A few weeks ago, I posted a “class size math problem” to illustrate how small elementary schools tend to generate outlier class sizes. The post received a lot of good comments—but nobody did the math problem! Specifically, the question was how many students you’d want to assign to a school that had ten (or, alternatively, fourteen) general education classrooms, and what the class sizes would be in each grade. The one constraint was that you had to assume that there would be a roughly equal number of kids in each grade level.
One purpose of the experiment was to show that it’s hard, in small schools, to have class sizes that stay in the neighborhood of the district’s class size goals. The goals, for most schools, are not to exceed 26 kids in grades K-2 and 30 kids in grades 3-6. We don’t want class sizes to exceed those goals, but if class sizes are too far below them, they undermine the district’s attempt to reallocate resources to higher-need schools. (More complete explanation here.)
Without mixing grade levels, this was the closest I could come to the class size goals, without exceeding them, in the ten-classroom school:
As you can see, many of the classes are very small—way below the district goal for grades K-2. That puts upward pressure on class sizes elsewhere and makes it harder to redirect resources to higher-need schools.
In the fourteen-classroom school, this was the closest I could come to the goals without exceeding them:
This school is significantly fairer to the district’s other schools, since its average class size is closer to the district-wide medians. It does less to undermine the district’s efforts to reallocate resources to higher-need schools. It accommodates a lot more kids. You could make those early-grade class sizes smaller—I’m sure many people would balk at the idea of a 26-kid kindergarten class—but only if you’re willing to live with smaller class sizes in the higher grades, too. As the upper-grade class sizes fall farther below the goals, class sizes elsewhere in the district would have to rise.
These scenarios assume an equal number of kids in each grade level. In reality, there is often a lot of variation in enrollment in the different grades. That’s a big part of what makes class sizes hard to manage in small schools. It’s actually hard to get much closer to the district goals than the “ideal” fourteen-classroom school, but the great advantage of larger schools is in their ability to handle that anomalous year-to-year variation, since they can spread the effects out over a greater number of classrooms.
In my next few posts, I’ll consider alternatives (such as mixed grades, paired schools, and the use of half-time teachers) that can help alleviate the class size issue in small schools.