Archetypes or ability? Clustering for modelling student mathematical competence

תקציר מקורי באנגליתarXiv:2607.26063v1 Announce Type: cross Abstract: Personalised learning systems often assume that mathematical ability is combined of discrete abilities, acquired sequentially and dependent upon first acquiring foundational abilities, and students often report different strengths. In this work, we explore the validity of these assumptions by applying clustering methods to a large dataset of 119,034 students, spanning 13 national-level exams sat in the United Kingdom and collected by the platform. Classifying question results as pass or fail, we use a Bernoulli Mixture Model to search for latent populations which would be indicative of discrete skill-sets. We find that few distinct clusters are present in the data and that the dominant factor is overall student ability, which is further sup