Flow with an intelligent tutor: A latent variable modeling approach to tracking flow during artificial tutoring

Increasing use of intelligent tutoring systems in education calls for analytic methods that can unravel students' learning behaviors. In this study, we explore a latent variable modeling approach for tracking learning flow during computer-interactive artificial tutoring. The study considers three models that give discrete profiles of a latent process: the (i) latent class model, (ii) latent transition model, and (iii) hidden Markov model. We illustrate application of each model using example log data from Cognitive Tutor Algebra I and suggest analytic procedures of drawing learning flow. Through experimental application, we show that the models can reveal substantive information about students' learning behaviors and have potential utility for describing the learning flow. The models differed in the assumptions and data constraints but yielded consistent findings on the flow states and interaction modalities. Based on our experiential analyses, we discuss strengths and limitations of the models and illuminate areas of future development.