Measuring growth in students' proficiency in MOOCs: Two component dynamic extensions for the Rasch model.

Massive open online courses (MOOCs) are increasingly popular among students of various ages and at universities around the world. The main aim of a MOOC is growth in students' proficiency. That is why students, professors, and universities are interested in the accurate measurement of growth. Traditional psychometric approaches based on item response theory (IRT) assume that a student's proficiency is constant over time, and therefore are not well suited for measuring growth. In this study we sought to go beyond this assumption, by (a) proposing to measure two components of growth in proficiency in MOOCs; (b) applying this idea in two dynamic extensions of the most common IRT model, the Rasch model; (c) illustrating these extensions through analyses of logged data from three MOOCs; and (d) checking the quality of the extensions using a cross-validation procedure. We found that proficiency grows both across whole courses and within learning objectives. In addition, our dynamic extensions fit the data better than does the original Rasch model, and both extensions performed well, with an average accuracy of .763 in predicting students' responses from real MOOCs.