Thursday, September 01, 2005

No Bell Curve Here

Tomorrow is the last day to drop without a W, so I am being sure to tell my calculus students where they stand. I've printed up grade reports with all their scores and comparing them to the class average (right now a frighteningly high C+) and giving them their ranking in the class.

As of right now, 10 students have A averages, 7 students have Bs, 6 have Cs, 1 D, and 10 Fs. The highest average is 100% (2 students), and the lowest is 12%. And a lot of the As are really high As: the #5 ranked student in my class has a 97.9% average. As most of my students are used to being the best students in their math classes, I thought that knowing where they stood in my class would be a good motivator.

This makes it a very hard group to teach. Most of the best students have taken calculus before. As there are plenty of them, I need to think about what I can do to keep them from getting bored. Yet, I don't want the bottom cohort to get further behind. From what I can tell, though, there are very few well-prepared and hard-working students near the bottom of my class. The unprepared would be better served by a lower-level class, and the slackers need to either get to work or be prepared to fail. I don't know what to recommend for the rest of the failing students, though. I don't know why they're failing, so I don't know what to recommend.

Not surprisingly, I tend to identify most with the bored students near the top of the class, and I need to keep reminding myself that it is OK for them to be bored sometimes and that they are probably well-equiped to entertain themselves during boring classes. But the bored students are also likely to end up in trouble later (so far we have only had quizzes and homework -- no exams yet), as their pre-existing knowledge of calculus is sloppy and incomplete. Trying to show off what he knew from before, one student responded to my quiz question about using a calculator to guess lim_{x \rightarrow 0} \frac{\sin x}{x} by noting that it could be evaluated by L'Hopital's rule -- putting himself in what I consider to be a bit of a chicken-and-egg situation.

I have meetings all afternoon, but if they get boring, I might entertain myself by concocting clever examples to perplex my top students.