Cognitive Modeling to Represent Growth (Learning) Using Markov Decision Processes

Over time, teachers collect a great deal of information about each student. Integrating that information intelligently requires models for how the students’ proficiency changes over time. Armed with such models, teachers can filter the data—more accurately estimate the student’s current proficiency levels—and forecast the student’s future proficiency level. Furthermore, partially observed Markov decision processes (POMDPs) and recently developed computer algorithms can help tutors create strategies for student achievement and identify at-risk students. Implementing this vision requires models for how instructional actions change student proficiencies. This paper introduces a general action model (also called a bowtie model) that separately models the factors contributing to the success or effectiveness of an action and the proficiency growth under success and failure. The paper shows how the general action model expresses prerequisites and changes in action effectiveness due to Vygotsky’s zone of proximal development.