Does a Cusp Catastrophe Explain the Relationship Between School Size and Academic Achievement? Evidence from the Kingdom of Saudi Arabia

The evidence regarding the relationship between school size and academic achievement is unequivocal as studies have provided support for both linear and nonlinear analytical means. Specifically, we hypothesized that the relationship between high school achievement as measured by the GPA and aptitude is best described by a cusp catastrophe model when simultaneously accounting for the contribution of school size. This hypothesis is based on the premise that as school size increases beyond a functionally optimal size, for a given level in the asymmetry variable (aptitude), high school students' achievement is expected to become discontinuous, erratic, and reach chaotic behavioral levels. Data were collected from 52,854 students who were educated in 547 schools in the Kingdom of Saudi Arabia. Using Cobb's conceptualization of the cusp catastrophe results indicated that school size defined as the number of students distorts the relationship between aptitude and GPA suggesting an optimal number of students associated with increases in achievement as a function of aptitude. This finding was also replicated using the student-to-teacher ratio as a bifurcation term. It is concluded that the role of school size is complex and requires the engagement of additional analytical methodologies.