Fractals, Algorithms, and Us: Teaching objectives

The content of the course was designed around the following broad goals, assembled from my own experiences as a queer New Mexican Chicano mathematician and labor organizer at the University of Chicago:

• Establish mathematics as a living, breathing subject, part of the lived experiences of the student, their communities, and their ancestors. In particular, students should feel emotions throughout the course, reflect upon them, and then connect them to the practice of mathematics. Instead of the cold and sterile presentation of a typical math class, where knowledge is "about information only" (as said beautifully by bell hooks) and colored only by half-hearted attempts at connecting to reality through contrived word problems, we should immerse ourselves in the context of what problems people were actually trying to solve in their daily lives as they developed these mathematical ideas.
• Explore math, and access to mathematical knowledge, as a dynamic political force that changes the world rather than existing separately from it. This goal is both contemporary and historic in its focus. I also intentionally wanted to challenge the usually individualistic and thus ironically disempowered saying that “knowledge is power.” Instead, I wanted students to reckon with how math as a social construct, together with its perceived neutrality, has contributed and continues to contribute to mass disenfranchisement, colonial violence, and the modern surveillance state.
• Challenge the Eurocentric bias of mathematical history. Because math didn’t begin with the Ancient Greeks! Instead, the goal should be to center indigenous people throughout history to understand how their lives played into the mathematics they developed and used. Especially taken with the goal described in the first bullet point, wherein math is thought of as an inseparable part of the human experience rather than an abstract set of rules dreamt up by some boring and long-dead European men, I hoped that students would begin to see for themselves the colonialism inherent in modern mathematical practice.
• De-center the Teacher as the Source of Knowledge. In most modern math classes the Teacher enters the space of waiting students, projects ignorance upon them, and then proclaims Knowledge upon the chalkboard. The students are measured by how dutifully they are able to act as empty vessels to be filled by said Knowledge, signaling whether they should be invested in or divested from by future Teachers and institutions of Knowledge. All told, there can be no learning without the Teacher and their Knowledge; the Teacher is the subject, rather than the students. Instead, I aimed to facilitate an environment where students enjoyed a high degree of agency over their education, especially through student-led projects and breakout groups. Check out Pedagogy of the Oppressed for more of what inspired me here.
• Develop a working knowledge of programming and some basic algorithms. This goal is very personal to me, deeply connected to my own quest for agency and self-actualization. Despite growing up with a mother who taught me to love math before I could speak, I hated the subject for most of my childhood because of my experiences with math education in school. The thing which allowed me to fall back in love with the thing I have spent my professional life studying was a teacher, Mr. Maier, who gave me a book called Processing: A Programming Handbook for Visual Designers and Artists. Armed with this book, I'd steal away whenever I could to our high school's ancient computer lab and create. Programming allowed me to explore gravity, magnetism, fractals, art, predator-prey behavior, music, and so much more (some old code is here—please remember no one had taught me about commenting or style yet) in a completely new, self-driven way. So, with this class, I wanted to teach students to code with the aim of developing a heuristic approach to both mathematics and problem solving so that they could feel empowered to investigate things on their own.
• Expose the students to mathematical topics and material resources they would ordinarily not encounter in high school. This goal was geared especially toward contemporary topics, like machine learning and chaotic systems, whose applications range from predicting the weather to scheduling employees' shifts. So the idea would be that we could black-box some computationally complicated prerequisites for the sake of giving students an intuitive understanding of deeply pervasive modern ideas. Also, the University of Chicago has 3D printers, laser etchers, and video games labs—I wanted students to have access to these amazing materials and resources.

These guiding principles led to the following learning objectives. Students will:

• Explore math as a social and political concept through weekly readings and reflections. This objective includes both following a narrative throughout human history which expresses math as a collective endeavor to solve problems and also understanding the colonial context of math research and education.
• Write algorithms to solve polynomials, sort lists, and render fractals. The first is a five-thousand-year-old problem, the second is both instructive and delightful, and the latter unlocks infinite creativity.
• Be comfortable manipulating complex numbers. This particular set of numbers is not only necessary for understanding many concrete examples of chaotic dynamics and the emergent fractals, but also deeply related to the problem of equation solving. Since this was an endeavor necessary to the lives of countless humans (millennia before Greek societies came to be), the complex numbers feel like an appropriate avenue toward humanizing mathematics. 
• Develop a working knowledge of basic programming concepts, including logic, loops, conditionals, and functions, via the Python language. Programming is an increasingly essential skill set in the modern world, but learning how to code also equips students to question on their own in the way that I once did in high school.
• Collectively design and train a neural network to recognize handwritten numbers. Neural networks are an increasingly ubiquitous tool of modern data science and are a concrete example of a mathematical idea that is currently changing the world in a deeply politicized way.

In the next entry, we'll take these objectives and actually synthesize a reading list and collection of abstract mathematical topics into a real class. After that, we'll talk about the day-to-day structure of the classroom and how exactly it looked to facilitate student-led discussions and learning.