Thursday, May 29, 2008

Don't Be So Proud that Your Section is Full

Yes, yes, yes, I know that classes always fill up early for the guy who I think is clearly in the top 5% for teaching talent, personal charisma, and general likeability. It's obvious that he has a well-deserved cult following.

However, I've noticed that sometimes sections taught by people with Bad Reputations tend to fill up too -- but only when they're teaching courses that are near the top of list. We teach a lot of multi-sections courses, so we'll have Calculus-001, Calculus-002, ..., Calculus-055. (Those familiar with freshman comp, western civ, etc. probably understand this well.) The list is not ordered in any meaningful way. There's no relationship between section number and time of day, classroom location, or instructor's name. It's random.

In one of the most common modes that the students use to build their schedules, they use an option called "course search." The student will ask for the Calculus class, and the system will return the first Calculus course that fits in with what's already in the student's schedule. A student searching for Calculus may be asked by the system "Do you want to enroll in Calculus-001 that meets at 8am in the math building and is taught by Professor Mediocre?" The student can then either add that section (click OK) or search for another section. If the student tries again, the system might ask, "Do you want to enroll in Calculus-002 that meets at 11am in the math building and is taught by Professor Trouble?" If word hasn't gotten to this student about the Trouble, then the student might click OK because of the 11am time slot. Or they may spin the wheel again and see what Calculus-003 has to offer.

I'm teaching the Calculus Circus again in the fall. It's a big lecture class with 10 sections. In our online system, each of these sections shows when and where the lecture meets, my name, and when and where the recitation section meets. The slot for the TA's name says "UNKNOWN."

I took these 10 sections and obtained 10 ordered pairs of the form (section number, current enrollment). When I did a linear regression, I got the equation Enrollment = (-1.7)(Section Number) + 26.8, with r = -0.74. Looking at the data, I noticed two pretty clear outliers: the two section that have the recitation meet at 8am. When I take those out, I get the equation Enrollment = (-2.2)(Section Number) + 34.8 with r = -0.99. Sure, sure, sure, once I've cleaned up the data to only have eight points, I'm likely to get a pretty good linear fit. But, really, -0.99.