Shapes of Educational Data in an Online Calculus Course

This paper describes investigations in visualizing logpaths of students in an online calculus course held at Florida State University in 2014. The clickstreams making up the logpaths can be used to visualize student progress in the information space of a course as a graph. We consider the graded activities as nodes of the graph, while information extracted from the logpaths between the graded activities label the edges of the graph. We show that this graph is associated to a Markov Chain in which the states are the graded activities and the weight of the edge is proportional to the probability of that transition. When we visualize such a graph, it becomes apparent that most students follow the course sequentially, section after section. This model allows us to study how different groups of students employ the learning resources using sequence analysis on information buried in their clickstreams.