Modeling Student Learning: Binary or Continuous Skill?

Student learning is usually modeled by one of two main approaches: using binary skill, with Bayesian Knowledge Tracing being the standard model, or using continuous skill, with models based on logistic function (e.g., Performance Factor Analysis). We use simulated data to analyze relations between these two approaches in the basic setting of student learning of a single skill. The analysis shows that although different models often provide very similar predictions, they differ in the impact on student practice and in the meaningfulness of parameter values.