mathematics is not merely a theoretical framework but a vital call to action. It requires educators to critically assess their practices while valuing the rich tapestry of identities present in any mathematics classroom. As we encourage this paradigm shift, the focus should pivot from traditional measures of success towards building an inclusive discipline that champions equity and justice for all. By embracing the rehumanization of mathematics, we can strive for a future where every student feels seen, heard, and capable of contributing to the ever-evolving narrative of mathematics.

buenas tardes so I just want to start by acknowledging that as a white settler nation that we

tateyama and shamash and i think that that's important for us to always recognize that that we have this history

and that we need to be cognizant of in what ways we are thinking about trying to write those histories that we belong

to so my goal today is trying to offer some language for us to try to navigate this space of thinking about how do we

address social justice in mathematics and to try to think about moving from theory to practice I have two different

kind of dimensions that I'm gonna talk about one is at the level of classrooms how do we Rehim anice classrooms and the

other is how do we recommand eyes our discipline and think about citizens in society so I'm gonna do I'm gonna do

that so I've been doing work so there should have been one slide sorry I've been doing work related to equity for

about 22 years maybe a bit more and I've tried to come up with theories that kind of fully ground these these

more deeper notions of equity that kind of move beyond notions of access and achievement access and achievement being

the dominant axis that's here which basically is that we open the doors and we allow more people who are not

historically in mathematics to be part of the field and then we the achievement part is and then we make sure that they

do well in the discipline so they go on they they're successful they get jobs they're part of the pipeline they get

awards they do all those kinds of things but if we take seriously the notion that if I have to give up parts of myself to

be able to be seen as a legitimate participant in those fields if I'm not allowed to use algorithms that come from

my home country if I'm not allowed to speak my home my native language if I'm not allowed to bring all the parts of me

to this room or to this space when I'm doing mathematics and maybe that that's also part of equity and so that's where

the identity piece comes and it's part of what I call a critical axis which leads to also thinking about power and

power I think of an into way small pee-pee kind of in the learning space and in terms of being able to

bring all the parts of the self to the room and thinking who gets reavoice who gets credit for the kind of mathematics

that's being created in that space but big P is also and what ways to have opportunities to practice mathematics

that allows me to read the in justices of the world and then also transform society to address those justices so

I've kind of been talking about this for a while and I and I suggest I'm not going to explain Nippon bla but and I

suggest that it's a messy kind of thing that it's not a simple thing to help students the the dominant part is

helping students play the game or helping mathematical learners play the game and the changing the game is thing

is again not just thinking about how do we help more people be successful in the game but how do we expect that new

people who come into the field are going to ask different questions are going to practice mathematics in different ways

and that they're actually going to end up giving us and promoting a more vibrant version of mathematics because

it's going to attend to this kind of diversity of world view of world views but so I've been talking about that for

years and I feel like even when I've tried to deeply theorize it and say this is what I mean by equity I feel like

it's really kind of gotten taken up in a way that that that has been superficial or at least that has been not easy for

people to take up and so I've been asking myself lately is equity even a useful term for me anymore and I've kind

of come up with the decision that it's not not because it no longer works for me personally when I think of that word

used so often now it's like that word diversity that it kind of doesn't really mean anything anymore or at least it's

not clear what it means I liken it to the organic and natural movement of the 1970s so back in the 1960s and 70s when

somebody said that they had something that was natural or it was organic there was a certain standard we held ourselves

to right now it's you know Campbell Soup is organic and and you've got strawberries that are grown in fields

that the organic ones are grown right next to the non-organic ones it's the same distributor and you so you have to

because of historically what has happened with that word and how it has gotten taken up I think that it fails to

promote dialogue and visioning because when we're in a meeting and somebody says you know we really need to address

equity in our math department or in this committee as we're selecting a new person to come into our field we need to

be thinking about equity issues well we don't tend to stop ourselves and ask what do you mean by equity what do you

mean by equity we tend to all in our heads go yeah I agree that I want to address equity too but there's many

different versions out there and as a result we don't necessarily push ourselves to kind of theorize where

we're going with that and I would argue that we actually only really know that we're addressing equity when we're very

far away from the target so we can look at a at a math program and say you know we really have so few women in our

program or oh we have you know all of the people that are in our program don't represent the people that attend this

university or something we can say so that's very far away and we know we want that but as we start getting closer and

closer do we still feel like we know what this thing is we're trying to move towards maybe not and so I've said for

myself and again this always comes down to like when does language fail to help me think about complex problems that

word equity wasn't really helping me so much and I felt like I needed a new word and so lately I've been talking about

rehumanize Excel one we're going to talk about pre humanizing classrooms and I need to first start with if I'm saying

rehumanize already kind of animus and assumption that there's something that's dehumanizing right so let's start with

