Exploring Online Learning Data Using Fractal Dimensions

Data collected from online learning and tutoring systems for individual students showed strong autocorrelation or dependence because of content connection, knowledge‐based dependency, or persistence of learning behavior. When the response data show little dependence or negative autocorrelations for individual students, it is suspected that students are randomly guessing the answers or that they are inconsistent in learning behavior. In addition, the global and local rates of correct responses may reflect students' proficiency in the learning process. This study shows that the dependence of online data may be characterized by the fractal dimension as a summary statistic locally and globally. The rate of correct responses and the global and local fractal dimensions of individual students' responses may indicate their learning behavior in short and long learning windows. The results may shed light on when individual students are experiencing difficulties in the learning process.