A Markov Decision Processes Modeling for Curricular Analytics

The curricular structure and the complexity of the prerequisite dependencies in a curriculum are essential factors that impact student progression, and ultimately graduation rates. However, we are not aware of any closed-form methods for quantifying the relationship between the complexity of a curriculum and the graduation rate of those attempting to complete the curriculum. This paper introduces a new method that quantifies this relationship using Markov Decision Processes (MDP). The non-deterministic nature of student progress along with their evolving states at each semester make MDP a suitable framework for this work. We propose a novel model that is useful due to the fact that it provides a closed-form solution approach that can be utilized to perform "what-if" analyses around student progress through a curriculum. The results confirm the inverse relationship between the complexity of a curriculum and the graduation rate of those students attempting to complete it. This is validated using a Monte Carlo simulation method. The results also provide useful insights that may guide future work in this area.