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.

**Read more.*** [Image: Amy Loves Yah/Flickr]*