School Quality and Class Size

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451

Parents of K-12 children and students, especially those making plans about attending a college or choosing a high school, are concerned about the school quality. There are many factors which go into measuring how good a school is. However, one factor that seems worthwhile to take into account is the relationship between the number of students at a school and the size of the school's faculty.

A moment's thought will indicate that this is a more complex issue than it might seem at first glance. The faculty size at an elementary school may include guidance counselors, social workers, librarians, and psychologists as well as "teaching faculty." However, in comparing schools and school districts, it may be useful to compute "average class size." For example, one could count the number of fourth grade classes and the total number of students in these classes to get an average class size for the fourth grade. One could compute similar numbers for grades K-5. This is probably a useful measure for comparison but when students start to have more than one teacher for the classes at a grade level, things get more complex. For example, some schools, starting in the 6th grade, have the students move from one class to another rather than having one teacher. If foreign language is one such choice and one tries to get a class size for the whole grade, the numbers may be distorted because the school has Spanish classes that have average size 24 but Russian, Japanese, and Italian classes, which as a group, have average (mean) class size 9.

At the college level, just the simple statistic of computing total number of class enrollments divided by the number of sections being offered may create a picture that is misleading. A college may have many independent research classes with one or two students in each and other "lecture sections" where the number of students is as large as 250!

You have been hired by a new company which is going to provide ratings of colleges. One of the issues that the company wishes to have as part of its system involves student body size versus faculty size, and class size. Your job is to devise a reasonable system for comparing colleges centered on one or more numbers that address the question of class sizes at different colleges.