发表机构
STFC Hartree Centre; University of Manchester; University of Cambridge（STFC哈特里中心; 曼彻斯特大学; 剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究对英国11.9万名学生的考试数据应用伯努利混合模型聚类，发现学生数学能力的主导因素是整体能力，而非离散技能，且该可解释模型准确率达78%，为教育领域提供了新基准。
AI 中文摘要
个性化学习系统通常假设数学能力由离散能力组合而成，这些能力需按顺序习得，且依赖于先掌握基础能力，学生也常表现出不同的优势。本研究通过对平台收集的英国13项国家级考试的119034名学生的大型数据集应用聚类方法，探究这些假设的有效性。将题目结果分类为通过或未通过后，我们使用伯努利混合模型（Bernoulli Mixture Model）搜索能指示离散技能组合的潜在群体。研究发现数据中存在的不同聚类数量很少，主导因素是学生的整体能力，所得聚类的概率分布间存在高度线性相关性，进一步支持了这一结论。我们表现最佳的模型准确率达78%，与文献中更复杂的模型相比具有竞争力，同时更具可解释性。将该模型的性能与逻辑回归基线及k近邻（k-nearest neighbours）对比，发现使用每个题目的表现作为特征时，性能有小幅提升。这表明，虽然整体能力水平是预测表现的主导因素，但通过适配学生的确切优势，可实现小幅的进一步个性化改进，不过学生在不同科目间似乎未发展出显著不同的能力。本研究为机器学习在教育领域提供了国家级规模的测试，并为该领域提供了新的基准，展示了可解释模型如何达到具有竞争力的性能。
英文摘要
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
