A few weeks back, I was in Washington, D.C., for this year’s National Council of Teachers of Mathematics conference—by far the largest annual math education conference.
Being in D.C., there was one attraction I made a point to see: The National Portrait Gallery. In particular, I wanted to see one work by Kehinde Wiley, an artist mostly known for painting enormous and ultrarealistic portraits of African-Americans surrounded by rich, ornate patterns.
Former President Barack Obama tapped Wiley to paint his official portrait for the National Portrait Gallery, which features every president in history. If you haven’t seen it—and I hope I can say this irrespective of your political leanings—it’s stunning. (View the painting here.)
In one way or another, I have been a math educator my whole life. Looking at this painting, I reflected: “Where is the math?” I first thought of some simple contexts that could make for rich conversations:
About how many leaves are in the painting?
How much paint is needed to complete this painting?
Where it gets more interesting, in my opinion, are in the realistic contexts—that is, where there is no stock textbook lesson to guide you, and someone, somewhere actually has to try and solve the problem:
How can a conservator ensure the colors won’t fade over time?
How much is the painting worth?
In these contexts, mathematics is just a part of the solution, albeit an integral part. (But only Riemann integral.) There is a subtle problem, though. The most realistic problems require a lot of mathematical sophistication to approach and take far longer than a class period to solve, if there even is a solution. My goal for the conference was to get a pulse on today’s teaching, but it seems the real world always has this “simple” vs. “realistic” divide. Teaching addition is drastically different from teaching calculus, and I struggled to find the cluster inside a multidimensional Venn diagram.
When I read over my notes on the train ride home, a spark lit when I realized that many of the conversations I had and sessions I attended boiled down to math problems being a whole lot more subjective than many people think. Mathematics—all of it, no matter your experience—is a bit like a Kehinde Wiley painting: permanent, austere, and forever jazzed up by humanity.
Consider this question, which at first seems more mathematically abstract than human: Why are there 360 degrees in a circle? This question was the focus of a session titled “How Many Degrees Are in a Martian Circle? And Other Human—and Nonhuman—Questions One Should Ask!” The perhaps anticlimactic answer is the Earth revolves around the Sun once every 365.25 days, which humans retooled as degrees in a circle and rounded to 360. We rounded because 365.25 is a hideous number to work with, but 360 is easy. (“OK, it’s not divisible by seven, but nothing’s divisible by seven,” the speaker added, eliciting laughter from an audience of obvious math geeks.)
This tendency for us mortals to scrub the messiness in nature pops up everywhere. A few other times I spotted it over the course of the conference:
- A vinculum is a horizontal bar placed over expressions to section them off, identically to parentheses. There’s a reason we use parentheses over the antiquated—yet arguably easier to parse—vinculum: The human invention of the printing press needed everything to fit on a single line.