While there is much debate over the cost, wisdom, and effectiveness of different strategies for increasing the amount of learning time available in the average school year–such as increasing attendance rates, lengthening the school day, cutting out recess, and lengthening the school year–little attention has been paid to how much student learning time is reduced by disruptive student behavior.
Until now. A recent research study of educational productivity has provided an effective framework for better understanding this debate. The study also highlights the importance of teacher quality and raises questions about the cost-effectiveness of class size reduction proposals.
It’s easy to understand how the behavior of a single undisciplined child can severely disrupt a class of students and leave significantly less time available for learning. For example, if an unruly student monopolizes 20 percent of a teacher’s time and distracts other students at the same time, only 80 percent of the class time is left for learning.
What is less easy to appreciate is how even low levels of disruptive behavior on the part of all students also can result in a major reduction in the amount of time available for learning.
Unruly Students Affect Entire Class
In a paper presented to an American Economic Association meeting earlier this year, Edward Lazear, an economist at the Hoover Institution and Stanford Graduate School of Business, presented a model of how disruptions by individual students affect the time available for learning for the class as a whole.
“A student who is disruptive or who takes up teacher time in ways that are not useful to other students affects not only his own learning, but that of others in the class,” explains Lazear.
Lazear’s model calculates learning time as the time remaining after disruptions. For example, if the class has one student or 30 students, the time available for learning is 100 percent if there are no disruptions. But if, on average, each student disrupts the class 1 percent of the time, the time available for learning drops to 99 percent for a one-student class . . . and to just 74 percent for a class size of 30.
The big drop in learning time for the larger class is because each student’s potential 99 percent learning time is reduced by the disruptions of each of the other 29 students. For a one-student class, the time available for learning is 99 percent; for a two-student class, it is 99 percent times 99 percent, or 98 percent; for a 30-student class, it is 99 percent multiplied by 99 percent 30 times, or 74 percent.
In mathematical terms, the time available for learning is the percentage of time the student is not being disruptive raised to the power of class size, i.e.
Time available for learning =
(Percentage of time student is well-behaved) ^ (Class size)
Lazear’s model provides some striking insights when it is used to calculate the amount of learning time available in classes of different sizes with different levels of disruptions (see accompanying charts). The model makes it clear that even low levels of disruption significantly reduce the amount of time available for learning for all economically feasible class sizes.
For example, if, on average, each student in a class of 10 is disruptive just 1 percent of the time, the time available for learning in the class is only 90 percent. If the disruption level rises to 3 percent, the available learning time drops to 74 percent; at a 5 percent level of disruption., only 60 percent of class time is available for learning.
The fall-off in available learning time with increasing levels of disruption is even more striking at higher class sizes. With a class size of 25, only just over three-quarters of class time (78 percent) is available for learning with a 1 percent disruption level. With a 5 percent disruption level, the available learning time plummets to only just over a quarter of class time (28 percent).
Discipline a Substitute for Class Size
“Discipline is a substitute for class size,” states Lazear, explaining that the same amount of learning time may be achieved either by reducing class size or by enforcing stricter discipline in the classroom. For example, if class size is reduced from 25 to 20, the gain in learning time is always smaller than that produced by reducing the level of disruption by one percentage point.
This has significant policy implications, since the cost of reducing class size is very large, while the cost of educating a teacher on improved classroom management is quite low.
Eric Hanushek, an expert on class size research and also an economist at the Hoover Institution, interprets Lazear’s findings as being consistent with his views on the importance of teacher quality; Hanushek regards ability to manage the classroom as one of the big elements of teacher quality.
“If you think of teacher quality as affecting the amount of disruptions, which then has these important externalities of taking up classroom time, then a lot of that all fits together and I agree with it completely,” he said.
For more information . . .
Edward Lazear’s paper, “Educational Production,” will appear in the Quarterly Journal of Economics. It can be found on the Internet in Adobe Acrobat’s PDF format at http://faculty-gsb.stanford.edu/lazear/Personal/PDFs/educational%20production%20sept%2099.pdf. An HTML version is available on the Internet at http://www-hoover.stanford.edu/publications/digest/001/lazear.html .