that dehumanizing you may feel like dehumanizing sounds like that really strong word right dehumanizing it's

keeping you from being human right but actually if we think about this from a more complex way and we think well when

we say that word violence we often think violence is this you know kind of it hits you it's this it's this really

acute act but if we think about slow violence we could think about things that we're repeatedly required to

succumb to or that are that are done to us or that we're we're participating in and we might call

those microaggressions but I think sometimes to talk about them as microaggressions maybe misses what

mathematicians would be acknowledging because they might feel like microaggressions of the stuff that other

fields talk about and do and so if we think about the fact that mathematics is a compulsory subject you must take it

for this many years that it's required that we hold it up as the standard of intelligence in society so even if you

don't think of yourself as wanting to go into it as a career that there's implications for whether you think of

yourself as mathematical or not that continue on long into your adulthood and we think about the ways in which

mathematics often asks us to kind of leave parts of ourselves outside of the learning space or maybe even the

research space while we're doing it you can see that maybe there's some some parts of this that could feel like over

12 years of compulsory schooling and then maybe through graduate all the way through graduate school there may be

parts that could be felt like it's dehumanizing so I actually want you to turn to the person next to you and I

want you to hear if you're taking that that kind of slow violence notion of dehumanizing and you were gonna say what

do we think that students and maybe we'll say professors might feel is dehumanizing in doing mathematics what

kinds of things could arise for people so turn to the person next to you and what kinds of things could feel

dehumanizing okay what if some what are some things that people might be willing to share I saw what what what I loved is

that I saw a lot of body gestures right so there was a lot of this like you know when people were speaking to each other

so there was there was at least some clear emotion and some connection with things and maybe it wasn't you maybe it

was you were thinking about the things your students say or but is anybody willing to share something that they

felt like could could fall in that category of a feeling dehumanizing when you're doing mathematics yes

okay so I was recalling a moment when I was talking to a professor about incident with another professor that was

really challenging emotionally and it was an experience where I was like you know this happened to me and he really

had no way to respond other than he shouldn't have done that and then after all of this and there's tears and

everything involved he said to me well I hope the next time we meet we can talk about the math and I think that is just

an example of the way that often mathematicians are trying to say we don't need to worry about us and the

messy emotions that we bring the math is clean and easy and if we can talk about the math we don't need to worry about

we talked about the power dynamic between a professor and students sort of the idea that students are there not to

participate but to sort of just be subjugated and listen and be given information by a person in power yeah

yes oh those authority roles right and and what's very clear who's the expert and who's the novice and who's who

creates mathematics or at least is in charge of it and then who is supposed to be consuming it hi I think well as a

woman also whenever you see like this theorem was made by such-and-such last names and I think people always tend to

assume those last names correspond to male mathematicians and I remember one time in algebra class by a female

professor she said well this theorem is due to another and I was like well it's like it's a good thing you mentioned

because I feel like represented and soften we just you know forget like the people are doing these theorems but also

and you don't need me to call on you so if you have something you want to say you can just come to the mic I talk to

students a lot they the math education is to say they were taking an analysis class which is required for math

education and the first day of the class the distance command is the professor's who is in math education and then the

raising hands I said let's see how long you last this is actually this is not common then I

had another student that took differential equations and did poorly on the first exam and the professor which I

know will keep telling me great that you're bringing minority students and then he he called him to his office put

the university color catalog of courses and say what courses of this had you taken these days I said no what are you

doing here that student was the best grade in the final sir student not Peruvian descent I was determined and he

didn't tell me that until the day he got his ph.d which was three years later yeah and let's make us the last one

so in our group we were talking about code switching and how there's something in mathematics that makes it feel a

little different of having an identity as a mathematician and as you as a person and how sometimes the

mathematician part feels very in authentic to who you are in your personal life yeah yeah so that kind of

relates to that like leaving parts of you outside of the mathematics right and when I when I've asked so I've been

going around the country and talking to people about this and I've been asking you know K to 12 students I've been

asking K to 12 teachers I've been asking mathematicians what kinds of ideas arise when these kinds of when you think of

that word dehumanizing and and we get this that you know the kinds of things that are being brought up here we also

get the you know the professor who's at the board and who's working out a problem and then

kind of just stops Midway and says and the rest is obvious or on the rest is just algebra right and and it makes

other people feel like but wait we have to do that work right like that that that's still required of us to finish

the problem and so I think I think that's been most striking to me is that when I've done this with people and I've

kind of asked them what are some of the things that come up many of the things that feel like they're dehumanizing for

students while they're learning mathematics can also be the things that feel like they're dehumanizing for those

who are teaching mathematics and not just at the k-12 level but also at the at the university level so this notion

