2025/11/06 by Julian D. Allagan, D S Singleton, Allagan, Julian D. +5
Computer Science · Decision Sciences · Social Sciences · #62H30 #62P25 #68T05 #97C70 #FOS: Computer and information sciences #Intelligent Tutoring Systems and Adaptive Learning #Machine Learning (cs.LG) #Psychometric Methodologies and Testing #Student Assessment and Feedback
paper · pdf · doi:10.48550/arxiv.2511.04667
openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28
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 ≥ 0.40) while 30% demonstrate poor discrimination (D < 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.