An Illustration of the Use of Markov Decision Processes to Represent Student Growth (Learning)

Over the course of instruction, instructors generally collect a great deal of information about each student. Integrating that information intelligently requires models for how a student’s proficiency changes over time. Armed with such models, instructors can filter the data—more accurately estimate the student’s current proficiency levels—and forecast the student’s future proficiency levels. The process of instructional planning can be described as a partially observed Markov decision process (POMDP). Recently developed computer algorithms can be used to help instructors create strategies for student achievement and identify at-risk students. Implementing this vision requires models for how instructional actions change student proficiencies. The general action model (also called the bowtie model) separately models the factors contributing to the success or effectiveness of an action, proficiency growth when the action is successful, and proficiency growth when the action is unsuccessful. This class of models requires parameterization, and this paper presents two: a simple linear process model (suitable for continuous proficiencies) and a birth-and-death process model (for proficiency scales expressed as ordered categorical variables). Both models show how to take prerequisites and zones of proximal development into account. The filtering process is illustrated using a simple artificial example.