that we're measuring and categorizing bodies for students this feels like it's tracking right it feel it may feel like

which calculus course you're in is a freshman and then it then when we think of the parallel version of that we can

say well in what ways are professors being assigned to particular courses and in what way are those people being

positioned in the math department depending on who are the people that they're teaching or what level

mathematics that they're teaching and in what way are we categorizing and measuring bodies in that way we can

think about each one of these as we go down the list and talk about the fact that evaluation for example that doesn't

honor complexity could be what are the things that a math student or a math learner is feeling like they are getting

out of the class or that they are that they are gaining and growing but that's not captured by the grade and same thing

with I think math professors you may feel like you've been able to move a student you know from here all the way

over here and that somehow doesn't doesn't look like it's very effective if that person that moves all the way here

gets the C in the class when you have colleagues who may have people who are right here and they move them that for

that much further and get a get a B so so again I think thinking about in what ways are we as even as professors are we

allowed to be human as math professors what what what's expected of us to be able to bring to the math classroom or

to the math learning space that that allows us to be whole and in that same way in what way

we expected to everyone have the same exam so that every you know that feels like it's addressing equity it's being

fair everybody has the same access to the same information and everyone's in some ways being expected to be on the

same page then in what way does that strip professors of being able to have their own autonomy on the things that

they teach and and being able to communicate it in ways that might speak to students based on who those students

are and I'm going to come back to the one about rule-following instead of rule breaking because I think it's something

that's that's pretty important but I think another piece of it is this idea that somehow mathematics is separate

from politics and from values and from ethics students often have told me that they feel like in math classroom all you

really need is a brain and some kind of a stylist so whether that's a brain and a computer a brain and a you know paper

pencil a brain and a calculator a brain it but it's this idea that you shouldn't bring like you don't need your body to

do mathematics the rest of your body you just need a head to do mathematics and so I think that that's pretty striking

and it also makes me wonder if we think that mathematics is not political not cultural not any of these other things

then how do we remind ourselves that it's a human endeavor so I've been talking about this term rehumanize and I

want to say a little bit more about what it means for me why is it useful for me to say rehumanize instead of saying

equity well first of all I want to start with the re INRI humanizing rehumanize inform me the emphasis on that re

humanizing is to honor the fact that for centuries humans and if we want to go back millennia living beings have been

doing mathematics in ways that are humane it's not that we have to invent something new for people to be doing we

and then you go to school and school teaches you that you're no longer mathematical or at least it teaches you

that you're only mathematical if you follow these sanctioned ways of representing the stuff that you're doing

and you measure up against what has come before you in mathematics and so that repart is really acknowledging that

have been things that have been erased that we and but and yet people persist right there still ways in which people

practice mathematics outside of a classroom in the everyday world throughout history and also that we have

multiple versions of mathematics that are going on it also addresses the politics and the recognition that

mathematics operates with honor and privilege in our society and you might wonder wait what does that mean unearned

privilege mathematics so we can start with the idea that how we've set up our society we can analyze we've set up

society so that mathematics and rational thinking and logic and abstraction all become these kind of highest levels of

intelligence rights this this thing that we that mark some people as being smarter than other people in society and

you know it because those of you that have said to in conversation when you meet somebody on a on a bus or at a

party or something and you say you're a mathematician you get a particular response from people right what's one of

the things you hear when you when you say to somebody you're a mathematician you must be smart right you must be

smart that's not what I call the adulation and I find that there's also another piece that comes with that what

other things do we tend to hear I was always so bad in math that's the confession I feel like we hear this

adulation and the confession and if you're a person of color there's also the Incred you Incred that that it's

good how could it be how could it possibly be that you are a mathematician right so there's that third part if you

layer on that person of color and you're mathematicians and so we might ask ourselves well why is it that we've set

up our society so that we use mathematics as the proxy for intelligence why we could have a society

where how you relate to other people measures intelligence where whether you think holistically is really a sign of

intelligence whether your artistic is intelligence there's so many other things we could do and it's somewhat

arbitrary right that we use mathematics as the thing that makes somebody intelligent that doing math doing well

in mathematics is something that makes people intelligent and then we prepare you ate that myth not we personally it

gets perpetuated that there are some people who are just naturally good at mathematics and some people who are not

naturally good at mathematics and if you're one of those people who's not naturally good at mathematics then it's

okay to say things like I was never good at mathematics but people aren't walking around society worried about things like

in other subjects so we don't have people saying well is that I am big pentameter thing and poetry and is it 13

lines or 14 lines and a sonnet and people aren't worried and and carrying this kind of baggage with them but you

talk to people in everyday life and there's a lot of trauma that people have experienced through mathematics through

feeling like they might somehow be better if they went back and took more classes you hear this I hear this in

