Modelling the Way: Using Action Sequence Archetypes to Differentiate Learning Pathways from Learning Outcomes

During the semester break, 36 second-grade students accessed a set of resources and completed a series of online math activities focused on the application of the model method for arithmetic in two contexts 1) addition/subtraction and 2) multiplication/division. The learning environment first modeled and then supported the use of a scripted series of steps for solving mathematical word problems. As students completed the activities, the learning environment captured their event-related data. We then used a combination of Affinity Propagation, an automated form of clustering, and sequential pattern mining to convert the activity logs into interpretable activity sequences. Analysis of the activity sequences identified distinct patterns of behavior that strongly predicted which students would transit from the familiar addition/subtraction word problem activity to the unfamiliar multiplication/division word problem activity. Students who showed the greatest and least compliance with the script were the least likely to attempt the multiplication/division activity. Students who showed more of a schematic problem solving process were more likely to continue to the multiplication/division activity.