“案例驱动”的《常微分方程》课程教学创新与实践

Innovation and Practice in Teaching the Course of “Ordinary Differential Equations” Driven by Cases

摘要: 本文以《常微分方程》课程为对象，针对其教学中长期存在的理论抽象、应用脱节、模式单一等核心问题，提出了“案例驱动”的教学创新模式。通过重构教学内容、实施“三阶融合”教学策略、构建智能教学环境、改革评价体系等系统性举措，实现了从“知识传授”到“能力与思维培养”的教学范式转型。实践表明，该模式显著提升了学生的学业成绩、建模能力与创新素养，同时促进了教师教学科研能力的双向发展，形成了可复制、可推广的课程改革经验，对推动数学类核心课程的数字化转型与跨学科融合具有重要的借鉴意义。

Abstract: This paper focuses on the course “Ordinary Differential Equations” and proposes a “case-driven” teaching innovation model to address long-standing core issues such as abstract theory, disconnection from practical applications, and monotonous teaching patterns. Through systematic measures including restructuring teaching content, implementing a “three-stage integration” teaching strategy, building an intelligent teaching environment, and reforming the evaluation system, the model achieves a paradigm shift from “knowledge transmission” to “ability and thinking cultivation.” Practice demonstrates that this model significantly enhances students’ academic performance, modeling skills, and innovative literacy while fostering the bidirectional development of teachers’ teaching and research capabilities. It forms replicable and scalable curriculum reform experience, offering important insights for promoting the digital transformation and interdisciplinary integration of core mathematics courses.