Thursday, September 12, 2019

Fractals, Algorithms, and Us: Preface

I've been thinking a lot about how to share my experiences from this summer. A handful of friends had suggested that I describe the process of developing my syllabus, framed around some of my teaching goals, then use the actual teaching of the class as a sort of data gathering to either support or refute my hypotheses. I took studious notes and kept a journal of the whole experience, in addition to keeping hold of all the students’ work, so this seemed right—the idea was to submit the final result for publication in a variety of pedagogy journals and it seemed like the right thing to do as I prepare for the job market.

As a good scientist, I tried to outline a report structured in the same format as the lab reports that my incredible AP Chemistry teacher (shout out to Ms. Varoz) taught us to write in high school—complete with an abstract, introduction, methods, results, discussion of theory, and conclusion. I even gave it a grand title:

"Fractals, algorithms, and us: a case in practicing critical pedagogy in math education."

This was me overcompensating for my general lack of formal pedagogical knowledge, a fear that everyone would immediately recognize that I'm just some math grad student who has spent his professional life working in national laboratories, has only taken a single non-STEM course since high school, and has no place occupying the same space as trained pedagogy experts. The resulting write-up, of course, was something that felt entirely cold and dehumanized, which is completely antithetical to what I set out to do with this class in the first place.

In my day-to-day life as a working mathematician, I have to use big words all the time: homotopy equivalence, ℚ-acylic, semi-locally simply connected, and quasifibration, to name a few. While of course these words have their uses in conveying very precise meaning with respect to one another in the contexts of research, they have the added bonus of acting as a sort of linguistic veneer which signals to the people around me that, despite ongoing imposter feelings, I'm qualified to exist as a graduate student in the UChicago math department.

But, when writing about my teaching experiences, suddenly I don't have big words to hide behind anymore!

Appropriately enough, it was by reflecting on an experience from this summer that I was able to move past these imposter feelings (or at least some of them—as anyone with imposter syndrome will tell you, it's an ongoing battle). While discussing the political opinions and activities of Albert Einstein and other scientists in the context of nuclear weapons research, one of my students said something very astute:

"I feel like if he said that stuff today, people would tell him to stay in his lane. Like, that he's just a physicist and it's not his place to talk about it."

The name Einstein is synonymous with genius. As we go through school and generally exist in society, we often hear his name in the context of physics—relativity, the photoelectric effect, E=mc², and so on. Occasionally other details enter the popular zeitgeist: we might hear pleasant anecdotes of an aged Einstein pausing on his daily walk to help fix a child's bicycle or sharing a can of beans with someone seeking help with her homework, or tales of an Einstein speaking out against American racism, or occasionally more scandalous rumors of an Einstein who might've stole work from his first wife Mileva Marić and might've failed out of math classes in his youth (he definitely didn't do the latter, at least). But we rarely, if ever, hear about the Einstein who vocally opposed war, the Einstein who proudly held union membership in AFT Local 552, the Einstein who was staunchly anti-capitalist, or even just the Einstein whose diary contained jarring examples of Orientalism.

This passing comment in my class inspired a wonderful student-led conversation about intellectual labor, shared responsibility, and exactly who wins in a society where workers are defined by their jobs and simultaneously told that what they toil to produce doesn't belong to them. But the students in my classroom also made an explicit point: a lack of formal education in a thing should not invalidate the feelings and wisdom you glean from directly experiencing said thing. These narratives of "stay in your lane," when used by those in power, cow people from exercising agency over their lives. To my students, this conclusion came from the tale of a physicist—not a statesman or political scientist or military general "qualified" to have an opinion on war. But, upon reflection, they realized these were the same sort of feelings that many of them have associated with math, science, and education for much of their lives—we are made to feel stupid and powerless by people who ostensibly know more than us. After all, to see evidence of the apparently universal trauma we all share around math, all it takes is telling a stranger in nearly any social gathering my field of study: almost without fail, the response is either “Oh I hate math” or maybe “I’m so bad at math!”

In the same way, the practices of critical pedagogy did not begin when the modern giants like Friere and McLaren started using big words to describe it. Instead, as noted by bell hooks in the introduction of Teaching to Transgress: Education as the Practice of Freedom: "We learned early that our devotion to learning, to a life of the mind, was a counter-hegemonic act, a fundamental way to resist every strategy of white racist colonization. Though they did not define or articulate these practices in theoretical terms, my teachers were enacting a revolutionary pedagogy of resistance that was profoundly anticolonial." Like everything else, these ideas were part of the lived experiences of everyday people doing work long before they were studied by the modern-day academy.

So before we begin, let me be forthright: I am a mere mathematician and teacher of mathematicians, completely untrained in the more abstract and jargon-heavy aspects of pedagogy but equipped with almost a decade of experience in actually teaching. I'm not pretending to be all-knowing, especially when it comes to the millennia of shared human experience in passing on knowledge which I am only just learning about. I simply love my work and I love my students: my life has been hugely shaped by my experiences with both. I am also not a lone pioneer of these ideas by any means and do my best to attribute ideas to those who have come before me whenever possible.

As such, I present the following of my 2019 summer teaching both humbly and excitedly. Check back regularly as I will be using this blog to tell the stories of creating and conducting this course. I hope this medium will facilitate a more genuine sharing of the journey, free from the fears of my journal editors, their scathing emails, and wildly inaccessible paywalls.

If you are a teacher, STEM or otherwise, I hope that some of these anecdotes might inspire you to try something new, share your own experiences too, or maybe both and more. If you once were or still are a student, I hope that these stories can help to give you a new perspective on math in which you are empowered to create, rather than being inundated by formulas and shared trauma.

I have only my experiences to share. Join me, won't you?

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