Time on task is an important predictor for how much students learn. However, students must be focused on their learning for the time invested to be productive. Unfortunately, students do not always try their hardest to solve problems presented by computer tutors. This paper explores student disengagement and proposes an approach, engagement tracing, for detecting whether a student is engaged in answering questions. This model is based on item response theory, and uses as input the difficulty of the question, how long the student took to respond, and whether the response was correct. From these data, the model determines the probability a student was actively engaged in trying to answer the question. The model has a reliability of 0.95, and its estimate of student engagement correlates at 0.25 with student gains on external tests. We demonstrate that simultaneously modeling student proficiency in the domain enables us to better model student engagement. Our model is sensitive enough to detect variations in student engagement within a single tutoring session. The novel aspect of this work is that it requires only data normally collected by a computer tutor, and the affective model is statistically validated against student performance on an external measure.
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