{"ID":2845484,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.04667","arxiv_id":"2511.04667","title":"Multi-Method Analysis of Mathematics Placement Assessments: Classical, Machine Learning, and Clustering Approaches","abstract":"This study evaluates a 40-item mathematics placement examination administered to 198 students using a multi-method framework combining Classical Test Theory, machine learning, and unsupervised clustering. Classical Test Theory analysis reveals that 55\\% of items achieve excellent discrimination ($D \\geq 0.40$) while 30\\% demonstrate poor discrimination ($D \u003c 0.20$) requiring replacement. Question 6 (Graph Interpretation) emerges as the examination's most powerful discriminator, achieving perfect discrimination ($D = 1.000$), highest ANOVA F-statistic ($F = 4609.1$), and maximum Random Forest feature importance (0.206), accounting for 20.6\\% of predictive power. Machine learning algorithms demonstrate exceptional performance, with Random Forest and Gradient Boosting achieving 97.5\\% and 96.0\\% cross-validation accuracy. K-means clustering identifies a natural binary competency structure with a boundary at 42.5\\%, diverging from the institutional threshold of 55\\% and suggesting potential overclassification into remedial categories. The two-cluster solution exhibits exceptional stability (bootstrap ARI = 0.855) with perfect lower-cluster purity. Convergent evidence across methods supports specific refinements: replace poorly discriminating items, implement a two-stage assessment, and integrate Random Forest predictions with transparency mechanisms. These findings demonstrate that multi-method integration provides a robust empirical foundation for evidence-based mathematics placement optimization.","short_abstract":"This study evaluates a 40-item mathematics placement examination administered to 198 students using a multi-method framework combining Classical Test Theory, machine learning, and unsupervised clustering. Classical Test Theory analysis reveals that 55\\% of items achieve excellent discrimination ($D \\geq 0.40$) while 30...","url_abs":"https://arxiv.org/abs/2511.04667","url_pdf":"https://arxiv.org/pdf/2511.04667v1","authors":"[\"Julian D. Allagan\",\"Dasia A. Singleton\",\"Shanae N. Perry\",\"Gabrielle C. Morgan\",\"Essence A. Morgan\"]","published":"2025-11-06T18:53:07Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}