Multi-Method Analysis of Mathematics Placement Assessments: Classical, Machine Learning, and Clustering Approaches
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917065877618688 |
|---|---|
| author | Allagan, Julian D. Singleton, Dasia A. Perry, Shanae N. Morgan, Gabrielle C. Morgan, Essence A. |
| author_facet | Allagan, Julian D. Singleton, Dasia A. Perry, Shanae N. Morgan, Gabrielle C. Morgan, Essence A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-Method Analysis of Mathematics Placement Assessments: Classical, Machine Learning, and Clustering Approaches Allagan, Julian D. Singleton, Dasia A. Perry, Shanae N. Morgan, Gabrielle C. Morgan, Essence A. Machine Learning 97C70, 62P25, 62H30, 68T05 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. |
| title | Multi-Method Analysis of Mathematics Placement Assessments: Classical, Machine Learning, and Clustering Approaches |
| topic | Machine Learning 97C70, 62P25, 62H30, 68T05 |
| url | https://arxiv.org/abs/2511.04667 |