speaking to adults and I don't hear them saying they need to go back and take you know a class in history or something

else so it acknowledges that that mathematics is operating with this unearned privilege in society in the

same way that whiteness operates with unearned privilege in other words we use whiteness as this measure by which we

judge other people and it becomes the normal it becomes the standard and we do the same thing with mathematics we you

know in the in the comic that I sometimes use as well that Lily brought up about the purity of the disciplines

right and the mathematicians with the far end and is saying oh I didn't see all you people down there it's because

math is the is the kind of that's the the standard by which we're judging all these other how far away are you from

this thing right and and I would argue that that it's also cannot be decoupled from this white supremacist capitalist

patriarchy society this white settler society that we live in there are a because mathematics is a human endeavor

that means mathematics also is rife with power and identity issues that come with those people who practice it we can't

separate those those two things so rehumanize ignite it sometimes in the literature in critical mathematics or in

even like critical ethnic studies we get this this emphasis on deconstructing and on and critiquing what's happening

around us and that is a really important tool right being able to think about how do we make sense of the world that's

around us and how do we not just accept the world that's around us as the only way we could be operating but that we're

reimagining other ways to be but we first have to kind of start with that critique that deconstruction but then re

humanizing mathematics says we don't just stop with identifying how is mathematics potentially connected to

things like wealth and dominance and compliance so there's people out there like Cathy O'Neil who's written weapons

of mass destruction there's chaos monkeys is another book that that was written that kind of talks about the

role of mathematics and algorithms in particular that can end up having very dehumanizing effects in society and so

there's this work that's out there that's talking about that but then I think we need to ask ourselves okay so

if we know that this is that like the awful stuff we don't want to keep doing how does that help us think about well

so then what do we want to be doing right and that for me is that is the review man izing part two is that it's

recognizing that it's it's coupling now with with belonging and with joy and with healing and with connection that's

different than just critiquing what we don't like when we see things about mathematics that could feel dehumanizing

and I say that Riku man izing is a verb or that this concept of your humanizing is a verb and that it's and that it's

action-oriented so we're not trying to move towards a rehumanize mathematics as if there is an endpoint we are saying

that we are going to be that this this action requires constant vigilance that it's going to require constant reframing

and new iterations of what this thing is and that by virtue of that it's also going to mean that it seeks evidence

from the populations that we say we're trying to humanize math rehumanize mathematics for that they actually feel

that that feels rehan izing so I often say to kind of K to 12 teachers that you know we can't

just start with that space of I teach like the next students or I'm in it I'm in a hispanic-serving institution and so

I'm gonna bring in the the vigesimal system of base 20 and talk about Mayans and how this was part of their to

every and feel like that is gonna do its part to reef you man eyes mathematics if that doesn't feel real humanizing to the

students that I'm teaching right so I alone don't get to decide that something is refew Minh izing for other people it

requires this this process of of checking in and of and of reframing and and rethinking and and again in a

constant vigilance and it it I could we could name it but what so why not call it decolonizing mathematics why do we

call it Rehan izing mathematics and again I would say that we could and I've actually referred to this as living

mathematische I have an article that actually takes seriously I don't take decolonizing as a metaphor I take

decolonizing seriously and if I was going to hold myself to that standard and say we want to talk about land and

sovereignty and erasure of culture and language and things like that then if we take that seriously then we have to take

seriously the fact that humans really shouldn't be the center of our universe if we recognize that we are the younger

brothers and sisters of animals and plants and rocks and bodies of water then what might that mathematics look

like so what I'm framing here is review man izing mathematics but I've also for myself taken it to another space where I

hold myself to a different set of standards and the thing that helps me with me humanizing mathematics is that I

borrow the work of Emily's style who first wrote about windows and mirrors back in 1996 and she was talking about

the curriculum as a mirror and a window and the the reason I like that that idea is that often times when we're in that

equity language when we're in that inclusion language when we're in the diversity language what happens is that

we unknowingly perpetuate this notion that this is this is the stuff we do for other people or for those people but

it's not something that we would do throughout for through all of our mathematics but it's what you do when

you're trying to be more inclusive of other people or what you're trying to affirm other people when we think about

the fact that we are all humans which means that we all need to be affirmed and see a portion of ourselves in

experience that we're doing with mathematics but also we need a window onto another world and to see things

that maybe we'd never seen before that both those pieces are important and those aren't just important for people

of color people who've been historically oppressed those are people those are important aspects that window and mirror

for all people and so for me it very much relates to to the concept of in la Kitsch which recognizes that we are all

simply vibrations in this cosmos that we are all interconnected and it begins with this idea of in luggage is I that I

am another you and you are another me and that in moving through this world in a way that acknowledges and that affirms

and that recognizes that that is our connection that we have the opportunities to think very differently

