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

arXiv: https://arxiv.org/abs/2511.04667 · HTML: https://mlsanity.com/paper/2511.04667/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 55 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Educational data mining and learning analytics: An updated survey](https://mlsanity.com/paper/2402.07956/) (2024)

## Abstract (arXiv)

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.