本文创新性地构建了一种以学生为中心的高等数学“1 + 1”混合式教学模式,该模式在学时分配、内容层次划分、自学方案设计以及个性化课程资源建设等多个维度,均提出了一系列行之有效的解决策略。这些策略的实施,不仅显著增强了教学效果,还为地方本科院校在推进一流课程教学改革方面提供了参考与启示。This paper establishes a student-centered “1 + 1” blended learning model for higher mathematics, which proposes a series of effective strategies across multiple dimensions, including the allocation of class hours, layering content, self-learning programs, and the development of personalized course resources. The implementation of these strategies has not only significantly enhanced teaching effectiveness but also provided reference and inspiration for local undergraduate institutions in advancing reforms for first-class curriculum teaching.
以高等数学课程中的“微分方程的概念及可分离变量方程”内容为例,深入探究了以“学思用”数学思维进阶为主线的教学创新设计。对教学内容进行重构,融入思政元素,采用案例式教学,通过线上至线下、自学至互学、低阶至高阶、理论至应用的有机转化,有效提升学生高阶数学思维的培养。Taking “the concept of differential equations and separable variable equations” in advanced mathematics courses as an example, this study explores in depth the innovative design of teaching that focuses on the advancement of mathematical thinking through “learning, thinking, and application”. Refactoring the teaching content, incorporating ideological and political elements, adopting case-based teaching, and effectively enhancing the cultivation of students’ higher-order mathematical thinking through the organic transformation from online to offline, self-learning to mutual learning, low-level to high-level, and theory to application.
