标题： 多方法分析数学分班评估：经典方法、机器学习和聚类方法 显示英文标题

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

摘要： 这项研究使用多方法框架结合经典测验理论、机器学习和无监督聚类，评估了对198名学生进行的40题数学分班考试。 经典测验理论分析显示，55%的题目达到优秀区分度（$D \geq 0.40$），而30%的题目表现出较差的区分度（$D < 0.20$），需要替换。 第6题（图表解读）成为考试中最有效的区分题，达到完美区分度（$D = 1.000$）、最高方差分析F统计量（$F = 4609.1$）和最大随机森林特征重要性（0.206），占预测力的20.6%。 机器学习算法表现出卓越的性能，随机森林和梯度提升分别达到97.5%和96.0%的交叉验证准确率。 K均值聚类识别出一个自然的二元能力结构，边界为42.5%，与机构设定的55%阈值不同，表明可能存在过度归入补救类别的现象。 两簇解决方案表现出极高的稳定性（引导程序ARI = 0.855），下簇纯度完美。 各方法的汇聚证据支持具体的改进措施：替换区分度较差的题目，实施两阶段评估，并将随机森林预测与透明机制结合。 这些发现表明，多方法整合为基于证据的数学分班优化提供了坚实的实证基础。 显示英文摘要

摘要： 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.