Category: Philosophy on Math

The Challenge: Pick YOUR favorite proof, or mathematical fact and illustrate it. What’s beautiful about it? Why do you love it? I really, truly want to know.

Materials Needed: Really depends on your pick!
Math concepts you could explore with this challenge: Philosophy on Math. Mathematical communication.

Only 10 left until we reach the goal of 100 Math Art Challenges.

A thing I’ve noticed is that since I took a pause after George Floyd was murdered (there were just more important places for my and everyone else’s attention) is there’s a notable slow down of engagement. Which is totally fine, of course. Part of my capturing and recording all of them here on this blog is so they’ll be around and available whenever you want to play or when schools start up again in the fall. But I would like to encourage folk to engage again and to capture a bit of the magic that I felt when folk were spinning them into something new nearly every day. So the last 10 will come out over the next 10 days. The finale will be August 5th.

Another part of the slow rate they’ve been coming out recently has been that I’m trying to be a bit more thoughtful about them, which has led to a big of paralyzation on my part. I spend a lot of time thinking, “Is this even worth people’s time? Is it meaningful enough? Is it connected to enough things?” And while those musings are important to me, there comes a time when I’ve mused enough and need to just create and publish. So for the last 10, I wanted to expound a bit on what I’m prioritizing and what I’ve been musing about as I’ve planned these last 10.

I can’t stop thinking about how much of math is trapped by the expectation that math needs to be calculation centered – involving symbols and paper scratching. Of course there is freedom that comes with exploring the meaning behind those symbols and scratching, but there are so many other ways to experience and expand math. I think a lot about the de-colonization and re-humanizing of mathematics and how worship of the written word is wrapped up in preventing us from expanding our perception of what mathematics is.

Mathematics is beautiful. That’s important to me.

Mathematics is powerful. It can persuade for good and evil purposes.

I want to help us explore mathematics in ways that celebrate the historical importance of mathematics in a variety of cultures, and in ways that expand your idea of what math is and can be.

Finally, mathematics can be used to exclude when it’s too mystified. Part of me thinks that by keeping the planned #MathArtChallenge-s to myself, I’ve been a bit exclusionary. So I’m posting at least the titles of all remaining 10 below. Feel free to engage early if that’s exciting to you. I have put a lot of work into this, but it’s not my endeavor alone. It wouldn’t be anything if y’all hadn’t engaged.

So the last 10 will be:

91. Monday, July 27th: 3D Cube letter shadows suggested by Sam Shah

92. Tuesday, July 28th: W.E.B DuBois’ Data portraits

93. Wednesday, July 29th: Polyhedra creation based on vertex descriptions

94. Thursday, July 30th Friday, July 31st: A final Islamic Art design

95. Friday, July 31st Saturday, August 1st: Magic Squares & Circles

96. Saturday, August 1st Sunday, August 2nd: Rational Tangles & Candice Price

97. Sunday, August 2nd Monday, August 3rd: Creative origami sculpture

98. Monday, August 3rdTuesday, August 4th: The most beautiful proof I’ve ever seen

99. Tuesday, August 4thWednesday, August 5th: Hidden in Plain View quilting patterns, oral history, and the Underground Railroad

100. Wednesday, August 5thThursday, August 6th: Celebration (So this one’s still a bit of a secret – indulge me, but if you want to play along you probably want to get a hold of some twisting balloons, which is maybe enough for you to guess what I’m planning.)

The challenge: Define math art for yourself, capture an example of it in a picture (or a series of pictures), and share with #MathPhoto20 and #mathartchallenge.

This week #MathPhoto20 and its organizers, Carl Oliver and Erick Lee, are also going to be engaging with the #mathartchallenge by creating some math art challenges and posting those with the same hashtags. Our hope is to spark a discussion about math art, photography, and where and how we see math in the world.

The context: Math art is a poorly defined term. Definitions can be challenging, but clear, precise definitions help us communicate better. I’ve occasionally found heated disagreements quickly resolve once its noticed folk involved are using different definitions. For example: I usually hold that lines do not need to be straight, but for the sake of proving some geometric properties in Euclidean geometry, I’m happy to situationally accept the requirement of “straight”.

The Math Art Challenge has been on hiatus for about a week now. Mostly because it’s jarring to see folk happily engaging in math art while protestors are getting arrested. I couldn’t conscionably post things about the Hilbert curve, knowing it would divert time and energy that we need focused elsewhere.

I am keenly aware that a lot of white educators are doing more harm than good right now. Often because we’re moving too fast in an attempt to assuage guilty feelings that are hard to sit with. I am trying to let myself sit with and consider those feelings while also making sure that I am taking thoughtful, productive action and planning to be in this for the long haul. Because we need to be here beyond this week. Especially white folk. Especially white educators.

