Assessing cognitive growth in mathematics using multinomial logistic regression within Bloom’s taxonomy in higher education

Understanding how students transition through cognitive levels in mathematics remains central to curriculum design and quality learning assessment. The study examined whether domain competencies in algebra, functions, trigonometry, calculus, and probability jointly predict students’ transitions across Bloom’s taxonomy in engineering mathematics, to validate Bloom’s hierarchy and identify domain-specific levers for higher-order thinking. This study fits bias-reduced and L1-regularized multinomial logistic models to data from 488 students across four technical universities and assesses generalizability via nested 5 × 5 cross-validation, reporting accuracy, log loss, Brier score, and classwise AUC. An XGBoost multiclass classifier provides a convergent machine learning extension; Shapley additive explanations (SHAPs) quantify global feature importance and visualize the nonlinear dependence of predictors on predicted Bloom’s-level probabilities. Out-of-sample performance was stable across folds: application 57.7% ± 2.0, log loss 1.181 ± 0.068, Brier 0.594 ± 0.039; comprehension 52.7% ± 3.7, log loss 1.178 ± 0.048, Brier 0.601 ± 0.026; HOT 48.5% ± 5.0, log loss 1.203 ± 0.084, Brier 0.627 ± 0.031; and knowledge 42.7% ± 6.2, log loss 1.333 ± 0.084, Brier 0.674 ± 0.039. Discrimination was strongest at L1/L5 (AUC ≥ 0.85), with Probability and Algebra showing the highest permutation importance (ΔLogLoss 0.168 and 0.133; ΔBrier 0.061 and 0.053). To enhance interpretability, the study incorporated an XGBoost-based machine learning framework with Shapley additive explanations (SHAPs). The hybrid model attained 83% classification accuracy (log loss = 0.44; Brier = 0.24), confirming robust prediction of Bloom’s cognitive levels. SHAP analysis revealed falg (algebraic reasoning) as the dominant feature influencing level transitions, underscoring the hierarchical interaction among mathematical domains. Bloom’s hierarchy is empirically supported yet interdependent across domains. Probability and algebra are principal levers for advancing higher-order cognition. Universities should ensure Embedded Bloom’s-aligned analytics and probabilistic/algebraic scaffolds in course blueprints and item banks to track and accelerate transitions toward HOT.