提高大学生基于神经网络和多重回归模型的高等数学问题解决能力
1Peking University, Beijing, 100000, China.
Scientific reports
|November 29, 2025
概括
这项研究引入了一个新的二维系统来评估大学生在高级数学中的解决问题能力 (PSA),整合认知和行为因素. 这些发现突出了认知维度对PSA的重大影响,为智能教育系统提供了宝贵的见解.
科学领域:
- 教育心理学教育心理学
- 教育中的人工智能
- 认知科学 认知科学
背景情况:
- 目前对大学生高级数学问题解决能力 (PSA) 的评估面临局限性.
- 现有的框架往往无法全面整合认知和行为方面的方面.
研究的目的:
- 开发PSA的双维评估系统,包括认知和行为维度.
- 为PSA评估提出并验证MVO优化的一种混合CNN-BiLSTM-Reg模型.
- 研究综合认知行为模型的预测能力和可解释性.
主要方法:
- 建立了一个基于皮亚杰的认知理论和肖恩菲尔德的行为框架的二维评估系统.
- 开发了一种混合卷积神经网络-双向长期短期记忆回归 (CNN-BiLSTM-Reg) 模型.
- 使用多节优化器 (MVO) 优化了混合模型,并采用了回归引导的注意力机制.
主要成果:
- 综合认知行为模型实现了高预测准确性 (R2=0.95,RMSE=5.32).
- 认知维度对PSA (78.6%) 有显著的贡献,逻辑推理是关键因素 (β=0.35).
- 通过MVO优化,模型性能提高了13.7%,干预组的PSA改善率是对照组的3.3倍.
结论:
- 这项研究验证了整合认知和行为维度来评估PSA的有效性.
- 拟议的CNN-BiLSTM-Reg模型提供了可解释性和预测准确性之间的平衡.
- 这项研究为智能教育提供了具有预测和教学价值的技术框架.
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