Optimizing mathematics placement: A machine learning approach comparing predictive algorithmic models

Abstract

Choosing the best criteria to place incoming college freshmen into the appropriate first semester courses proves to be a challenge for all subject areas, but for mathematics in particular. It is crucial that universities give students an opportunity to succeed by avoiding placing them in courses with material that is too advanced for them, but just as crucial, if not more, that universities do not place student in remedial classes when they do not need them. In this study we use data from over 21,500 algebra students at a midwestern university over eleven fall semesters to train a variety of machine learning algorithmic models to predict whether or not students will be successful in intermediate algebra and college algebra based on their high school GPA and all four individual components of the ACT. Of these five scores, we find that only GPA and Math ACT are significant predictors of success in algebra courses. We implement algorithms based in optimization, information, and metric space theories. Although they approach this problem with different perspectives, we find they all consistently give similar accuracies on the testing data and similar predictions. The main conclusion of this analysis is that a combination of GPA and Math ACT is the best predictor of success with GPA being the most important factor. We use this information to make recommendations for optimal initial mathematics courses based on an incoming student’s high school GPA and Math ACT score.