Multi-Method Analysis of Mathematics Placement Assessments: Classical, Machine Learning, and Clustering Approaches

• URL: http://arxiv.org/abs/2511.04667v1
• Date: Thu, 06 Nov 2025 18:53:07 GMT
• Title: Multi-Method Analysis of Mathematics Placement Assessments: Classical, Machine Learning, and Clustering Approaches
• Authors: Julian D. Allagan, Dasia A. Singleton, Shanae N. Perry, Gabrielle C. Morgan, Essence A. Morgan,
• Abstract summary: This study evaluates a 40-item mathematics placement examination administered to 198 students.<n>It uses a multi-method framework combining Classical Test Theory, machine learning, and unsupervised clustering.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 ($D < 0.20$) 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.

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