about mathematics and so again it's it's not just a window in a mirror in a sense of the curriculum needs to be that way

but it's it's recognizing that when weary humanize mathematics that we are moving towards mathematics as this verb

as this thing that we do and not just something that is that reflects back on us as in we use mathematics as a tool or

we use mathematics as a language but that we actually live mathematics in a more recommand eyes way so in these

images you know we when we ask students what is mathematics I you know we see the beauty the complexity the

interconnectedness the humanity of mathematics the the rangoli structures that are at the top with the women who

are in India those are done with with chalk but often they are done with rice in in doorways and so people are making

these these complex structures that get brushed away every single day as people walk in and out of their house so so

when I again when I say rehumanize acknowledging that there are people that are doing this work and that we we don't

need to kind of move to something different but this is not the things that of mathematics that most students

would feel like oh I would name that but these are not the images that that come to mind but we see people who everyday

are playful who are joyous who express themselves through the activity of mathematics and so if we take seriously

that notion of um of students making meaning and moving through the world and thinking out loud

about mathematics in ways that may not be sanctioned with the current versions that we use then and we and we take that

really seriously then we can see how that perspective would give us a greater potential for connecting teacher-student

and new forms of possible mathematics and so you might wonder well what do I mean by students and new students

teachers and new forms of mathematics so for me new forms of mathematics is recognizing than historically when we've

when we've decided to ignore or or break a rule we've decided that we no longer want to go along with what has been

sanctioned before us is how we'd get gotten new forms of mathematics so we could think of in 17th century when just

people decided we didn't want to follow Euclid's fifth postulate that's how we get non-euclidean geometries we have

cantor who's decided that well maybe infinity is not this singular thing maybe we can have multiple sizes of

infinity right and this is how we can get complex numbers this is how we can get irrational numbers this is how we in

each one of those cases there was somebody who decided that maybe this thing that everybody else is following

is not exactly the thing that that makes sense to me and so in what way might that be cultivated so you might say okay

this all sounds good but what does this look like if I'm actually gonna try to name it or see it in a classroom so

again we're at the classroom level so I say that there's actually eight things that I hold myself accountable like okay

if I'm gonna say that this stuff is important what does it mean for me I am NOT suggesting these are the eight

dimensions of rehumanize amass Mattox I am saying that these are the dimensions that have that have been important for

me when I start to take these things into consideration and I'm not going to go deeply into each one of them I think

what you should note though is that as you're reading the blue is what I would actually look for so if we take the

participation in positioning we would say many times our students feel paralyzed to not be able to move forward

because we're not there to you know you in a k-12 classroom this is a very common thing you have kids sitting there

raising their hands and waiting for the teacher to come because and even they're surrounded by tons of other kids who

potentially could be helping them make sense of that problem so it's when we think about Authority only being

traditionally the authority is in the text or it's in the teacher somebody said something to me recently that was

really powerful he said he actually wrote the textbook that his students are using and so somebody had come to him in

office hours and the student had said to him well the text says and he was going on and on about this thing and he kept

going back to well the text says the text says and he said okay so first of all will he be was thinking in his head

like well that's me I'm I'm the one who wrote the book so like it's not this you know kind of you know sterile entity

somewhere over there I actually wrote it and also what do you think but I thought I thought that was kind of interesting

that that you know even the student couldn't acknowledge this is this very person I know and wrote the text and I

still don't see it as this person said I see it as the text said in some kind of authoritative it must be true okay so

I'm not going to talk about all these I talked a little bit about windows and mirrors here's the other four dimensions

and I actually want to talk a little bit about well I want to say I'm actually want to say when something really very

quickly about broadening math math mathematics so again this has more to do with K to 12 but I think it also has to

do with how what our requirements in math programs so in K to 12 programs we have backwards engineered this notion

that calculus is the end-all be-all if you take calculus as a high school student you get your you know calculus

carrying card you get to take with you throughout society and you get to say I was an a/b calculus student or I was a

ap doubt of this course and I now get to be in this course and right we get we get but and so in some ways the the

curriculum that we teach in the United States gonna be very clear because other countries don't do it this way but in

now you're learning geometry now you're learning probability now you're learning and in much of what we're showing

students of what when we're presenting this is what mathematics is we're basically saying it's a continuum from

algebra to calculus and that's a particular version that's that's somewhat arbitrary that we've chosen

that to be mathematics to represent to students we can imagine other forms of mathematics that we would use to present

to students this is mathematics why aren't we doing topology with high school students why aren't we doing

graph theory why aren't we doing combinatorics through card tricks why aren't we doing knot theory I mean

there's so many other things that we could be doing why aren't people learning to work in other bases so many

of the things that we could be doing and it could also kind of really emphasize that spatial reasoning portion that

