facts, memorization, learning: part 2

I am now going to disagree with myself. (Perhaps.)

As an undergrad, when not running off to a neighboring college and devouring their classics curriculum, I wore a math-major hat.

Klein bottle hat! (CC-licensed by Flickr user <a href="http://www.flickr.com/people/mrsbluff/">Kari_Marie</a&gt;)

One of the outstanding features of my college was that most of the tests in my major were timed, open-book, take-home tests. This, I have to say, played to my strengths: I have a deep grasp of many mathematical ideas and a ghastly memory for details. When my classmates got into ferocious discussions about their favorite theorems, the fine details and applications and limitations thereof, I’d sit there twiddling my thumbs and wondering if I belonged in that major, because hell if I can remember details like that. But an open-book test? Awesome. I can look up all the stuff I forget.

My aforementioned Latin students occasionally asked for open-book tests, thinking that would mean the tests would be easy and they wouldn’t have to study. I told them every time how wrong they were. I did give an open-book final to one of my eighth-grade honors classes one year, a group of brilliant and hard-working boys I trusted with that kind of kryptonite; they’re in college now and I suspect they’re still peeved at me.

Because, the thing was, I studied for those. OK, in college, I didn’t really know how to study, but I was clear that there was a study process for this kind of test, and it would be at least as brutal as for a closed-book test. Because, see, the people writing closed-book tests always had bounded expectations of what we test-takers would know. They might be hard tests — I felt like someone had physically beaten me after the second-semester freshman physics final — but I also recognized a lot of it from the homework or textbook (which I had read nonstop for a week; physics and I had already established a brutality-oriented relationship). I was asked to know the whole course, sure, but not (too much) to innovate beyond it.

But math? Math could ask me anything. Math tests expected an encyclopedic knowledge of every relevant theorem, its conditions, its corollaries, its applications…every proof technique we’d touched upon…everything. And it turns out you can’t look up everything on the fly, for a three-hour test, unless you already have a passing familiarity with it. I could look up those details I’m no good at remembering, but I’d better understand — perfectly and fast — how to apply them. For that matter, I’d better know exactly where in the book to look, or be very good friends with the index, and know where everything in my binder was (I indexed that too) because I didn’t have time to flip through it all hunting for the one problem that could save me.

All of which is to say: math, the one subject where I could genuinely look everything up, was also among the hardest for me. The kinds of questions my teachers felt free to pose, in the look-everything-up world, required a broader, deeper, more sophisticated understanding — certainly of the concepts — and even of the universe of available facts (if not the facts themselves) — than any of my other classes.

The world we live in, the real world with the Internet and all its facts at our fingertips and, increasingly, in our pockets, is a world even more unbounded than my math tests. At least there I could get away with knowing nothing more than Dedekind cuts and Cantor diagonalization and a few dozen other things like that; the world might ask me anything. How do you study for an untimed, take-home, open-book test of infinite scope?

You will, to be sure, forget the details. But you may well have to understand…everything.