Friday, October 18, 2019

Inclusive pedagogy and neoliberalism

At this moment in Chicago, there are 35,000 workers from the Chicago Teachers Union (CTU) and the Service Employees International Union (SEIU) Local 73 out on strike. These everyday people—teachers, clinicians, support staff, special ed classroom assistants, custodians, security officers, bus aides, park supervisors, attendants, landscape laborers, and more—are picketing not only for themselves but for the common goodTheir demands include affordable housing for students, sufficient teacher prep time, and class size caps; proper staffing of school librarians, nurses, social workers, clinicians, and counselors; fair pay and benefits for Chicago Park District workers; and, ultimately, the dignity and resources they need to do their jobs. My own union of graduate employees at the University of Chicago, Graduate Students United (GSU), has been zooming across Hyde Park to both help bolster the lines and keep sharp our own picketing skills, as has the University of Chicago Labor Council.


At the same time, the coalition of faculty at the University of New Mexico (United Academics of UNM) have won their union election by a huge margin (almost identical to GSU's from two years ago). This is rad in and of itself, but especially wonderful to me because Albuquerque is my hometown. In the words of Professor Nick Estes: "with a union we can better serve our students and thus better serve ourselves as workers of UNM." and "with a union we can increase hiring and sustaining Native faculty."

These folks are truly inspiring, as are the people of Chicago and Albuquerque coming to their aid. To those of you who insist unions should stay in their lane and only fight for wages... well, frankly, you're racist.

As any of the amazing educators currently out on Chicago picket lines or in New Mexican classrooms will tell you, teaching is hard. Furthermore, going on strike and witnessing true collective power in the face of oppression profoundly changes the ways you teach, as evidenced by these blog entries.

With all this in mind, I've talked a lot about neoliberal education (remember Irami Osei-Frimpong's video?) and I want to make a note here on what is called "inclusive pedagogy," just because it's come up a lot for me the last couple of weeks. Inclusive pedagogy refers to a paradigm of teaching which acknowledges the varied backgrounds, learning styles, and abilities of all the learners in a particular classroom, which is of course very important and cool. At the same time, "inclusivity" has become a buzzword in a lot of liberal institutions and, as a result, you see a lot of teaching workshops centered around it. That's good, right?

My big beef with the rise of ~inclusivity~ is that institution-sanctioned spaces rarely do their due diligence in making white, wealthy, male, and otherwise privileged people uncomfortable with the current state of affairs. That means these workshops fail to confront the reality of racial capitalism in perpetuating a stratified society, where simply making our ivory towers more inclusive passes as a radical act. To borrow the words of Professor Chanda Prescod-Weinstein: "I harp on liberalism here because I think too often liberals who believe we should seek to grow the status quo ('America is good, it just needs to be better!') co-opt the language of those trying to destroy the status quo ('America is an imperial project built on genocide!')"

We academics should be working to remake the institutions of higher education—as political, economic, and social engines—to serve working people, not to just promote a handful of black and brown and female faces while perpetuating the ongoing underlying system of stratified exploitation.

Now, this quarter I've been attending a Fundamentals of Teaching in the Mathematical Sciences seminar run by two graduate workers, Karl and MurphyKate. These two are both brilliant mathematicians, dear friends, and incredible instructors who constantly strive to be better and I love them very much. They are running these workshops under the close supervision of the Chicago Center for Teaching at UChicago and this week was specifically on inclusive math pedagogy.

We opened with an exercise that I think can be useful to warm up academics who come from a great deal of privilege and haven't thought a lot about what it's like to not be themselves in educational contexts: we broke into small groups, were given a bag of supplies, and told to build mobiles. The secret was that different groups had different items in their bags—some had wire, glue, markers, glitter, scissors, and other materials, but my group only had a clothes hanger, paper, and some tape. After we created our mobiles, Karl and MurphyKate graded them—the groups that had received plentiful resources were praised but the rest of us, held to the same standard, were critiqued harshly despite creative efforts. At the conclusion of the exercise, we were asked when we realized the distribution of resources was unequal, what our reaction was to these asymmetries, and how it felt to be judged in such an unjust way. As you might expect, the groups with lots of resources hoarded them while those with very little tried to find ways to cooperate.

