*Math Problem #1. If a teacher devotes 20 percent of class time to one-on-one instruction, in a class of 30 students, how much more time does the teacher have to spend with each student when the class size is reduced to 15? (You may use a calculator)*

*Math Problem #2. If each student in a class of 30 disrupts the rest of the class an average of 2 percent of the time, how much uninterrupted learning time is left for teaching? How much is the learning time increased if (a) disruptions are reduced to 1 percent? (c) class size is reduced to 15? (You may use a spreadsheet program)*

While recognizing that “class-size reduction has lately gone from being a subject of primary academic interest to a policy juggernaut,” a group of international researchers last November recommended legislators should consider lower-cost alternatives—such as attracting better teachers—”before they commit billions more on reducing classes across the board.”

Just a month later, a new report on a reduced class-size intervention program for disadvantaged children in Wisconsin reaffirmed the critically important role teachers play in raising student achievement.

In a thoughtful review of studies of class size and academic performance in last November’s *Scientific American*, Ronald G. Ehrenberg, Dominic J. Brewer, Adam Gamoran, and J. Douglas Willms point out class-size reduction has one obvious drawback: “It costs plenty.” They note the state of California alone has spent more than $1.5 billion annually over the past several years to reduce class sizes to 20 or fewer in kindergarten through third grade … with only a “tiny effect.”

The impact achieved by another class-size reduction experiment—Wisconsin’s SAGE (Student Achievement Guarantee in Education) program—is much greater than that seen in California, but SAGE is not just about reduced class sizes. SAGE is a targeted intervention program aimed at raising the academic achievement of disadvantaged children not only by reducing class sizes to 15 in kindergarten through third grade, but at the same time implementing a rigorous academic curriculum, providing before- and after-school activities, and implementing professional development plans.

Students in classrooms adopting this four-part intervention package show a significant performance advantage over students in non-SAGE classrooms in all grades, although the gains do not widen over time. However, the most significant finding emerging from the SAGE experiment is the overriding importance of good teachers and good teaching techniques. (See “Smaller Classes No Remedy for Poor Teachers.”)

In their *Scientific American* paper, Ehrenberg and colleagues point out that little research has been done on alternatives to reducing class sizes. In particular, they note, “no one has studied the relative costs of attracting better teachers as opposed to reducing class sizes.”

They also raise a much more fundamental issue: How do small classes actually work to produce improved student performance? The conventional wisdom, they say, is that small classes “minimize disruptions.” The proponents of smaller classes also claim they free teachers to focus more individual attention on students and to use more creative instructional techniques. This latter claim does not stand up very well, according to the researchers.

**No Change in Teaching Style**

“[S]tudy after study has found that educators rarely change their instructional styles to match the size of their class,” report Ehrenberg et al. Even teachers in the acclaimed Tennessee STAR reduced class-size experiment did not change their teaching styles in smaller classes, despite participating in a summer professional development program. Moreover, whether classes are large or small, “educators seem to devote the same overall amount of time to individual instruction.”

**More One-on-One Time**

With fewer children in each class, each child can receive more one-on-one attention from the teacher. Although Ehrenberg et al. suggest any such increases in one-on-one attention would not be enough to account for any significant differences in academic performance, a few simple calculations raise some questions about that conclusion.

For example, if one-on-one time is equally distributed throughout a class of 25, each student could have the teacher’s undivided attention for just 4.0 percent of the time. If the class size is reduced to 15 and all other things remain the same, the undivided time with the teacher increases to 6.7 percent.

Although a teacher may spend only a small portion of the total teaching time for one-on-one interaction with students, this 67 percent increase in the time available for such interaction represents quite a substantial increase. Even a reduction in class size from 30 to 20 would produce a 50 percent increase in the amount of time available for one-on-one interaction. These calculations suggest smaller classes, by substantially increasing the time for student-teacher interaction, should produce substantial increases in student achievement.

**Minimizing Disruptions**

The effect of reducing disruptions in a classroom may be analyzed using a model developed by Edward Lazear, an economist at the Hoover Institution and Stanford Graduate School of Business. Lazear was interested in how disruptions by individual students affect the time available for learning for the class as a whole. His basic model calculates the available learning time as the time remaining after disruptions. (See “Do Classes Need to be Smaller or More Orderly?” *School Reform News*, September 2001.)

For example, Lazear’s model shows that if each student in a class of 30 disrupts the class 1 percent of the time, only 74 percent of class time is available for learning. That’s because each student’s disruptions reduce the available learning time for all other students.

Lazear’s model permits an estimation of the gain in learning time from reducing class size for different levels of student disruption. For example, in classes where each student is disruptive 2 percent of the time, the available learning time for a class of 25 is 60 percent of total class time. Reducing the class size to 15 increases the amount of learning time to 74 percent, a gain of 23 percent in learning time. Although each student is just as disruptive as before, the disruptions affect fewer students and there are fewer students to be disruptive.

The more disruptive the class, the greater the gain in learning time when class size is reduced. At a 5 percent level of disruption, the gain in learning time from reducing class size from 25 to 15 is a spectacular 64 percent, from 28 percent to 46 percent. Conversely, the less disruptive the class, the smaller the gain in learning time when class size is reduced. At a 1 percent level of disruption, the gain in learning time from reducing class size from 25 to 15 is 10 percent, from 78 percent to 86 percent.

**Policy Implications**

If the aim is to increase the amount of time available for learning, this may be achieved in two ways: either by reducing class size, or by enforcing greater discipline in the classroom.

For example, in a class of 25 students, reducing the level of student disruption from 5 percent to 3 percent increases the amount of available learning time by 68 percent, from 28 percent to 47 percent. This is the same gain that would be achieved by keeping the disruption level constant and reducing class size to 15.

As Lazear points out, “Discipline is a substitute for class size.” This has significant policy implications, since the cost of reducing class size is very much greater than the cost of teaching an educator improved classroom management techniques. As the last two years’ reports from the SAGE experiment have shown, the impact of different teaching styles on student achievement is substantial, independent of class size changes.

**For more information …**

The *Scientific American* paper, “Does Class Size Matter?” by Ronald G. Ehrenberg, Dominic J. Brewer, Adam Gamoran, and J. Douglas Willms, is available at the Web site of *Psychological Science in the Public Interest*, which published a longer version of the paper in May 2001: **http://www.psychologicalscience.org/newsresearch/publications/journals/pspi2_2_text.html**

Reports on the SAGE experiment are available at the Web site of the Center for Education Research, Analysis, and Innovation in the School of Education at the University of Wisconsin-Milwaukee: **http://www.uwm.edu/Dept/CERAI/sage.html**