Alternatives to Math Placement Exams: A Look at Discriminant Analysis, Neural Networks, and Ensembles of Networks

Implementing a technique that is efficient yet accurate for college student placement into the appropriate mathematics course is of significant importance. Universities often assign students to entry-level mathematics courses based on mathematics placement examination scores. In this paper, the authors examine alternative placement strategies. Using multiple regression analysis, the accumulative high school grade point average, mathematics SAT, and the final grade in Algebra II were found to be the best predictors of success on a mathematics placement examination. Using these features, entry-level mathematics placement based on neural networks is contrasted with discriminant analysis, and proposed as an alternative to testing. Results demonstrate neural networks outperform classical discriminant analysis in predicting the recommended mathematics placement. Furthermore, preliminary results suggest ensembles of networks may provide additional benefits. Consequently, a trained neural network or ensemble of networks can be an effective alternative to a written mathematics placement test.