Because I'm scheduled to teach Dr. Hand-Waver's class for her next week, we've been having an ongoing discussion about educational philosophy. Basically we're trying to decide an age-old quandary: do you cover the lower-level material until you're sure the class has mastered it? Or do you only do so until they have the absolute basics down, then move on to more advanced topics that they might find more interesting?
Dr. Hand-Waver usually falls in the former camp (as do I), but as time goes on she's thinking more and more about the latter course of action.
To illustrate my argument for the first course of action--getting the class to master the basics before moving on to more advanced topics--I trotted out a story of a former tutor client, a 9th grader in pre-algebra. His mom hired me to help him learn to solve for 'x', but I found I could not do that. See, when I first got there, he was working on problems like this:
(2/3) x + 1 = 5
He understood that he had to subtract one from both sides to get (2/3)x = 4. But after that he was stumped. Of course I told him that he had to divide by 2/3 next, but he really didn't seem to understand that. We played around with some other problems for a while, and it became clear that he could solve 2x = 4 just fine.
So what was his issue? Simple: he couldn't do fractions. Years ago, his teacher had moved him on because she should...and now it was coming back to bite him.
"If they don't understand the basics," I told Dr. Hand-Waver, "They won't be able to do the more advanced stuff. It will make them feel stupid."
"Yes," she said, "But if they don't do the advanced stuff, they will think that our subject is all menial math. And they will hate it. I want them to love it."
She's right, of course. We decided the only way to cover everything in that class was to have the students put in more time. But the only way that would happen is if the students did it outside of class--which they won't do voluntarily.
In the mean time we're stuck trying to figure out the best way to find a happy medium between covering the cool, advanced material and the necessary basic material. If anyone has any suggestions, I'd be happy to hear them.