The widespread adoption of online courses opens opportunities for the analysis of learner behaviour and for the optimisation of web-based material adapted to observed usage. Here we introduce a mathematical framework for the analysis of time series collected from online engagement of learners, which allows the identification of clusters of learners with similar online behaviour directly from the data, i.e., the groups of learners are not pre-determined subjectively but emerge algorithmically from the analysis and the data.The method uses a dynamic time warping kernel to create a pairwise similarity between time series of learner actions, and combines it with an unsupervised multiscale graph clustering algorithm to cluster groups of learners with similar patterns of behaviour. We showcase our approach on online engagement data of adult learners taking six web-based courses as part of a post-graduate degree at Imperial Business School. Our analysis identifies clusters of learners with statistically distinct patterns of engagement, ranging from distributed to massed learning, with different levels of adherence to pre-planned course structure and/or task completion, and also revealing outlier learners with highly sporadic behaviour. A posteriori comparison with performance showed that, although the majority of low-performing learners are part of in the massed learning cluster, the high performing learners are distributed across clusters with different traits of online engagement. We also show that our methodology is able to identify low performing learners more accurately than common classification methods based on raw statistics extracted from the data.
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