I cannot remember a time when people were not decrying the state of mathematics education in America. Or a time when there weren’t occasional stories in the newspaper or on television about how American kids are falling behind their peers in Japan, Europe, and recently China in math education.
I cannot remember a time when school districts across the nation were not cutting back on their arts curricula, because shrinking school budgets and increasing focus on standardized testing were forcing them to focus only on “core subjects.”
Lately I have been thinking that these phenomena are related by more than just money and America’s bizarre lack of focus on school funding. With the stimulus bill now signed into law and the mathematics education in America promising to bring our schools into the twenty-first century, this has been on my mind lately.
We tend to view students in two very broad categories: “artistic” kids and “intellectual” kids. This is a crass generalization, but it’s true. Society, by and large, expects people to be one or the other. Rarely both.
Which is to say that there is not an expectation that an artistic kid will be any good at math, science, or engineering. Nor is there any expectation that intellectual kids should have any interest in or aptitude for art.
Frankly, I think that’s crap. I think that every kid has a creative side regardless of their skills in the sciences. And I think that every kid has an analytic side, regardless of their skills in the arts.
And I know, because I’ve lived it myself, that math and art can reinforce one another. Math can be used to teach art and strengthen one’s creative side. The desire to make art can be used as a springboard from which to teach math.
I suspect that my school experience as regards math and art was pretty typical. We didn’t have any art classes after about the fourth grade. And math class was, well, dull. The typical kid argument, “I don’t see how I’m ever going to need this in my life,” resonated with me just as strongly as anyone else.
This was back in the Dark Ages, when I had the free time of a high school student and my computer’s speed was measured in kilohertz rather than gigahertz (think about that for a second).
But after school, the situation was entirely different. I was a latch-key kid, so when I would come home at the end of the school day the choice was mine for how to spend my time. I could watch daytime TV, or play around on my computer. I don’t know about you, but there were only so many Magnum, P.I. reruns I could take.
For fun, I did a lot of messing around with plotting math formulas.
Sounds geeky, but there wasn’t much else you could fit into the computer in those days. I plotted all kinds of functions, just to see how they behaved and what cool patterns I could put onto the screen.
In algebra class, we learned that irrational numbers were the square roots of negative numbers. We learned that recursion was primarily a trick for generating Fibonnacci numbers. Ooh, yippee. I couldn’t have cared less. But when the great fractal craze of the late ’80s and early ’90s hit, it led me back to irrational numbers and recursion as a means to draw cool stuff on the screen.
In trigonometry, they drilled into us the definition of sines, cosines, and tangents as the ratios of the sides of right triangles. Drier than the Sahara, that. But at home, trigonometry functions became endlessly fertile ground for creating swirly patterns ranging from spirographs to models of planetary motion.
In pre-calculus, we learned about derivatives as the slopes of mathematical formulas, and how to relate the slope of a curve to the direction perpendicular to that, it’s “normal” direction. You have no idea how full the margins of my notebooks were with aimless doodles during those lectures.
But when the concept of ray tracing hit the scene, suddenly derivatives, slopes, and surface normals were good for something – they are indispensable in realistic ray tracing.
Every one of those subjects was dull as dirt in the classroom, but interesting at home. And the visual results of each were beautiful in their own ways, even rendered in the shockingly crude graphics of the day.
It was all math in service of pretty pictures.
I learned more trig, algebra, and even calculus from my trusty old Radio Shack “trash-80” computer than I ever did from a classroom.
In hindsight, the reasons are obvious. Because it was fun. Because it was undirected, free exploration without rules or boundaries. Because it engaged both the creative and the intellectual sides of my brain at the same time.
I learned the math because I needed to learn it to solve problems that were exciting to me, for my own reasons, and on my own terms.
My experience was certainly atypical for that era. At the time, few people had computers at all, let alone ones with any graphics capabilities. I was lucky. But today that’s just not true.
Today, computers that would kick the transistors out of my clunky old TRS-80 are increasingly ubiquitous in schools. Today, there is a wealth of free software available that serves this particular intersection of math and art, Processing being my latest favorite new toy in that respect.
The march of technology has made it possible now to replicate in the classroom the experience I had from playing around with my computer in high school.
And to do it for cheap.
So while we’re busy spending some of that stimulus money – and hopefully a lot more to come in the near future – to rebuild aging school buildings, let’s not lose sight of the fact that we need innovative, 21st century curricula and teaching methods as much as we need those 21st century school.
My own experience tells me that we could do a lot worse than to start with some type of integrated math-and-art program. We have the computers. The software is free. We just have to do it.
For me, this has been a life-long process. The joy and satisfaction of using math to make art has never left me. These days, it’s easier than ever to indulge. Wikipedia is an awesome resource for re-learning concepts and formulas that I was exposed to in school but which never had any appeal until I find that I need them in order to play around with one creative idea or another.
The image I used above to illustrate this post is the result of just such an exploration, this time into matrix math and least-squares estimation.
Not because I wanted to geek out over the math, but because the math is a tool to answer the creative question “what do you get if you draw lots of short, random little lines over the interesting features of an image, and color the lines the same as the underlying image?”
And yeah, they supposedly taught me matrices and least-squares in the U.W. College of Engineering. But it wasn’t any fun back then.
If we can use modern tools to give every kid the chance to discover the joy in math, and thereby give them a life-long zeal for learning, we will be miles – no, make that kilometers – farther along in our goal to raise our kids’ education up to the levels they’ll need to compete in today’s global economy.
About Jason Black
A staff member at Northwest Progressive Institute, a strategy center fighting to restore the American promise.
