This outstanding TED Talk by Barnard’s president is mainly about choking under pressure. But how interesting that the example Professor Beilock spends most time on is girls’ learning math.
One of the excellent points she makes so well is that there’s a difference between knowing how to do something, and being able to do it when the pressure’s on. And as you have probably experienced yourself, the pressure is in some sense always on.
I’ve experienced this since my school days, and I’ve done my share of studying this issue and experimenting with various best practices. When it comes to preparation for math tests of any kind, I consider this issue to be of equal importance to actually learning math.
I know. It sounds like heresy. But I know it’s right. So we use a three-pronged approach to preparing for math tests and math competitions alike:
Learn the necessary math to fluency
Identify and resolve all your performance/execution issues (per the above)
Strengthen your ability to critically deconstruct and to creatively synthesize
We give equal weight to these keys to success, because we understand that it isn’t just about what you know. It’s also about what you can do, and how you feel when you do it.
Brian Greene makes the point about science, and it holds just as true for math: “We rob science education of life when we focus solely on results and seek to train students to solve problems and recite facts without a commensurate emphasis on transporting them out beyond the stars.”
Interested in communicating with a faraway friend without allowing anyone to eavesdrop on you? Of course you are; this problem affects a middle-schooler’s daily life, and yet it is also the basis for modern commerce: communicating your credit card number over the Net without allowing a thief to eavesdrop is a non-negotiable requirement for our economy. How is this problem solved? First, you try for a while. Then let’s talk about prime numbers and see what they can do for us.
Interested in taking a rocket to the moon? Well, if you want to drive a spaceship, you probably ought to understand how gravity works differently from your intuition when you’re far from Earth. Let’s talk about ellipses, and while we’re at it, let’s predict the next approach of Halley’s comet. (And if you’re a high-school sophomore or so, we can talk about inverse-square laws while we’re at it.)
What if we picked up a signal for an alien civilization on our radio telescopes tomorrow? Do you think they’d speak English? Not a chance. Let’s think about how we would communicate without a shared language, a shared culture, even a shared planet? Well, there’s one thing we have in common with any race advanced enough to send us a signal like that: they know math. Let’s think about how that might work…
One of the biggest rarely-asked questions in math is simply “why should I care?”