新工科背景下人工智能赋能高等数学与工科专业融合教学实践研究

Research on Integrated Teaching Practice of Artificial Intelligence-Empowered Advanced Mathematics and Engineering Majors under the Background of Emerging Engineering Education

摘要: 新工科建设对工科人才数理应用与工程创新能力提出更高要求。针对传统高等数学教学存在理论与专业脱节、教学模式固化、教研壁垒突出、抽象知识教学手段单一等问题，本文构建跨学科教研协同 + 人工智能赋能的数专融合教学模式。通过建立高数与工科专业课教师联合教研机制，开发工程应用型教学案例；依托GeoGebra仿真、雨课堂智慧教学平台实现可视化教学与精准分层育人。以极限–导数模块的机械摆杆运动案例开展课堂实践，并探讨模式跨院校推广的现实路径。结果表明，该模式能够培养学生工程数学思维，提升数理建模求解能力，可为新工科背景下公共基础课改革提供参考。

Abstract: Emerging engineering education puts forward higher requirements for engineering talents’ mathematical application ability and engineering-innovation literacy. Aiming at the prominent problems in traditional Advanced Mathematics teaching, such as disconnection between theory and specialties, rigid teaching modes, disciplinary barriers between teaching-research groups, and insufficient visualization for abstract knowledge, this paper constructs an integrated teaching mode featured by interdisciplinary teaching-research collaboration and artificial intelligence empowerment. We establish a joint teaching-research mechanism for mathematics and engineering teachers, and develop engineering-oriented teaching cases. Supported by GeoGebra simulation and Rain-Class intelligent teaching platform, visual demonstration and personalized stratified teaching are realized. Taking the mechanical pendulum-rod motion case of limit and derivative as practical carrier, the teaching practice is carried out, and the practical paths for cross-university promotion of the mode are discussed. The practice shows that the proposed mode can cultivate students’ engineering mathematical thinking and improve their ability of mathematical modeling and problem-solving, which provides references for the reform of basic courses under emerging engineering education.