Improvement of college students’ higher mathematics problem solving ability based on neural network and multiple regression model

This study aims at the limitations of the evaluation of Problem Solving Ability (PSA) in college students' advanced mathematics problem-solving. It constructs a dual-dimensional evaluation system integrating cognitive dimensions (conceptual understanding, logical reasoning, etc.) and behavioral dimensions (time allocation, operation sequence, etc.) based on Piaget's cognitive theory and Schoenfeld's behavioral framework. Meanwhile, this study proposes a hybrid model of Convolutional Neural Network-Bidirectional Long Short-Term Memory-Regression (CNN-BiLSTM-Reg) optimized by Multi-Verse Optimizer (MVO). Through a regression-guided attention mechanism, the model converted multiple regression coefficients into neural network weights, achieving a balance between interpretability and prediction accuracy (R²=0.95, Root Mean Square Error (RMSE) = 5.32). The experimental results show that: The contribution rate of the cognitive dimension to PSA reaches 78.6% (β = 0.35 for logical reasoning). Ablation experiments verify that MVO optimization improves performance by 13.7%. The prediction error of the time dimension decreases from 6.85 at the beginning of the semester to 4.06 at the end of the semester. The improvement range of PSA in the intervention group is 3.3 times that in the control group. This study confirms the scientific nature of the integrated modeling of cognition and behavior, and is expected to provide a technical framework with both prediction function and teaching guidance value for intelligent education.