I’m just now starting “summer”, and I want my time this summer to be spent thoughtfully planning for how I can do better, and how I can help support other educators to do better this fall. As I’m considering what I can contribute to the dismantling of white supremacy, specifically that within schools, right now, I’m trying to hold these things in my mind: 

• I am not an expert in community organizing, nor in the dismantling of police brutality. I can listen to, support, and lift up the voices of those who are. 
• I am growing my expertise in math education, and how math art can be used in math class to refocus education on patience, deep thinking, and connection making. 
• Whiteness pervades math curricula and the structure of math classes in America, and it must be dismantled. 
• Math classrooms are deeply segregated. Both the students that comprise them, and the way curriculum is presented. If we are to change that, I believe the fundamental structure of math classes has to change. 
• Many of the followers of the #mathartchallenge are white educators. It is not lost on me that when I post pretty math art, it gets many likes, while posts about #BlackTransLivesMatter gets crickets. I can marry the two better so that when you come to me for math art, you also are challenged to consider how you are upholding or dismantling white supremacy. 
• Given COVID-19, there has never been an easier time for us to change what math class looks like. We already know that the fall will be different. Let’s seize on that. 

The whole impetus for the #MathArtChallenge was a desperate need to stay in touch with students after we left the school building. I knew worksheets and traditional lessons would not engage them, but that math art could, and it could do so in a meaningful way. Like pretty much everything else that happened this spring, the MathArtChallenge was put together haphazardly, without a lot of deep thought going into the specific outcomes nor goals beyond getting students to engage somehow in mathematical thinking from afar. 

I know many teachers are doing great work in their classes, and some people may really have broken out of the factory model of education, but too many math classes (including mine) are still primarily focused on getting through a list of standards rather than championing our student’s brilliance and giving them space to direct more of their own learning.

Considering it now, had I thoughtfully planned from the beginning, here are the goals I’d like to see accomplished by the #mathartchallenge, all of which are aimed at disrupting the factory model of education.

1. Create a bank of resources, that anyone, but teachers specifically, can draw on, to inspire creative mathematical thought. Aware that teachers commonly only use resources directly connected to their curriculum, I will do my best to go back and tag each of the Math Art Challenges with content standards. I understand that ease of use will make the resource more likely to be used. I also know that simply by virtue of being art, math art opens possibilities for students to creatively explore mathematically. That is simply less true (if at all) of traditional standards-based learning. 
2. Research and share the historical context for as many #mathartchallenge-s that I can. If we’re to decolonize the curriculum, we have to stop pretending that all math comes from Europe and that the only mathematical thinkers worthy of celebrating are old white dead men. That takes active, intentional work and planning. To that end, I’m committing to also spending much of my summer updating, revising and adding to the Mathematicians Project. With respect to the #mathartchallenge, that will also mean doing things like connecting the Islamic geometry challenges to actual mosques where the original designs were found. Highlighting mathematicians, specifically non-white mathematicians, who do work related to each challenge. We need to connect math to history. And specifically to the history that has so long been denied Black and Brown students. The history that centers the brilliance of their ancestry. 
3. Encourage patient, slow thinking in classrooms. Art takes a while. That’s a huge benefit. The factory model of education has not worked for way too many students, and it doesn’t take much thinking to know why. When I seek to learn a new math concept, I mentally prepare to take enormous amounts of time to deeply engage. I give myself room to explore paths that may very well take lots of time and lead to dead ends. I don’t place a schedule on when I must have reached mastery. Though I get why people create and use pacing guides, if we’re to center math class on actual mathematical thinking and on our student’s humanity, we need to throw those in the trash heap. Yes, definitely, some standards will have to go. Tough. We should be focused on teaching students how to learn, not making sure they know every math concept we can cram in. If they know how to learn, they can teach themselves whatever concept they didn’t get in school when it becomes necessary for them. I truly believe this shift makes math class more welcoming and reflective of what math actually is. 
4. Plan for necessary reflection and connection making. I have, thus far, utterly failed at this, trusting that in the process of creation, we end up naturally reflecting and making connections. But if we’re to effectively use math art not just as a healing source (though that is a wonderful and necessary thing that art can provide), we need to be intentional in the ways we’ll ask students to process their creations. To this end, I plan to spend time this summer going back to formulate reflection questions that can be used broadly, for any #mathartchallenge-s, and specifically, to be used for individual ones. 

I want to be clear that I understand that planning to disrupt a factory model of education is not going to happen overnight, nor am I the first to encourage or work toward it, nor does this work absolve me from doing work elsewhere: supporting protests, engaging politically, being intentional with how and where I spend money.

I am teaching two new-to-me classes next year, and I already hear voices in my head:

“You still have to prep them for the test”

“How will your co-workers react?”

“What will the parents say?”

“You need to hit all the chapters.”

I want to be clear. Those voices are the ingrained white supremacy that pervades education. I firmly believe that slow, deep mathematical thinking, as opposed to a factory model, will benefit students. So I need to research and prepare to teach this way, and to address these voices, focusing primarily on my student’s brilliance and humanity. 

This summer, I do plan to finish out the 100 Math Art Challenges. They are not likely to come out one per day, because I hope to actually take the time that summer affords me to do more intentional research. I hope to have each of the coming challenges rooted in some sort of larger context, whether that is through connection to a non-white mathematician working in a related field or through historical connections. 

As with anything, collaborative work is stronger than individual work. If you are interested in helping me with this, I would love to collaborate. I am also keenly aware that my plans may need to change as I progress through this. Push back on any and all of this is welcome, especially if it centers student learning and making math class more equitable for students.