By the time the seventh e-mail about coursework and assignments arrives in my in-box, the guilt is too much to take. The online class I signed up for started on Sept. 17, and as the unopened emails pile up from Coursera, I haven’t watched a single lecture or done any work. But hey, having the flexibility to take in lectures at whatever pace you please is one of the attractions of such courses. The fact they’re free is another. In any event, it’s time to buckle down.
Everyone in higher education is obsessed with MOOCs (Massive Open Online Courses) these days, and taking one sounded like a good idea. Whenever the local community college mails out the latest list of classes that are open to the public, I always find something that is not only interesting but also somehow “good” for me—maybe Woodworking, Web Design Basics, or Advanced Gardening. I should take that, I find myself saying.
A MOOC seemed even more appealing. Yes, there’s the free thing (I’m a Moneyland guy, so free goes a long way with me), but also there’s the idea that I could be taught by a world-class professor. Somebody from MIT or Princeton, or, in the case of the class I signed up for, Stanford.
After considering many options, I decided on a course called Introduction to Mathematical Thinking. It certainly qualified as “good for me” in the way that we’re all supposed to keep growing and expanding our knowledge base and perceptions and whatnot. Plus, Stanford is known as the place that churns out engineering, entrepreneurial, and mathematical geniuses by the truckload. I’d sure like to learn how to think more like the people there, especially if it helps me start a company that one day will get bought for billions by Google.
Another reason I signed up for this class is because in the video introduction for it, the professor, Keith Devlin—who looks and sounds like a long-lost Monty Python troupe member—repeatedly said that this math course involves almost no math. This sounds like the math course for me! I read on USA Today that more than 50,000 students are also signed up for Devlin’s course, and I hope that I’m not the most clueless of all.
As I watch Devlin’s first lecture, which seems more like an introductory pre-lecture, he offers the analogy that high school math is like learning to drive a car, while college math—the kind that requires “mathematical thinking”—is akin to mastering automotive technology, designing and building a car. The key to high school math (algebra, geometry, calculus—stuff I was pretty good at) is following rules and thinking entirely inside the box, Devlin says. College math, by contrast, requires outside-the-box thinking.
His phrases are wonderfully romantic, and also terribly confusing. But at least there’s no math. When the video freezes a few minutes in, I feel a surge of relief. Here is my excuse for giving up on being able to think like a mathematician.
I click on Lecture 1. Damn, it works just fine. The video is 29 minutes long, mostly just Devlin in a button-down shirt talking with a white-screen background. I keep listening as I find myself clicking around the Web, checking e-mail, reading random Tweets.
I should be mowing the lawn, or putting together a grocery list, or doing something more productive. It’s amazing how quickly you can second-guess an idea when you don’t have any skin in the game.
There are a few quizzes sprinkled throughout the lecture. You have to complete them in order to get a certificate for the course (though you don’t have to get the answers right), and their basic purpose is to check if you’re paying attention and sort of getting the material.
At one point, Devlin’s lecture becomes something of a lecture, as he advises students who haven’t done the Background Reading (I’m one of them, of course) to do so now before continuing the video. He doles out phrases like “Math is alive!” and “mathematics makes the invisible visible,” which are as intriguing as they are puzzling. And passages like this from the Background Reading are difficult to wrap my brain around:
“These days, mathematics books tend to be awash with symbols, but mathematical notation no more is mathematics than musical notation is music. A page of sheet music represents a piece of music; the music itself is what you get when the notes on the page are sung or performed on a musical instrument. It is in its performance that the music comes alive and becomes part of our experience; the music exists not on the printed page but in our minds. The same is true for mathematics; the symbols on a page are just a representation of the mathematics. When read by a competent performer (in this case, someone trained in mathematics), the symbols on the printed page come alive—the mathematics lives and breathes in the mind of the reader like some abstract symphony.”
I don’t know how to fix a car, or read sheet music, and now I’m beginning to think I won’t be able to think like a mathematician either. As Devlin continues on and busts out terms like “function,” “injectivity,” “differentiality,” and “epsilon-delta definitions,” I come to the conclusion that there is in math in this math course. How could I have been so foolish? This was a trick—a mathematician’s trick, practiced only by those who understand mathematical thinking. All I can think of is calling it quits.
But these thoughts occur to me just a few hours after I delivered a lecture myself to my two sons, who had been pleading with me that they wanted off of the swim team because “It’s too hard.” “That’s not a good reason to give up,” I told them, in my best, wisest caring-but-stern Dad voice. “If you quit every time something is difficult, you’re not going to do much in life—and you’ll miss out on all sorts of things.”
I try to follow my own words even as Devlin starts doing math on a piece of paper in view of the camera and demonstrates how to prove there are infinitely many prime numbers. As he utters the phrase “If p is a prime of the form 4n+1, then p is a sum of two squares,” I figure 5,000 students just dropped out. Maybe 10,000.
Nonetheless, I press on and make it to the end of the first lecture. Devlin encourages us to participate in online forums and study groups. At the forums, amid subject lines like “Anybody from the Balkans?,” I feel reassured that I’m not the only one who is lost. I feel myself bonding with an artist from Tokyo, who admits feeling “very frustrated and stupid” because he can only follow maybe 10 percent of the math. “Can I get anything out of this course?” he wonders (as do I). “My math skills may be lacking.”
I press on to the first assignment. It involves rewriting statements so that they are without a hint of ambivalence or double meanings—so that they are perfectly precise, like mathematical thinking and equations must be. Writing is what I do, and I plow through with a confidence that makes me uneasy. I finally think I know what I’m doing, and for some reason that leaves me even more confused. MOOC mania, indeed.