Control knowledge tracing: Modeling students' learning dynamics from a control-theory perspective

A student's learning system is a system that guides the student's knowledge acquisition process using available learning resources to produce certain learning outcomes that can be evaluated based on the scores of questions in an assessment. Such a learning system is analogous to a control system, which regulates the process of a plant through a controller in order to generate a desired response that can be inferred from sensor measurements. Inspired by this analogy, this study proposes to model the monitoring of students' knowledge acquisition process from a control-theory viewpoint, which is referred to as control knowledge tracing (CtrKT). The proposed CtrKT comprises a dynamic equation that characterizes the temporal variation of students' knowledge states in response to the effects of learning resources and an observation equation that maps their knowledge states to question scores. With this formulation, CtrKT enables tracking students' knowledge states, predicting their assessment performance, and teaching planning. The insights and accuracy of CtrKT in postulating the knowledge acquisition process are analyzed and validated using experimental data from psychology literature and two naturalistic datasets collected from a civil engineering undergraduate course. Results verify the feasibility of using CtrKT to estimate the overall assessment performance of the participants in the psychology experiments and the students in the naturalistic datasets. Lastly, this study explores the use of CtrKT for teaching scheduling and optimization, discusses its modeling issues, and compares it with other knowledge-tracing approaches.