I once caught an 11th-grader who snuck a cheat sheet into the final exam.
At first, he tried to shuffle it under some scratch paper. When I cornered him, he shifted tactics. "It's my page of equations," he told me. "Aren't we allowed a formula sheet? The physics teacher lets us." Nice try, but no dice. The principal and I rejected his alibi and hung a fat zero on his final exam. That dropped his precalculus grade down from a B+ to a D+. It lingered like a purple bruise on his college applications.
Looking back, I have to ask myself: Why didn't I allow a formula sheet? Cheat sheets aim to substitute for memorization, and I hate it when my students memorize things.
"What's the sine of π/2?" I asked my first-ever trigonometry class.
"One!" they replied in unison. "We learned that last year."
So I skipped ahead, later to realize that they didn't really know what "sine" even meant. They'd simply memorized that fact. To them, math wasn't a process of logical discovery and thoughtful exploration. It was a call-and-response game. Trigonometry was just a collection of non-rhyming lyrics to the lamest sing-along ever.
Some things are worth memorizing--addresses, PINs, your parents' birthdays. The sine of π/2 is not among them. It's a fact that matters only insofar as it connects to other ideas. To learn it in isolation is like learning the sentence "Hamlet kills Claudius" without the faintest idea of who either gentleman is--or, for what matter, of what "kill" means. Memorization is a frontage road: It runs parallel to the best parts of learning, never intersecting. It's a detour around all the action, a way of knowing without learning, of answering without understanding.
Memorization has enjoyed a surge of defenders recently. They argue that memorization exercises the brain and even fuels deep insights. They say our haste to purge old-school skills-driven teaching from our schools has stranded a generation of students upriver without a paddle. They recommend new apps aiming to make drills fun instead of tedious. Most of all, they complain that rote learning has become taboo, rather than accepted as a healthy part of a balanced scholastic diet.
Certainly, knowledge matters. A head full of facts--even memorized facts--is better than an empty one. But facts enter our heads through many paths--some well-paved, some treacherous. Which ones count as "memorization"?
I define memorization as learning an isolated fact through deliberate effort. The process can unfold two basic ways.
First, there's raw rehearsal: reciting a fact over and over. When I had to memorize a speech for ninth-grade English, I huddled in the school library for 90 minutes, whispering the words to myself again and again, until they settled into my memory. The process was slow, dull, and stilted. I forgot the speech within weeks.
Raw rehearsal is the worst way to learn something. It eats up time and requires no real thinking. So of course, it's popular among students ranging from my Oakland 15-year-olds to Harvard undergraduates. During a unit on memory, I once heard a psychology student recite, "Raw rehearsal is ineffective," before proceeding to practice her vocabulary using the same technique she'd just denounced.
Second, there are mnemonics and other artificial tricks--songs, acronyms, silly rhymes. In sixth grade, for reasons only heaven knows, I memorized 48 prepositions (about, above, across, after...) to the tune of "Yankee Doodle." I can still recite them.
Such tactics certainly work better than raw rehearsal. But they don't solve the underlying problem: They still bypass real conceptual learning. Memorizing a list of prepositions isn't half as useful as knowing what role a preposition plays in the language.
So what are the alternatives? How can students learn facts, rather than memorize them?
First, there's repeated use. Like raw rehearsal, it relies on repetition to chisel a fact into memory, but unlike that method, it comes naturally (without "deliberate effort"). In 10th-grade English, I wrote a paper on Robert Frost's apocalyptic poem "Once by the Pacific." I read it dozens of times, dissecting every phrase. Months later, standing on a rocky, storm-swept beach, I found that I could recite the poem by heart. I never set out to memorize it. I just...did.