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In this paper, we investigate the correspondence between student affect and behavioural engagement in a web-based tutoring platform throughout the school year and learning outcomes at the end of the year on a high-stakes mathematics exam in a manner that is both longitudinal and fine-grained. Affect and behaviour detectors are used to estimate student affective states and behaviour based on post-hoc analysis of tutor log-data. For every student action in the tutor, the detectors give us an estimated probability that the student is in a state of boredom, engaged concentration, confusion, or frustration, and estimates of the probability that the student is exhibiting off-task or gaming behaviours. We used data from the ASSISTments math tutoring system and found that boredom during problem solving is negatively correlated with performance, as expected; however, boredom is positively correlated with performance when exhibited during scaffolded tutoring. A similar pattern is unexpectedly seen for confusion. Engaged concentration and, surprisingly, frustration are both associated with positive learning outcomes. In a second analysis, we build a unified model that predicts student standardized examination scores from a combination of student affect, disengaged behaviour, and performance within the learning system. This model achieves high overall correlation to standardized exam score, showing that these types of features can effectively infer longer-term learning outcomes.
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