数学分析课程三维教学模式的探索与实践

Exploration and Practice of a Three-Dimensional Teaching Model for Mathematical Analysis Course

摘要: 数学分析教学长期面临一项结构性难题：概念高度抽象、证明要求严密、计算步骤繁杂，三者相互交织，使学生在学习过程中承受较重的认知负担。传统的“定义–定理–证明–例题”教学流程以知识逻辑为主线组织课堂，对学生认知过程的关注相对有限。本文从学生认知规律出发，提出“概念扎根–证明外化–计算贯通”三维教学模式。三者围绕优化学生认知过程的目标协同运转，将教学改革的重心从内容选择转向认知过程的优化。本文呈现该模式的理论基础与实施框架，以期为数学分析教学改革提供参考。

Abstract: Mathematical analysis teaching has long faced a structural challenge: the interplay of highly abstract concepts, rigorous proof requirements, and complex computational procedures imposes a heavy cognitive burden on students. The traditional “definition-theorem-proof-example” teaching sequence, organized around the logic of knowledge transmission, pays limited attention to students’ cognitive processes. From the perspective of cognitive laws in learning, this paper proposes a three-dimensional teaching model of “Concept Rooting-Proof Externalization-Computation Integration”. These three dimensions operate in concert toward the goal of optimizing students’ cognitive processes, running through the three stages of pre-class, in-class, and post-class instruction, and shifting the focus of teaching reform from content selection to the optimization of cognitive processes. This paper presents the theoretical foundations and implementation framework of the model, aiming to provide a reference for the teaching reform of mathematical analysis courses.