Even though I think this exercise was fairly tame—no one had even brought up words like “race” explicitly yet—I could see a few folks take what was being discussed very personally as they started connecting dots. The room, by the way, was overwhelmingly white and male. As we moved on to think about axes of identity which could lead people to feel excluded in a math classroom, a friend of mine brought up gender and was immediately met with a retort that "2/3 of my calculus students are regularly female, so I disagree." While we were discussing methods we use to encourage collaboration, an attendee became visibly agitated when I said that I regularly pause class to remind my students that math is not an individual endeavor and we ought to be working collectively to create spaces where we can be wrong and learn together.

I'd rather not dwell on those really unpleasant interactions; props to Karl and MK for mediating them. Instead, I'd like to focus on the takeaways that have been bouncing around my head this week after speaking with other BIPOC and radical educators, in particular during a course on Critical Pedagogy with Dr. Cheryl Richardson.

A few people in the math educator workshop had trouble thinking about ways they could be inclusive with respect to race and ethnicity in their classrooms: "Instead of dividing up a cake, do I pick... I don't know, something else from another culture?" Yeah, someone actually said that. The underlying sentiment they were expressing match those I encounter a lot in pedagogy spaces, where sometimes even the facilitators make excuses for me (usually the only STEM person in the room) by saying "Oh but in math, the answer is right or wrong—so all this doesn't apply."

How do you make your class culturally relevant when all you’re doing is computing integrals? We lecture, we have homework, and we have tests—how do you make that inclusive? Don’t our students just care about their grades anyways? There’s no way to be inclusive when all that matters is doing calculations!

These ideas are all connected. Also, to be clear: If you are worried that your students only care about their grades, rather than the content of your course, then you should reflect carefully on yourself and what the environment you create in class says about your priorities. Do you only spend class time doing things that will be graded, either by homework or quiz or exam? After all, how can we expect students to value the collective struggle for knowledge if we ourselves do not? This last bit is a reference to a passage from bell hooks' Teaching to Transgress, flagged by a friend from Dr. Richardson's class (who would like to remain anonymous):

"On another day, I might ask students to ponder what we want to make happen in the class, to name what we hope to know, what might be most useful. I ask them what standpoint is a personal experience. Then there are times when personal experience keeps us from reaching the mountaintop and so we let it go because the weight of it is too heavy. And sometimes the mountaintop is difficult to reach with all our resources, factual and confessional, so we are just there collectively grasping,
feeling the limitations of knowledge, longing together, yearning for a way to reach that highest point. Even this yearning is a way to know."

My friend pointed out, I think truthfully, that this idea of yearning as a way to know "would freak out a UChicago student."

Remember, the hallmark of modern education is that it relies on a market-type analysis to evaluate both teachers and students. As said on neoliberalism by Irami Osei-Frimpong: "the principles of our analysis lead us to believe that it is irrational to invest in people... unless those people show themselves to be poised to increase in value in terms of quantifiable assessments." There’s no time in today’s classroom for wonder—just facts and the cold evaluation of regurgitated facts, so we can decide who is worth investing in and divesting from! This is why inclusivity, in the context of modern higher education, often just gets reduced to cosmetic changes in metrics rather than truly transforming our pedagogy. After all, how the heck are we supposed to quantify a student's yearning??

I try to make my classroom more inclusive by learning about how math as a discipline is tied to political power and human experiences, both historically and today, and connecting these ideas to the lives of my students. I do that by giving weekly readings, by making time in class to discuss these readings, and by asking students to journal about their thoughts in an ungraded format; I intentionally provide space that is separate from the economized endeavor of technical knowledge, where "the answer is right or wrong" and comes with an all-important grade attached. But this isn't the only way to be inclusive and I'm excited to continue learning for the rest of my life about the many ways that I can be better.

