# Archetypes or ability? Clustering for modelling student mathematical competence

arXiv: https://arxiv.org/abs/2607.26063 · HTML: https://mlsanity.com/paper/2607.26063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [Instructions and Guide for Diagnostic Questions: The NeurIPS 2020 Education Challenge](https://mlsanity.com/paper/2007.12061/) (2020)
- [BOBCAT: Bilevel Optimization-Based Computerized Adaptive Testing](https://mlsanity.com/paper/2108.07386/) (2021)
- [Improving prediction of students' performance in intelligent tutoring systems using attribute selection and ensembles of different multimodal data sources](https://mlsanity.com/paper/2403.07194/) (2024)
- [NeurIPS Competition Instructions and Guide: Causal Insights for Learning Paths in Education](https://mlsanity.com/paper/2208.12610/) (2022)
- [A Conceptual Model for End-to-End Causal Discovery in Knowledge Tracing](https://mlsanity.com/paper/2305.16165/) (2023)
- [Accurate Predictions in Education with Discrete Variational Inference](https://mlsanity.com/paper/2509.23484/) (2025)

## Abstract (arXiv)

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 supported by the high degree of linear correlation between the probability distributions of the resulting clusters. Our best performing model achieves an accuracy of 78 percent, competitive with more complicated models in the literature whilst being more explainable. Comparing this models performance with logistic regression baselines and with k-nearest neighbours, we find a small improvement when using performance on each individual question as features. This suggests that whilst overall ability level is the dominant factor for predicting performance, small further personalisation improvements can be made by tailoring to a students exact strengths, but that students do not appear to develop strongly differing ability across topics. Our work offers a national scale test of machine learning in education and offers a new benchmark for the field, demonstrating how explainable models can reach competitive performance