Improvement of college students' higher mathematics problem solving ability based on neural network and multiple...

Area of Science:

• Educational Psychology
• Artificial Intelligence in Education
• Cognitive Science

Background:

• Current evaluations of college students' advanced mathematics problem-solving ability (PSA) face limitations.
• Existing frameworks often fail to integrate cognitive and behavioral aspects comprehensively.

Purpose of the Study:

• To develop a dual-dimensional evaluation system for PSA, incorporating cognitive and behavioral dimensions.
• To propose and validate a hybrid CNN-BiLSTM-Reg model optimized by MVO for PSA assessment.
• To investigate the predictive power and interpretability of the integrated cognitive-behavioral model.

Main Methods:

• Constructed a dual-dimensional evaluation system based on Piaget's cognitive theory and Schoenfeld's behavioral framework.
• Developed a hybrid Convolutional Neural Network-Bidirectional Long Short-Term Memory-Regression (CNN-BiLSTM-Reg) model.
• Optimized the hybrid model using the Multi-Verse Optimizer (MVO) and employed a regression-guided attention mechanism.

Main Results:

• The integrated cognitive-behavioral model achieved high prediction accuracy (R²=0.95, RMSE=5.32).
• Cognitive dimensions significantly contributed to PSA (78.6%), with logical reasoning being a key factor (β=0.35).
• MVO optimization enhanced model performance by 13.7%, and the intervention group showed a 3.3 times greater improvement in PSA compared to the control group.

Conclusions:

• The study validates the effectiveness of integrating cognitive and behavioral dimensions for evaluating PSA.
• The proposed CNN-BiLSTM-Reg model offers a balance between interpretability and prediction accuracy.
• This research provides a technical framework with predictive and pedagogical value for intelligent education.