Saturday, September 5, 2009

The class matching problem

In Slate, Emily Bazelon talks about the class assignment problem. This is the annual task schools face in allocating students to classes. They need to do it on the basis of getting a good mix on classes and avoiding relationships with problematic external effects; for instance, separating out would-be bullies. The problem is that parental (and indirectly, child) preferences intervene. They have preferences for friends but also, and this is where it gets much stickier, for teachers. And that makes the whole class assignment problem far more complex.

Bazelon examines the moral issues here -- should a parent engage in what is essentially a zero-sum game? If you push to have your child in a class with a particular teacher, that pushes another out.

The school rules evolve as a response to this. One of my favourite games, is to "guess the incentive problem" when I see some sort of rule. For instance, in our school, class assignments for the next year are sent out on December 23rd (this is Australia, so the school year is the calendar year). This makes it impossible for anyone to actually receive them until well into the summer holidays when there is no one to complain to. Why this policy? It is clearly designed to put a lid on parental complaints and also it prevents aggregation of information as to who got into other classes.

But this is not to say that there is no input of parental and child preferences. This occurs earlier where children are invited to list four others they would like to be in a class with next year. They must include at least one child outside of their current class. They are not allowed to place a preference for children they would like to avoid. And then the list is sent home and must be signed off by their parent. This system is fine with us and we have not engaged in 'out of the game' lobbying.

I have long tried to implement a scheme when allocating students to syndicate groups for assignments. It looks pretty much like the one my school uses but on a smaller scale. I hadn't thought of getting parental sign-off for MBAs though. Next time perhaps.

It is interesting to see the diversity of approaches that are put in place across schools. For instance, from Slate,
At Orangewood Elementary, a public school in Phoenix, Ariz., parents are invited to request a class assignment ahead of time, so long as they follow an established set of rules. The principal, Andree Charlson, explained to me that she asks parents first to sit in on the class they think they want, to see whether the teacher's instructional method really appeals to them rather than going on vague hearsay. She honors requests only when they jibe with her own and her teachers' sense of what makes for a good class mix. That includes balancing the number of boys and girls, including a range of ability levels, and not putting too many kids with behavioral problems in the same classroom.
Ha! They impose signaling costs on the parents as to how serious they are. Not a bad approach but it is costly on the school too.

One suspects that there might be an actual solution to the class assignment problem. In economics, Al Roth and others have studied matching problems -- for instance, how interns are allocated to hospitals when the interns and hospitals have their own rankings. And New York schools are trying to work this out with respect to getting siblings into the same school. My guess is that this might be of use in coming up with a mechanism for class assignment.