Saturday, August 28, 2010
Small steps, big goals
Despite the variations, every semester strikes the same themes: how do you learn? how do you study? how do you succeed? how do you pass?
And there's always a few students who want the secret—the magic short-cut that will put them on the royal road to learning math easily. Apparently they think we are hiding some sort of trade secret that enabled us to become math teachers. We must guard it jealously lest we lose our strangle-hold on algebra!
While I disdain one-size-fits-all solutions to students' problems, there are some fairly uniform basic principles. For example, success is usually proportional to effort. Different students must put in different amounts of effort to achieve equivalent success, but the basic principle still holds. Thus I tell my students they have to gauge for themselves how much effort (which translates significantly into allocation of time) they must put in.
In an attempt to encapsulate the idea in a simple bite-size aphorism, I have told my classes, “Do a little every day.”
They blink at this, of course. It sounds deceptive.
“Only a little?” they ask plaintively.
“Gosh, no,” I tell them. “At least a little.”
It's a good lesson, and one that I learned later than I should have. During my last encounter with grad school, trying to teach a full-time load at my college while carrying a full-time academic load as a university student, there wasn't a lot of slack in my schedule. Determined not to let things slide (at least, not too far), I solemnly resolved to do a little work on my dissertation every day. Every day. No exceptions. Without fail.
I didn't slice my hand with a subtle knife and swear a blood oath, but I did the next best thing.
I told my grad school classmates.
It became an enjoyable game that anyone could play.
“So, Zee, what did you do last night?”
Occasionally I was reduced to paraphrasing Oscar Wilde:
“I was working on the methodology section of my dissertation all day, and took out a comma. In the evening I put it back again.”
And, sadly enough, that was often too close to the truth. Other times, however, an interesting thing happened. I'd be exhausted and ready for bed and then I'd realize I still had to discharge my solemn obligation to tinker on the dissertation. At least a little. Resolving to postpone sleep for just a few minutes, I'd sit at the computer and fire up the word processor. A paragraph. Let's just get one more paragraph in there.
And then, magically, I'd awaken from a trance to discover that half a dozen pages had been written in a two-hour altered state. (Perhaps elves had slipped in and moved my fingers over the keyboard.) Not that this occurred every time, of course, but still often enough to provide the quantum jumps that really advanced my progress toward graduation.
As with any project, completion won't occur without participation. You have to do something.
And that's what I tell my students.
When it's early in the semester, students tend to be in a hopeful mood and try to nod their heads agreeably when their instructor says something. However, the last time I gave an algebra class a harangue similar to the above, one of my students seized on the “math genius” comment.
“But what if you are a math genius?”
The speaker, a lanky kid sitting near the back of the room, was instantly the center of attention.
“If you're a math genius,” I replied, “then you should definitely talk to your math teacher. I know very few and I welcome the opportunity to meet another. Are you indeed a math genius?”
I neglected to point out that the density of math geniuses in college-level introductory algebra classes is extremely close to zero, but no doubt a math genius would have understood what I meant by that.
He nodded his head.
“Yeah, I am,” he modestly admitted. “This stuff is very easy. Very easy. No one should complain about having to take algebra because it is, like, totally easy to do.”
His classmates regarded him with keen curiosity. So did his instructor, for that matter.
“I'm glad to hear that you think so,” I said. “I'm inclined to agree with you, but most of your classmates probably have differing opinions. May I ask how you arrived at your conclusion that algebra is super easy?”
He nodded his head again.
“Yeah, sure. I took it during the summer at the extension center. Like I said, totally easy!”
Everyone paused for a long moment, considering what he had said.
“That raises another question,” I pointed out. “Why are you enrolled in this class if you've already taken algebra during summer school and found it totally easy?”
He regarded me with a trace of exasperation.
“I said it was easy, Dr. Z. I didn't say I passed!”
Apparently it was so easy that it failed to capture his attention.
“Oh, good point,” I said agreeably.
I turned my attention back to the rest of the class.
“Okay. Are we clear, everybody? Even math geniuses can occasionally have trouble with algebra, so commit yourself to working on it—at least a little!—every day of the semester. Let's see how successful you can be.”