Teaching is hard. So is inclusivity. If you want to make your classrooms inclusive, workshops are great but just going to one and expecting to learn the secret two-second fix isn’t enough. Justice takes work, from learning the political history of mathematics to making intentional spaces for discomfort, from organizing a democratic union to trusting our students' capacity for yearning. As teachers, our battle with neoliberalism is eternal—both in New Mexican universities and in Chicago streets.

Saturday, October 5, 2019

Fractals, Algorithms, and Us: Discussion and reflection

Hey all, sorry for the long break! Life has been a bit hectic but I'm back and excited to share more.

In Fractals, Algorithms, and Us, students were regularly assigned readings that we would discuss and journal on in class. This post is about the way I facilitated these activities and is split into three sections: an introduction on why we did it, the actual process of doing it, and final thoughts on feelings in math. Of course, you are free to skip around to the bits you are interested in—I tried to keep sections pretty self-contained.

Motivation

There is a great deal of talk in math circles about the so-called math-phobia that grips our world, in which most everyday people excitedly distance themselves from this practice we call mathematics. Many mathematicians talk about their goals of eradicating this social ill, together with some analysis for the current state of affairs.

It is my humble opinion that math-phobia isn't just some superficial problem with the way we teach or talk about math or even the more structure issues of who teaches it—these are symptoms rather than the root cause. Instead, I believe that this phenomenon is deeply connected to the profound disconnect most people feel between mathematics and their lives; the many forms of oppression associated to the institutions of mathematics, often compounded upon people who identify across multiple axes of marginalization; and the resulting collective trauma we nearly all share around this thing called math. 

I am, of course, not the first person to present such an analysis—check out Professor Peter McLaren's Life in Schools: an Introduction to Critical Pedagogy in the Foundations of Education, for example, to see an explicit discussion of education through the lenses of class, labor, culture, ideology, and hegemony. Moreover, these deeply institutionalized problems are inextricable from neoliberalism, colonialism, and the mass disenfranchisement of black, brown, and indigenous peoples in the U.S. and across the world.

Quick aside: If you are unfamiliar with the concept of neoliberalism, by the way, here's a great video by Irami Osei-Frimpong at the University of Georgia on what it is and how it relates to education. Something he points out which I really took to heart is that when a student comes into my office to argue for 5% back on a homework set that is worth 3% of their grade (rather than searching for deeper insight on the math they may have missed out on) it’s because they’ve internalized that the answer to this question "What is education?" is "What my test scores tell me it is." Education has become fundamentally about students' assessments, not to equip them for self-determination as workers, partners, citizens, human beings, and maybe even as mathematicians. 

All that to say: understanding power is deeply critical to building a better world. That was the founding premise of this course. As such, I wanted to facilitate a space in which students felt safe to be honest about the feelings associated with these oppressive institutions and to think actively about what it could look like to dismantle them. These ideas weren't based on my experience as a trained pedagogue so much as they were based on my experiences as an organizer. 

PS. If education is supposed to be about self-actualization, then dammit part of what we learn in school should be how to talk about our feelings!

Methodology

I'd like to explain the facilitation practice through example, by running through the first hour of the six-week class. But, before that, a quick two-paragraph anecdote.

On January 17 of 2012, I attended the first lecture of MATH 352: Basic Concepts of Mathematics taught by Professor Ivan Avramidi at the New Mexico Institute of Mining and Technology. I was 19 years old, in my first year of college, and believed I knew practically everything about math. Little did I suspect the question that would kick off the class: "What is an integer?" It was a frustrating question that stumped the room, where we could only answer by saying things like, "Uh... positive and negative whole numbers?" to which he would demand, "But what is a whole number!" We realized very quickly that we couldn't define the real essence of an integer, not without using other words that already carried that essence.

