高中与大学数学教育衔接视角下的极限概念教学研究

Research on the Teaching of Limit Concepts from the Perspective of the Connection between High School and University Mathematics Education

摘要: 极限概念是数学分析的核心基石，关乎学生从高中直观思维向大学形式化思维的过渡。调查发现，高中教学在建立极限直观认知方面有效，但形式化定义与代数证明训练不足，造成大学阶段的认知断层。为此，本文提出三项改进策略：渐进渗透ε-δ思想，搭建直观与形式化桥梁；构建“自然语言–几何直观–代数证明”融合的教学框架；强化不等式与误差控制训练，提升逻辑严密性，助力学生跨越思维鸿沟。

Abstract: The concept of limits is a fundamental cornerstone of mathematical analysis, playing a crucial role in the transition from intuitive thinking in high school to formal reasoning at the university level. Research indicates that while high school education effectively establishes an intuitive understanding of limits, there is insufficient training in formal definitions and algebraic proofs, leading to a cognitive gap during the university phase. To address this issue, three improvement strategies are proposed: gradually integrating the ε-δ approach to build a bridge between intuition and formalism; developing a teaching framework that combines “natural language-geometric intuition-algebraic proof”; and enhancing training on inequalities and error control to improve logical rigor, thereby assisting students in overcoming cognitive barriers.