Right-Sizing the Classroom

By Michael J. Petrilli and Amber M. Northern 11/22/2013

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Last month, USA Today reported that officials in the Brevard County Schools had broken Florida state law—on purpose. Their offense? Placing more kids in classrooms than Florida’s Class Size Reduction statute allows. Officials had done the math and decided that complying with state policy would cost more than the penalty they’d pay for adding a handful of students to each classroom. The estimated fines totaled roughly $170,000, which paled in comparison to the cost of the teachers that the district would have to hire to comply with the size-limiting mandate.

Yet it’s unclear how Brevard chose to allocate these additional students. Did administrators give every teacher more students in equal shares? Did they apportion shares to seasoned veterans or, more likely, to seniority-deprived new teachers? Maybe they drew straws?

But what if Brevard officials had chosen another option? What if they had assigned the “extra” students to their most effective teachers, leaving fewer pupils in classrooms presided over by weaker instructors? What would be the impact of such a practice on student achievement?

That’s the scenario that this empirical paper models. The idea is straightforward: Give the better teachers more kids and the weaker teachers fewer—then see what happens. It’s a common-sense option with many supporters. We know, for instance, that parents say they would opt for larger classes taught by excellent teachers, rather than smaller classes with instructors of unknown ability. In a study last year for the Fordham Institute, the FDR Group found that a whopping 73 percent of parents would choose a class with twenty-seven students—provided it is “taught by one of the district’s best performing teachers”—over a class of twenty-two students “taught by a randomly chosen teacher.” Further, given the choice between fewer students and more compensation, the teachers themselves choose the latter. In a well-done study of their own, Dan Goldhaber and colleagues found that 83 percent of educators in Washington State would prefer an additional $5,000 in compensation versus having two fewer students in their classes.

Yet, to our knowledge, no district assigns students to teachers based on their instructional effectiveness. Instead, pupils are divided roughly equally among teachers of the same grade in the same school, since parceling them out uniformly is viewed as fair to teachers.

But what if it’s not fair for kids? Or what if the costs fail to justify the benefits? We aimed to find out.

Given districts’ aversion to assigning students in this way, we were forced to simulate such assignment using actual data from one state (North Carolina). To perform this statistical maneuver, we approached economist Michael Hansen, a senior researcher at the American Institutes for Research. Dr. Hansen, an expert in labor economics and the economics of education, has ample experience mining North Carolina data and conducting simulations of this genre.

Hansen starts by examining the extent to which North Carolina already assigns students within schools based on teacher effectiveness. (He finds the state has a slight tendency to do so.) Then, he turns to the simulation, looking at fifth- and eighth-grade test scores. He uses three years of data (2007–10) to generate past value-added measures. For the fourth year, he estimates how teachers actually performed, and then he simulates what the impact would have been if students instead had been allocated to teachers based on their prior performance, with an eye towards maximizing student gains. The allocation process results in larger classes for the most effective teachers and smaller for the least effective.

The key finding: Minor changes in assignment lead to improvements in student learning. The results were relatively modest for the fifth grade; there, even when as many as twelve additional pupils were assigned to effective teachers, it yielded gains equivalent to extending the school year by just two days.

At the eighth-grade level, however, the results were much more robust. Hansen found that assigning up to twelve more students than average to effective eighth-grade teachers can produce gains equivalent to adding two-and-a-half extra weeks of school. Yet adding fewer students pays dividends, too. In fact, 75 percent of the potential gain from allowing up to twelve students to be assigned to the best teachers’ classes is already realized when allowing just six students to move. Specifically, adding up to six more than the school’s average produces math and science gains akin to extending the school year by nearly two weeks. This impact is the equivalent of removing the lowest-performing 5 percent of teachers from the classroom.

That last point is worth reflection. Moving a handful of students to the most effective eighth-grade teachers is comparable to the gains we’d see by removing the lowest 5 percent of teachers. And that is without actually removing them. As Hansen explains, “Class-size shifting enables the lowest-performing teachers to become more effective than they may be otherwise.” That’s certainly a good thing. But does it mean that we should hang onto persistently ineffective teachers? Given the cost of keeping them on the payroll, probably not. At some point, giving ineffective teachers the luxury of small classes becomes an unsustainable financial burden. Or, to put it another way, we should shrink some teachers’ classes down to zero students—and take the money saved thereby to bump up the compensation of effective teachers.

Last, Hansen examines whether this reallocation policy helps our neediest students gain more access to effective teachers. In a word, no. Gaps in access for economically disadvantaged students persist, primarily because the pool of available teachers in high-poverty schools remains unchanged under this strategy. Hence, this policy alone won’t remedy achievement gaps. (Recall that the reassignment occurred within schools; if it had been carried out across schools, perhaps the results would differ.)

As for costs, Hansen shows that some class-size variation already exists within schools (a differential of three to five students); presumably these small differences are not compensated. Perhaps then, principals could choose to assign these extra students to their most effective teachers without costing taxpayers an extra penny. After all, that’s the beauty of this strategy: It does not require a change in state policy or, in many cases, teacher contracts to make it happen.

In the end, one simple change—giving effective teachers a handful more students—could mean a big boost to student achievement. Still, this change has not been tested in the real world. We’ve now simulated its impact using actual data from an actual state. But which district or state will be the first to try it out in real classrooms?

-Michael Petrilli and Amber Northern

This first appeared on the Fordham Institute’s Flypaper blog.

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