moves away from a purely algebraic emphasis and we can ask ourselves in our math programs how do our mathematics

programs what we require of math majors in what way is that also potentially arbitrary in other words why do we

decide that these are the courses that people need to take as opposed to these other courses right so I'm gonna talk

about two of them when I talk about creation and body and emotions only because I think of the harder ones for

people to imagine like what was what would this actually look like so in creation I think that again if we

go back to this idea that somebody could say well maybe all lines aren't straight or maybe you know there's you know I can

imagine a triangle where it adds that the interior angles add up to more than 180 degrees and we might say that that

student just doesn't understand that right and we we can't imagine that students would create you know would be

that those kinds of ideas is actually what leads to creativity in mathematics and may lead to finding new things so if

we take the idea of K to 12 I'll start with K to 12 now I move up we start the idea of K to 12 and we say to students

you know you've got these four operations yeah addition and subtraction multiplication and division

right and they just learn them they've learned these are the things those are your tools

move on we're gonna build on those tools but we never really asked them to try to create any new tools or to try to think

about how to change those tools right and so from my perspective I think you know well what would it look like if

we had classrooms where we said to students here's for operations why don't you come up with a new one a

different one well what what could your fifth operation look like and what way would it be internally consistent what

would be your definition what would and so I think about that at a higher level and we think okay well why would that be

useful some people might feel like why would you do that that would just confuse students and it would just be

like an anything-goes kind of math classroom right like oh so we're just now gonna say students get to invent

their own mathematics and then how are we preparing that's not an equity issue like then we're not preparing them for

the next stages if they come in with this idea that they can just invent new things that violate our definitions of

previous things but we think about what mathematicians do this is what we do right how do you think about group

theory and you think I mean we just heard that lovely convert I'd love lovely talk bye-bye professor deliora

saying that we have things like so if we start with our definition of a group and we say well it has to it has to adhere

to the axioms of closure and excess associativity identity and invert ability but what if I want to break one

of those rules what if what do I don't really want it to fulfill all those things well if I am practicing learning

how to break rules I might say well what if it just only fulfills closure well that gives us a mono

what about only fulfills what if it pulls three of the four but not invertibility that gives us a quasi

group right I don't know about quasi groups until recently but most of you've heard about semi groups so again when we

think about the kinds of practices what happens at least at younger grades but we have to ask ourselves is any of that

happening at the university level and what way are we perpetuating this notion that people need to just take this stuff

on as truth that these are the tools you're allowed to use I think about a history of mathematics classroom and

often most history of math courses get taught like this here are the things that were proven at this time so that

means these are the tools you allow you're allowed to use right now and now I want you to do this set of problems

they ignore any of the socio-political things that were going on at that time as to why those things were sanctioned

or who might have been doing other things that just weren't acknowledged then and we we make it seem as if that's

now teaching people the history of mathematics so how about body and emotions I think often times we we think

that body and emotions shouldn't come into play in mathematics and somebody give you a problem it's

it's an ice cream problem so you have four different flavors of ice cream and you get to have two scoops so I want you

to tell me how many different combinations of ice cream can you have force for cough Lavers two scoops how

many combinations do you come up with just shout out an answer six thank you six how did you get six okay

and choose cake right right so you went straight to be efficient get it done right and choose K six yes

can somebody tell me how you can get a different answer somebody got not who didn't get six what did you get okay so

then you get 16 right so so I could decide that my senses matter and for me I agree with you I was right there with

the chocolate that was the example I was going to give as well I was going to say first we could say that if we're if

we're gonna exclude you can't have double scoops of the same flavor we could say well maybe the order of the

scoops matter right maybe I want to start with raspberry at the bottom or I would start with chocolate at the bottom

and have raspberry at top because it matters to me that like on the end I get my chocolate right

or maybe you assumed I was scooping in ways that went like this but what if my scoops were this then does that is that

a different so again thinking about the ways that younger grades we can be doing this but then at more sophisticated

levels we might be be doing that as well I'm not going to cover this example but you can reach out to me if you want to

hear more about a high school math teacher in Berkeley who uses students voices and and and they're singing to

understand the notion of derivatives so what if we want to make this happen more often right okay I'm on board I think

these would be some good ideas how do I make it happen this is they're kind of a little bit of the activism side well one

of the things is just to so they've got lots of things written up there my friend buddy got about what this tells

with social media you can take a picture and then you can always unpack it later so I think there's a part of me that's

like get as much in as you can because I may never get to talk to you again the the idea of misconceptions is one that I

think is really important for us to think about because this happens not just at the k-12 level but I think this

our classes by thinking about the misconceptions students may have coming in so we anticipate misconceptions and

we're told that that's actually a good thing to do that that's going to be addressing potentially equity issues

