高等数学课程思政三阶递进教学模式的构建与实践

The Construction and Practice of the Three-Stage Progressive Teaching Model for Ideological and Political Education in Advanced Mathematics Courses

摘要: 课程思政是当代高等数学教学改革的重要方向，但实践中普遍存在思政元素与数学知识分离、教学实施碎片化、评价机制不完善等问题。本文提出案例导入→问题驱动→思政升华三阶递进教学模式，以定积分概念的教学为案例，系统阐述该模式在高等数学课程思政中的具体实施路径。该模式通过情境化案例激发学生的学习动机，通过教师引导学生探究问题驱动其思维发展，通过提升学生价值观实现育人目标，最终形成知识传授、能力培养与价值提升的有机统一。同时，结合教、学与评一致性的理念构建多维度评价体系，将思政目标转化为可观测、可评价的学习过程。实践表明，三阶递进教学模式能够有效打破思政机械融入高等数学课程的困境，为高等数学课程思政提供可推广的有效实践路径。

Abstract: Ideological and Political Education is an important direction for the current reform of higher mathematics teaching. However, in practice, there are common problems such as the separation of ideological elements and mathematical knowledge, fragmented teaching implementation, and imperfect evaluation mechanisms. This paper proposes a three-stage progressive teaching model of case introduction, problem-driven ideological education, and ideological elevation. Taking the teaching of the concept of definite integral as an example, this paper systematically elaborates on the specific implementation path of this model in the Ideological and Political Education of higher mathematics courses. This model stimulates students’ learning motivation through contextualized cases, promotes the development of students’ thinking through teacher guidance, realizes the educational goals by enhancing students’ values, and ultimately achieves the organic unity of knowledge transmission, ability cultivation, and value enhancement. At the same time, based on the concept of consistency in teaching, learning, and evaluation, a multi-dimensional evaluation system is constructed to transform ideological goals into observable and evaluable learning processes. Practice has shown that the three-stage progressive teaching model can effectively break the dilemma of mechanically integrating ideological education into higher mathematics courses, providing an effective and scalable practical path for Ideological and Political Education in higher mathematics courses.