Wednesday, August 15, 2007

The informal economics of class size at Grinnell

I was involved recently in an Internet discussion of the effects of class sizes in public schools. If you have followed such discussions, you can guess how this one went. When data from studies finding very small effects resulting from very large investments in smaller classes came up, the teachers in the discussion protested mightily, offering tales of the difficulties of teaching huge classes in the present system. My own teaching experience also leads me to think of class size as an important factor. Here, however, I want to sidestep the normal policy debate to share my experience watching students negotiate the marketplace of course registration at Grinnell.

For starters, let's note that Grinnell students tend to be a politically liberal bunch who chose to attend a school that aggressively advertises the smallness of its classes; I'll wager almost all of them, if asked in abstract terms, would say that they value small classes as a policy objective and a personal preference.

Now here's what I mean about the marketplace of course registration. Let's say you have 50 students who can choose between two sections of the same class. The students choose in order, always knowing the current enrollment of each section. For whatever reason, they believe that the teacher of Section A is preferable to that of Section B.

We can model this easily. If the students all believe that class size is the only value worth considering, the two sections will each end up with 25. (#1 will chose Section A because the sizes are equal and the teacher is preferable, then #2 will go to B, #3 to A, and so forth.) If the students all believe that teacher quality is the only factor worth considering, you'll see 50 in section A and 0 in section B. More likely, you would actually see some kind of weighted preference, where students consider both factors and begin to choose section B as section A gets bigger--a 40-10 split would indicate a weaker preference for small classes than a 30-20 split.

In other words, the bigger the variation in freely chosen class sizes, the more weight students are putting on teacher quality relative to class size. The enrollments in the sections give you a lot of information about the population's values.

Viewing the choice from this perspective reveals that students tend to accept fairly large differences in class size before they let it trump perceived teacher quality. That's why every secondary school I know of (public or private, in any social setting) tries to make switching sections extremely hard. We can't know what choices students would make, but the barriers to switching imply a widespread assumption that left to their own devices, the students would choose exactly the model that some libertarian economists propose: bigger classes with the best teachers.

At Grinnell, students can often make exactly that kind of choice among sections or (more often) among classes that perform the same function in their course plan. Based on what I've seen, I would say that Grinnell students value perceived teacher quality much more than class size, to the point where most will readily become, say, the 21st person in the desired section rather than the ninth in another. I have seen students make switches because they value lower class sizes, but only in the most extreme cases by Grinnell standards (switching from, say, a section of 40 to one of 13), and even in those cases, very few students make the switch. I'm sure there are contrary anecdotes out there, but having seen a lot of preregistration numbers, I'm confident in asserting the general pattern.

I don't mean to imply that the Grinnell model would apply to other educational situations. I understand the problems with that translation. But I find this situation interesting because it involves a set of people making decisions that don't seem to match their abstract values.