The solution he finally gave, when we had no more guesses to offer, was simply: "An integer is an element of the set of integers!" which was both technically correct and apparently useless. His point, we'd later realize, was that abstraction via the language of sets, functions, and so on is a powerful tool for exploring and making rigorous the ideas we encounter every day.

This was an experience that really stuck with me. I liked the idea of giving students pause by posing a very fundamental question, one that we could unpack and think more about over the course of the six weeks we had together. So, after handing out the syllabus and putting up the day's agenda on the whiteboard, I asked the students to take out a piece of paper and write out a sentence or two answering a question:

"What is math?"

They didn't hand the papers in yet, but I'll spoil some of their answers:
  • "A system of numbers used to explain the world"
  • "The representation of real-world problems with abstract ideas and symbols"
  • "Ideas and observations that are quantified""
  • "The science and logic of shapes and arrangement"
  • "Techniques for calculations"
  • "Really really hard"
  • "A precise way to communicate"
Next I passed out an excerpt from chapter 22 of Bea Lumpkin's Joy in the Struggle, but before reading I told the students that throughout the course we would be covering material that could be difficult, triggering, or otherwise make different people uncomfortable; my goal was to facilitate an accepting and honest space to do our work. Then we wrote down a list of ground rules for our discussions, to make sure that we respected each other and ourselves. They came up with:
  • Don't be afraid to ask questions
  • Take space, make space (this means that students who are normally quiet should feel safe to take up more space, while those who speak a lot should be mindful of relinquishing it
  • Respect others with your use of technology (each student had access to a desktop computer, along with their cell phones)
  • Disagree with ideas, not people
  • Don't talk over each other 
  • Be respectful and open-minded
  • No hateful language
  • Challenge your own perceptions
I added:
  • Engage in good faith
  • Don’t invalidate experiences
Before proceeding, the students voted unanimously to uphold these principles in our discussions.
We also decided to use the practice of a "parking lot," wherein a corner of the whiteboard is devoted to points we want to revisit later so we can stay on topic.

We then read aloud, taking turns in different sections, on the re-discovery of the Egyptian notion of zero and Eurocentrism in mathematical history—in all subsequent sessions this bit would be done at home, but this was the first day of class. Afterward, we returned to the board and engaged in an exercise roughly adapted from what I’ve learned as an organizer. I asked the students: "Tell me some feeling words. How did reading this make you feel?" After some of the girls spoke up, I urged the boys to offer some feelings too.
  • Angry & disappointed 
  • Disbelief
  • Surprised
  • Proud
  • Excitement
  • Curious
Then I asked the students to unpack those feelings. I tried my best to record faithfully on the board:
  • Angry & disappointed
    • racism/bias/etc. reflected in the things we create
    • didn't think about how racists change/write history
    • omnipresence of these attitudes in all our institutions
  • Disbelief
    • what is the truth?
    • what else do we not know about our histories?
  • Surprised
    • human nature and values across millennia
    • how can science be racist?
  • Proud
    • Egyptian, Incan, Aztec, Mayan, Indian, Chinese, Islamic, Polynesian—math isn't just from Europe
    • math started in Africa!
  • Excitement
    • cool to see how math was connected to Egyptians' lives
    • liked seeing how similar ancient people are to us
  • Curious
    • when did people start doing math?
    • how can we learn more about ancient math?
When people would unpack a feeling, often someone else would want to add to it; this was allowed with the permission of the original feeling-giver or, otherwise, split into a separate point. This led to open discussion and naming tensions—I reminded the students that tensions are not necessarily bad since they help us grow—and added more to our feeling words. We used a stack, wherein I kept track of people waiting to speak; the stack was progressive in that I prioritized those who had spoken less. I spoke very little, less than 20% of the time according to my TA's measure, only to ask guiding questions or check if a particular rephrasing was acceptable while I copied thoughts onto the board.

