阶梯式问题链驱动下课堂教学与实践——以罗尔中值定理为例

Scaffolded Question-Chain-Led Pedagogical Practice—A Case of Rolle’s Theorem

摘要: 针对罗尔中值定理传统教学重结论识记、轻思维建构的突出问题，本文以数学核心素养培育为导向，构建以几何直观为载体、阶梯式问题链为主线的探究式教学模式，遵循“图形观测–规律猜想–反例证伪–条件推演–逻辑证明–迁移应用”认知逻辑，设计层级递进的系列设问，引导学生自主完成定理内涵与证明体系建构。最后选取两组基础均衡的平行教学班开展对照实验，测试数据显示：实验班在定理概念、规范证明、综合应用题型平均分较对照班分别提升12.7分、14.2分、11.5分，课堂主动探究参与率提升23.6%。实践表明，该模式可破解微分中值定理抽象难懂的教学痛点，为微积分定理教学提供可复制的实施范式。

Abstract: Traditional instruction of Rolle’s Theorem tends to prioritize rote memorization of conclusions over the construction of students’ logical thinking. Oriented toward developing core mathematical competencies, this paper constructs an inquiry-based teaching framework grounded in geometric intuition and scaffolded question-chains. Following the cognitive sequence of graphical observation, hypothesis formulation, falsification with counter-examples, condition reasoning, logical proof and transfer application, hierarchical guiding questions enable students to independently comprehend the theorem and build its proof framework. A controlled teaching experiment was carried out on two parallel classes with comparable prior academic performance. Test outcomes demonstrate that the experimental class achieved score improvements of 12.7, 14.2 and 11.5 points respectively in theorem-concept questions, formal proof tasks and comprehensive-application exercises. The rate of active in-class inquiry participation increased by 23.6%. The results suggest that this approach alleviates teaching difficulties caused by the abstractness of differential mean-value theorems and offers a replicable practical model for calculus theorem instruction.