Archetypes or ability? Clustering for modelling student mathematical competence

Synthesis: On 119,034 students across 13 UK national exams, Bernoulli Mixture Models found few distinct skill clusters — overall ability dominates. A simple explainable model achieved 78% accuracy, competitive with complex approaches. Small personalization gains are possible by accounting for individual question-level strengths, but students don't develop strongly divergent ability profiles across topics.

Relevance to AI in Education: This paper contributes to the understanding of Automated Assessment, Personalized Learning, and Student Experience. The findings have implications for Adaptive Learning systems, Formative Assessment design, and the broader Edtech Platform landscape. Future work should explore how these results generalize across STEM Education and Higher Education contexts.

This research connects to the growing body of work on AI Literacy and Teaching, highlighting both the promise and limitations of AI tools in educational settings.

What this means for practice

• Students. Aim at your overall mathematics score rather than hunting for a niche topic strength: across the 119,034 students, overall ability dominated every model's predictions.
• Students. Use question-level mock-exam feedback to find isolated weak topics, since the clusters that did differ in shape point to small, targeted personalization gains.
• Students. Expect less reliable predictions in the middle of the ability range, where every model had its highest log loss and topic-level feedback is least trustworthy.
• Students. Still treat the pass grade as the working target: a logistic regression over all questions reached 78% accuracy, competitive with more complex approaches.

Limitations

• The data are 13 UK national mock exams sat by 119,034 students, uploaded question by question by teachers to one platform; exams are chosen locally, so different students sit different papers.
• No demographic information was provided, so the authors could not quantify bias by gender, ethnicity, or socioeconomic status and instead examined performance across ability levels only.
• Coverage is secondary-school mathematics mock papers, so nothing here establishes that the single-ability finding holds in higher education or other subjects.
• Clusters were fitted per exam with a Bernoulli Mixture Model and few departed in shape from the overall score distribution, so the "archetypes" are weakly identified rather than clean profiles.

Citation

Benjamin Mawdsley, Tom Quilter, Richard Turner, Sarah Jackson, Paul Edwards (2026). Archetypes or ability? Clustering for modelling student mathematical competence. arXiv preprint.