Don’t Teach Math, Coach It
By Jordan Ellenberg for The New York Times
In a recent New York Times article, Don’t Teach Math, Coach It, Jordan Ellenberg, a mathematic professor at the University of Wisconsin, talks about how to get kids excited about math. He starts off with a short anecdote about how the young Norbert Weiner was shaped into a math prodigy by a father who would go from a gentle schoolmaster to a seething bully as soon as little Norbert flubbed a question. Weiner senior was clearly less about fun and more fury; Ellenberg, on the other hand, wants to take that general ethos of learning and turn it into a game—something that can be coached (assuming the coach isn’t the red-faced martinet many of us have had at some point). Trips to market to buy fruit or before-bed math problems can all be turned into games, as Ellenberg relates from personal experience.
Perhaps more significantly, Ellenberg stresses the importance of teaching math as though it were sport, in the sense that it is something that we can all learn to excel at with the right coaching. He argues that it’s not about getting the right answer so much as it is playing the game and finding ways to improve.
I really like Ellenberg’s approach to math as a game—and by extension something that is coachable. It’s about illuminating the inherent fun of math, so that the person learning doesn’t become frustrated and prone to thinking that they just weren’t meant to be any good at math.
What I didn’t like so much is that the article made learning and fun the sole province of children. I obviously think turning students on to math at a young age opens up a wealth of opportunities for them throughout life. But what I thought is just as noteworthy—and what the article completely glosses over—is how math and fun apply to adults as well, many of whom were once children who, at one time or other, convinced themselves that they weren’t any good at math.
As somebody who has tutored GRE/GMAT, I’ve had my fair share of students who start off with the notion that the only way to do math exercises is to slog through them. Typically, they are freighted with the nagging assumption that math exists in some inscrutable realm forever closed off to them. The best way to get them “out” of their heads and “into” math is by taking what they know—which is oftentimes quite a lot—and turning it into a little question on the fly. After they get a few questions correct, I’ll make the problems slightly more difficult. I often find myself having to motivate them through some of the tougher steps, since they’ll often make their inner voice audible (“I’m just not good at math”). But with a little positive feedback, we can usually overcome the on
Had I been like Norbert’s father, I probably wouldn’t have lasted very long as a tutor. But by trying to work with a student’s current level and, through mere encouragement, helping them make baby steps, I’ve seen students jump from the 40th percentile to well over 80.
I’m not trying to toot my trumpet, as there are obviously many tutors out there like me (and better). My point is that much of what is stopping students from growing in math is the tense environment that has allowed that negative voice to take root in the first place. By making math a game, even without a tutor by your side, you can start making improvements that will make that negative voice pause for a second.
For instance, a great way to improve your mental math ability is the following game: Take any four numbers less than ‘10’ and try to make the number 99. You can use any of the standard notations, +, –, x, /, !, exponents.
Let’s try 1, 2, 3, 4.
To get close to ‘100’, we’ll need to use some exponents. 4^3 x 2 x 1. This gives me 128. But that’s good because I know I can at least get over ‘99’. Next, I’ll try 3^4 = 81. But I still am ‘18’ less than 99, and I can’t ‘18’ from the remaining ‘1’ and ‘2’. The point is to play around with numbers so that you become adept at knowing your powers (you’ll want to use a calculator at first for those sums that you can’t do off the top of your head). Eventually, you should come to (3! + 4)^2 – 1 = 99.
Now, that negative voice in your head might already be starting up, saying that there is no way you would have ever gotten that. But that wasn’t an easy example. If you try larger numbers, it’ll be easier, and the more you practice, the better you’ll be. See, as long as you are playing games like this—whether as you waiting in or during a boring T.V show—you are working out your math brain, and by extension, doing a little bit to prove that voice wrong.