人工智能赋能下应用型高校高等数学三维创新教学改革与实践

Three-Dimensional Innovation in Teaching Reform and Practice of Advanced Mathematics in Application-Oriented Universities Empowered by Artificial Intelligence

摘要: 针对应用型高校高等数学教学中存在的“重推演轻应用、重讲授轻探究、重结果轻过程”三类问题，文章提出并实施了“内容–方法–评价”三维创新教学改革，并明确了人工智能赋能的实现路径。在内容维度，压缩冗余证明与繁琐推演，重构贴近专业的应用例题与课堂导入，将复习课提升为知识整合与跨学科联通的进阶课堂；在方法维度，依托雨课堂等智慧教学平台构建“课前诊断–课中精讲–课后伴学”的混合式教学闭环，运用学情数据智能分析、智能组卷与变式题生成、自然语言处理答疑以及数学软件动态可视化等人工智能技术，实现精准诊断、智能供给与直观呈现，并结合每章两课时的头脑风暴研讨课激活学生的探究与合作；在评价维度，构建能力导向的多元测评体系，依托过程性数据形成“评价–反馈–改进”闭环。实践表明，改革使学生课堂参与度提高、概念理解更加深入、知识应用与迁移能力显著增强，可为同类应用型高校高等数学教学改革提供参考。

Abstract: To address the three problems existing in Advanced Mathematics teaching in application-oriented universities, namely “the overemphasis on deduction rather than application, on lecturing rather than inquiry, and on summative results rather than learning process”, this paper proposes and implements a three-dimensional innovation in teaching reform based on “content - method - assessment”, and clarifies the implementation path of artificial intelligence (AI) empowerment. In the content dimension, redundant proofs and tedious derivations are condensed, professional application cases and classroom introductions are reconstructed, and review classes are upgraded into advanced sessions for knowledge integration and interdisciplinary connection. In the method dimension, a blended teaching loop of “pre-class diagnosis - in-class intensive lecturing - after-class tutoring” is built on intelligent teaching platforms such as Rain Classroom; artificial intelligence technologies, including intelligent analysis of learning behavior data, intelligent test paper assembly, automatic generation of variant exercises, natural language processing-based question answering, and dynamic visualization with mathematical software, are applied to achieve precise diagnosis, intelligent resource supply, and intuitive presentation, with two class periods per chapter devoted to brainstorming seminars to stimulate students’ inquiry and collaboration. In the assessment dimension, a competency-oriented multi-dimensional evaluation system is constructed, and process data drives a closed loop of “evaluation - feedback - improvement”. Practice shows that the reform has increased students’ classroom participation, deepened their conceptual understanding, and significantly enhanced their ability to apply and transfer knowledge, which can serve as a reference for Advanced Mathematics teaching reform in similar application-oriented universities.