多维叠加隐喻在积分概念教学中的构建与应用

Construction and Application of Multi-Dimensional Accumulation Metaphors in Integral Concept Teaching

摘要: 针对积分教学中维度跃升抽象、累次积分理解困难等问题，文章以概念隐喻理论为基础，构建了以“串珠缀线–梭织成面–叠纸为书”为主干的多维叠加隐喻体系，将定积分、二重积分、三重积分的核心概念映射到层层堆叠的生活经验之上。文章阐述了该体系的设计原则、映射结构与课堂实施方案，并结合辩证唯物主义认识论与刘徽“割圆术”进行了课程思政融合。初步教学观察表明，该隐喻体系有助于化解学生的认知障碍，强化概念性理解。

Abstract: To address the challenges of abstract dimensional leaps and iterated integrals in integral teaching, this paper constructs a multi-dimensional accumulation metaphor system centered on “beading threads - weaving fabric - stacking pages,” based on conceptual metaphor theory. This system maps the core concepts of definite, double, and triple integrals onto embodied experiences of layered accumulation. The paper elaborates on its design principles, mapping structure, and classroom implementation, while integrating dialectical materialist epistemology and Liu Hui’s “circle-cutting” method. Preliminary teaching observations indicate that this metaphor system may help reduce cognitive barriers and strengthen conceptual understanding.