Forty-five minutes into class, we wrapped up our discussions. I asked the students to write down a summary of their thoughts on the reading, only a couple paragraphs, for the next ten minutes before stretching their legs and taking a quick break. I also asked that they write a new answer to the first question, "What is math?" next to their original answer. A few examples:
  • "A universal understanding of the world around us that started with humans in Africa"
  • "Math is a shared human effort to solve problems and it doesn't belong to anyone"
  • "The combination of lived experiences across human history used to solve common problems"
  • "Fundamental to who we are as humans"
When we dismissed the first day of class, one of the students asked: "So—what is math?" I mention this as a point of caution because I don't like the idea of reducing the whole exercise into a riddle. After all, even if I knew a succinct or clever answer, it wouldn't make a whole lot of sense to suddenly center myself as the Source of Knowledge. I simply replied that we could figure out together, which turned out to be profoundly true.

In future classes, aside from giving out readings a week ahead of time, the principles of discussion and reflection were similar:
  1. Feelings—listing single words expressing the emotions evoked while reading.
  2. Unpacking—unpacking the aforementioned feelings and discussing together where they came from. 
  3. Tensions—reflecting together on things, either in the reading or in the discussion (careful to avoid accusatory language), which created tension.
  4. Journaling—give students time to write down final reflections on the reading, using guiding questions.
Sometimes we would vote to extend discussion time on certain hot-button matters. As the class progressed, I'd see students come in with their readings covered in highlighter marks with feeling words written throughout the text. That was pretty cool.

Final thoughts

I decided to move this section up in the blog lineup after an illuminating discussion with Professor Dagan Karp at Harvey Mudd who, among other things, pointed out some of the tensions in this class and suggested that I spend time unpacking them. I've also been really excited to write about this section since it is one of the more uncommon pedagogical features which sets this class apart from most other math courses (well, aside from nearly all the content) and one I'm very keen to continue exploring in the future. We talked about feelings and power in math class!

One of the most trademark aspects of mathematics is its powers of abstraction. Ranging from the simple use of numbers to the lofty realms of category and model theory, practitioners of math can extract the underlying essence of a particular concept in order to remove troublesome real-world details that inspired the problem in the first place. As espoused by many mathematicians (Dr. Eugenia Cheng, Scientist in Residence at the School of the Art Institute of Chicago, comes to mind) and evidenced by countless marvels of human invention, abstraction is an incredibly useful tool for solving problems. And solving our problems is why we’ve done mathematics for over forty thousand years! Indeed, a fascination with abstraction is why I am a mathematician (in particular, a topologist) rather than staying the course of physics or computer science from my undergrad career.

So why, when nearly every math course is at least implicitly predicated on the idea that abstraction is the premier feature of mathematics, did we devote two whole weeks of class time to exploring math as the amalgamation of the lived experiences of humans solving problems? Why did we spend so much time talking about feelings, power, colonialism, and so on, making the point that math is contextualized by the people who do it when, at the end of the day, 2+2 is always 4?

Because it can be both, of course, and we do ourselves an incredible disservice by pretending otherwise! In the words of Peter McLaren, we challenged the dichotomy of "technical knowledge" (the kind you measure with SATs) and "practical knowledge" (gleaned by describing and analyzing); instead, we replaced this false choice by embracing "emancipatory knowledge." According to McLaren:

"Emancipatory knowledge helps us understand how social relationships are distorted and manipulated by relationships of power and privilege. It also aims at creating the conditions under which irrationality, domination, and oppression can be overcome and transformed through deliberate, collective action."

Mathematics is simultaneously human and abstract, creative and logical, invented and discovered, beautiful and terrible, liberating and oppressive, indigenous and post-colonial, and there is no contradiction.

Announcing: How Chance Changes the World

Hello everyone! It's been a long time and I have a lot to update you all on. Firstly, I graduated! It wasn't something I expected ...