Course instructors need to assess the efficacy of their teaching methods, but experiments in education are seldom politically, administratively, or ethically feasible. Quasi-experimental tools, on the other hand, are often problematic, as they are typically too complicated to be of widespread use to educators and may suffer from selection bias occurring due to confounding variables such as students' prior knowledge. We developed a machine learning algorithm that accounts for students' prior knowledge. Our algorithm is based on symbolic regression that uses non-experimental data on previous scores collected by the university as input. It can predict 60-70 percent of variation in students' exam scores. Applying our algorithm to evaluate the impact of teaching methods in an ordinary differential equations class, we found that clickers were a more effective teaching strategy as compared to traditional handwritten homework; however, online homework with immediate feedback was found to be even more effective than clickers. The novelty of our findings is in the method (machine learning-based analysis of non-experimental data) and in the fact that we compare the effectiveness of clickers and handwritten homework in teaching undergraduate mathematics. Evaluating the methods used in a calculus class, we found that active team work seemed to be more beneficial for students than individual work. Our algorithm has been integrated into an app that we are sharing with the educational community, so it can be used by practitioners without advanced methodological training.