because we wouldn't want students to build on faulty foundations right like we don't want them to leave our

classroom and have these bad notions of this thing that doesn't make sense but if we go back to in Luckett and we

recognize that there's a part of you and me that you are a part are partly a me and I am you I'm not I'm not it's not I

am you you are me it's that I see a part of you and me and you you are another me and I am another you that if I recognize

that and I start with that idea that students don't have misconceptions students have conceptions then it

requires of me trying to stand in your shoes to first understand how does that make sense how could that make sense to

somebody that we wouldn't be working in a Cartesian plane and we wouldn't be in these kind of two-dimensional spaces and

that we could have a triangle where this interior angles don't add up to 180 degrees maybe it adds up to more than

180 degrees right so how could how can I step in the shoes of another student or one of my colleagues and say okay

instead of starting with this notion that I'm going to correct your misconception I'm actually going to

listen deeply and think about what insight does this give me or how could this internally make sense from the

perspective that you're talking about and then where does it potentially stop making sense and again maybe then we

generalize to there's there's a you know a general case that covers this particular

instance and again that I feel like that's that's what we do as mathematicians but it's starting with

that idea that that even small acts like not thinking that students have misconceptions and kind of going in with

that kind of critiquing of those misconceptions first but first acknowledging and affirming that there

isn't a part of you and me and a part of me and you we might also find ways to ask our students themselves in what ways

are our classrooms feel the humanizing to you maybe you wouldn't use that word dehumanizing maybe you would just feel

say in what way is this classroom affirming or not affirming of you or in what way does this classroom opera

opportunities for you to be fully yourself or not and then find out from them what are the things that matter and

then go do something about it what if you're kind of okay that doesn't feel like it's that difficult I can do those

things I'm in charge of my own classroom I can create exicted take exit tickets give me something that's a little bit

harder so I would say well one thing to do is to try to ask yourself when are you making transparent the culture and

the history of mathematics and how that relates to power structures so every time you hear yourself or somebody else

saying mathematics you should always be asking yourself whose mathematics that's a nice exercise to kind of get yourself

into another thing is that maybe people don't think about the ways that mathematics relates to power or what

kinds of things you know you you may be in a position because your math professors and your or your math

graduate students or that your people are deferring to you in terms of what kind of mathematics their kids should

take or do and they might ask you like is it important for my kid they might assume that it's important for their kid

to go in to have another year of calculus but you might be able to tell them but the people that we want to come

into our program we care more about people who can think deeply about ideas and so maybe your kid taking a research

course that would have them being to do some mathematics or maybe you're asked to act to consult with a school district

about what would be important and so thinking about when do we perpetuate this idea that that the that

end-all-be-all is calculus and if that somehow becomes the measure by which we can identify a good a good student so

calculus becomes the gatekeeper for universities that algebra is in the younger grades so maybe we need to

organize some informational sessions for parents and everyday citizens to understand these issues and to try to

think about how they would push back we might actually think about what how could we stage some kind of a protest

about the ways in which mathematics is not being used in to rehumanize our society and demanding that we maybe it's

demanding more about the k-12 system than it is about the university system but asking yourselves why are we

complicit with a system that says we have to cover all this material in this short amount of time and we don't

question what's the quality of the experience and I think in doing all of this in thinking about how we educate

ourselves how we educate other people I come back to sort of Chavez who always reminds me that once social change

begins it cannot be reversed we cannot uneducated has learned to read we cannot humiliate the person who feels

pride and we cannot oppress the people who are not afraid anymore and so when we take that into our own hands and we

ask ourselves well how might refute this concept of rehumanize amass Mattox affect my everyday work what are some

things that I can imagine differently I want you to turn to the person next to you and talk about that for a couple

minutes okay where were some of the things that you where were some of the things that you thought how my how my

tree humanizing mathematics are you were in conversation I had a hard time stopping that so how my tree humanizing

mathematics affects your everyday work so the way that I was thinking about how it would change it um I I sort of

thought of one when we think of what classical music is who do we think that classical music when we think of a

classical musician within go back Beethoven and we forget about all the different cultures we think of the

Eastern music we think of Chinese music Indian music and I get the feeling that we do the same thing when we have our

