Smart versus brilliant

I've been pretty sick this last week (a rarity for me, but it happens) and have already taken a couple days off for rest. As a result, I'm working through the weekend. Between the sickness and driving to and from NY to visit my parents, I did have plenty of time to think about various things.

One idea that I kept coming back to was how our education system is so biased towards making kids smart. That sounds like a pretty good thing. The point (or, at least, a significant aim) of education is to make you smarter, right? The rub is that there's a small percentage of kids who simply don't operate that way. They function on brilliance. Both techniques work, but they are not at all the same thing.

Smart, as I am using it here, means learning enough factual information that new problems are easily solved by fitting them into an existing framework. You need to divide 426 by 19. You've never done that before. But, you know how to do long division. There's no need to be afraid of that problem.

All well and good, but a brilliant kid won't likely use long division (unless forced, and then they'll probably mess it up). They'll just look at the numbers and say, "around 22". If pressed, they might look at the ceiling for a few seconds and say, "OK, a little more than 22." I'm not talking about idiot savants, here. A person who can immediately compute that 426/19 = 22.421 is a whole 'nuther thing. I'm just talking about normally intelligent kids who don't solve problems in a linear fashion.

If you ask the brilliant kid how they got that, they may have real difficultly explaining it. They probably don't know themselves. When I cooked up that example, I tried to follow my own thought process in answering it. It went something like this: 20x20=400. That's about the same as 19x21, I need at least 1 more. 22.something. It's actually very similar to how Genetic Algorithms solve optimization problems. Start with an answer that's certainly wrong but probably in the ballpark and then mess with it until it works.

The important thing to note is that it's not an algorithm. It's guessing. Unlike long division, I have no guaranteed path to success. I'm just poking at the answer until it reveals itself. Sometimes that doesn't work very well, but usually it does.

Now, you could certainly argue that, unlike a GA running on a computing grid that tries thousands of possibilities in a second, a person is going to have a mighty hard time getting 22.421 through trial and error. I would counter that by saying that there are almost no situations outside of finance or engineering where more than three significant digits are required. And, if you're doing finance or engineering by hand calculation, you are one of the world's truly great time wasters. That's what calculators are for.

Some educators seem to have grasped that these other "techniques" have merit and tried to work them into the curriculum. Unfortunately, they are being taught using the "smart" paradigm. That's a complete disaster. If you're going to go the smart route (and that is the way to go for the vast majority of kids), you need techniques that are trustworthy. A small, but effective repertoire of skills is far more useful than a vast array heuristics that may or may not help in any given situation.

If you're going to teach these things at all, they need to be taught as brilliancies. Honestly, I'm not really sure how you do that. Nobody every taught me and every other person I know who's comfortable doing rough arithmetic in their head also developed their techniques on their own. I think the best you could do is encourage guessing and substitution as starting points and the kids who like that approach will figure out how to use it. For everybody else, long division works just fine.

The sad part about all this is that, in trying to broaden the curriculum, they've made it even harder for kids to find their way through it. Yaya was completely bowled over by all the tricks she was being taught in elementary school. She was fine with just following steps, but if she had to actually pick which steps to apply, she got lost quickly. And, if she picked one that made the problem harder rather than easier, she was very quickly frustrated.

Meanwhile, I don't think this is helping the brilliant kids one bit. Having to actually show their steps slows down the intuitive leaps that make the whole guess and adjust process work so well.

You might derive from my choice of words that I think brilliant is better than smart. I don't. I just used those words because they seemed to fit. As both approaches work, I don't see why either should be more than a preference. My concern is that, by trying to present brilliant as smart, that preference becomes less obvious and kids are just getting confused. Most sort it out, of course, but some don't. I personally know of at least two kids who are seriously struggling in Middle School math right now solely because it was presented to them so badly in Elementary School.