基于OBE理念的微积分教学设计——以极限的$\epsilon -\delta$语言为例

Calculus Teaching Design Based on the OBE Concept—A Case Study of the $\epsilon -\delta$ Language of Limits

摘要: 成果导向教育强调以学生学习成果为中心组织教学活动。针对微积分教学中学生对极限的$\epsilon -\delta$ 语言理解困难等问题，本文以极限严格定义教学为例，尝试从OBE理念出发重构课堂设计：先提炼出不同极限过程的共同框架，再引导学生将该框架迁移至一元函数、左右极限、无穷远处极限以及多元函数极限等不同情境。教学设计的重点由定义记忆转向概念理解、逻辑表达与知识迁移，有助于提升学生对极限本质的把握和应用严格数学语言分析问题的能力。

Abstract: Outcome-Based Education emphasizes organizing teaching activities around students’ learning outcomes. Addressing the difficulties of students in understanding the $\epsilon -\delta$ language for limits in calculus teaching, this article takes the teaching of the strict definition of limits as an example and attempts to reconstruct classroom design from the perspective of OBE philosophy. Specifically, it first extracts the common framework underlying different limit processes, and then guides students to transfer this framework to various contexts, including limits of functions of one variable, one-sided limits, limits at infinity, and limits of multivariable functions. The focus of the teaching design shifts from memorizing definitions to conceptual understanding, logical expression, and knowledge transfer, which helps improve students’ understanding of the essence of limits and their ability to analyze problems using rigorous mathematical language.