This picture sits atop an interesting article in Slate magazine, titled “You’re not actually bad at math” and subtitled “A new way to think about how to reason.” Although I call the article “interesting,” it’s ultimately disappointing. It raises several questions. First of all, who is the intended audience? Apparently it consists of people who think that they’re bad at math, and the article intends to dissuade them of that self-image. Right?
Assuming that the answer is yes, our second question is why the article is accompanied by this elegant but confusing picture? What does it have to do with math? Or with self-image about success in math? “Actually,” as the author might put it, I can answer those questions, but then again I’m not the intended audience.
Third, the article raises expectations with this entirely reasonable paragraph that appears right after the opener:
The idea that someone can be bad at math is wrong, and it hides several harmful assumptions. It’s an excuse to justify individual failure, rather than a real understanding of mental capabilities. Giving up on math means you don’t believe that careful study can change the way you think. No one is born knowing the axiom of completeness, and even the most accomplished mathematicians had to learn how to learn this stuff. Put another way: Writing is also not something that anyone is “good” at without a lot of practice, but it would be completely unacceptable to think that your composition skills could not improve.
This paragraph is well-intentioned, and it’s probably even true. But how persuasive is it to readers who already have self-doubts about their mathematical ability? Perhaps they’ve been studying hard for years and still feel surrounded by classmates with natural abilities who just effortlessly “get it.” Of course it’s not effortless, but there’s a heavy dose of reality in the perception. If you think you are “bad at math,” you may not be seeing how much your more successful classmates have been practicing, but you do see quicker signs of understanding in class even before anyone has practiced. This can be frustrating and can reinforce the “I’m just not good at math” point of view. The difficulty is that you’re only seeing the tip of the iceberg; you can’t see the years of prior practice that have made their quick understanding possible. You are inadvertently confusing the process with its result.
The author, Chase Felker, goes on to make some good points, so it’s worth reading this short article, despite some doubts on my part. In particular, I’m not convinced that he really has found a selling point when he argues that math is baed on “pure logic” and “abstract reasoning”; he’s right, but that’s exactly what turns so many students off, so I wouldn’t press the idea. On the other hand, I do like this observation of his:
All of high school math is basically a one-way linear staircase that leads to calculus. If you fall off at any point, you’re doomed. Calculus prep has infiltrated the curriculum to such a degree that I think people conflate doing algebra with all of math. Students spend so much time memorizing computational tricks that they don’t get to see anything else—that those algorithms have a logical derivation, and that plenty of math isn’t even like that.
This is why Weston and some other schools have introduced courses like Applied Discrete Math, which counters that perception. Read the whole article; there’s a lot of food for thought there, despite my reservations.