Learning from errors: co-clustering students’ answer types in a digital learning environment to verify task design on linear equations

This study is concerned with establishing a means to generate better methods to analyse and learn about task design for digital learning environments. Specifically, we utilise data consisting of over 2 million unique answers from a popular Danish digital learning environment, matematikfessor.dk, to solve 892 unique tasks dealing with linear equations. Utilising the Multinomial Infinite Relational Model (MIRM), which can account for extensive didactical coding of the five most popular answers to each of the 892 tasks, we successfully co-clustered students and tasks into groups for further analysis. The results showed that the analysis of these clusters of tasks can provide access to valuable information on the difficulties students in four respective groups face and what kind of specific tasks and knowledge pertinent to what types of tasks actually affect students’ problems or difficulties anticipated by the task designer.