Idol mathematicians who do we think of I think of gals within the firm ah we think of all the people in Europe so

maybe we have to change who we admire as men as mathematicians and we have to show where students said the Mayans are

there the Aztecs are there like people the the tribes are there people in the East are there so being more aware of

who we want their students to idolize and also like I was guilty of this I remember early when people said like oh

like look at Euler's theorem I would be like no like why are you saying you later I will get mad at this right on

last slide I don't know the last item that we as faculty need to think of a classroom as a way of engaging students

and we just have no idea what it means to be an effective communicator we started a couple minutes late right okay

we were also talking about assessment and this idea that we have in mathematics that things are either right

or wrong and thinking about how much anxiety that produces many students and then so just thinking of ways of

changing a sentiment that depends on the size of the classroom and it might also mean that we're going to be working more

but yeah we said that we really as students appreciated whenever the professor or the instructor

would encourage us to explain our train of thought and not just solve the problem yeah and I just want to share

quickly that the wonderful mathematician at Wheelock College Deborah Berkovitz shared with me one of the things that

she does with her classes she has she teaches a calculus class and every Friday she'd have an exam and the

students would stress out about that exam and felt like it somehow it didn't fully measure them some people it was

about test anxiety but for some people they just felt it they just didn't fully get to express what they'd learned and

so she came to the practice of having them still do the exam every Friday but they would take a picture with their

phone of the big of the exam and they would go home and then they would analyze their exam and think about being

able to point out what were some things that they did that were quite beautiful or were quite efficient or were quite

whatever that they were proud of and what things did they realize that they had still didn't understand at that time

but then went and taught themselves or went and understood it more deeply and could now come back to it where they

felt like there wasn't these one-time you either know it or you don't know and we move on and she found that in

the solutions to problems everyone felt a sense of kind of ownership of wanting to offer their perspectives and and it

just changed that that dynamic of what was happening in terms of assessment yes I think one I think one of the issues

that we face as mathematicians is the assumption that mathematicians are academics right throughout this whole

conference it's been oh sit with a faculty member or a student but there hasn't been sit with a professional

mathematician or sit with somebody from industry or somebody from government even throughout your talk you're talking

about what we can do in the classroom or as students whereas as a professional mathematician I face the same issues of

telling somebody on a mathematician and then having to explain what that really means and know I'm not gonna balance

your checkbook because I don't balance my own but then to your last point there one of the things that we face in my

office is how do we evaluate people who are so to speak doing mathematics versus people who are leading the

mathematicians so if you're enabling all of these mathematicians to do your work to do their work how do we how do we

judge that for promotion versus the people who are proving the theorems I guess this last one okay so so I was

reading Twitter is a big Personal Learning Network for me so I just always get great ideas and one which came from

a business article that sort of an expose about a research article that the message was as long as we continue to

evaluate people by the same metric as we were evaluated we will always get the same people at the top right and so I

think we have to look more broadly at how we're evaluating to get a diverse pool and and I think yeah it's a big

right and and it's a big challenge to the system about what we consider to be good enough to get ranked so I just have

a couple of more slides that I wanted to read and I wanted to talk about the discipline so if we're thinking about

the discipline and not just classrooms we need to think about how our mathematicians trained the only part I

want you to really pay attention to is the part that's in blue I mean certainly you can read the whole thing but it's

this idea that we create this there's this myth of an apolitical benevolent science that prevails and that the end

product of the training with these very technical isolated things isolated from social and economic context is that we

get a training of a narrow specialist one taught to perform scientific miracles without considering their

political implications and I the part I don't have in blue but I should feel like should be in blue is it's a

reliable tool of the power structure that this training creates an ingrained sense of elitism and we could think

about the ways in which when students are taught regardless of what level we're talking about when you are taught

something that feels like it's an arbitrary rule or a tool that you're supposed to use and it doesn't make

sense to you in some ways that's the training ground for making sure that we have a compliant society because when

you learn how to follow rules that feel arbitrary to you and you don't know how to question those you can be expected to

be in a particular place in society and so I want to leave us with some questions about thinking about what is

our role as mathematicians thinking maybe about if we recognize anti-social elements of math and how are those

affecting our relationships with each other on this planet what is it that everyday citizens what ways can we help

everyday citizens deconstruct that relationship between mathematics and dominance and compliance and make people

more aware this is the last quote so back in 1973 almost 50 years ago there was a group that was called scientists

and engineers for social and political action that's ESPA it later turned into the science for the people that operated

conference in Ann Arbor Michigan and there's a number of working groups and there's probably a chapter that is

getting started somewhere near you so be on the lookout for that but I think that the question we have to ask us is if

we're thinking about a mathematics for the people for the people and by the people then we need to recognize that

political nature we need to make sure that it has access for all people we need to make sure that there is

knowledge for movements with social change and where is it previously I feel like much of the work that we have done

feels like it's humans in the service of mathematics I'm asking us to think radically and reimagine what might be

for a mathematics in the service of humans and I don't mean that we have a mathematics and the service of humans

that suggests that all mathematics needs to be applied I do mean that if we think of mathematics as the search and science

and affirmation of patterns for problem-solving and for joy then we can imagine how somebody operating an 8

dimensional space is mathematics in the service of humans and if we agree that these are the kinds of things that we