融合农业案例的函数连续性与间断点教学研究

A Study on Teaching Function Continuity and Discontinuity Points with Integrated Agricultural Cases

摘要: 高等数学是农林类高校本科阶段必修的公共基础课程，函数的连续性与间断点作为微积分学科的核心基础知识点，既是后续微分、积分、微分方程学习的必要前提，也是衔接数学理论与农业生产实践的重要桥梁。本文以函数连续性与间断点的教学内容为载体，立足农林专业人才培养目标，将农业相关案例与求真务实、持之以恒、辩证统一的思政素养深度融入课堂教学过程。通过挖掘连续性、间断点的数学内涵与农业生产规律、乡村振兴使命的内在关联，构建“数学知识 + 农业应用 + 思政育人”三位一体的教学模式。为客观检验该教学模式的育人实效，本文采用准实验研究设计，设置实验组与对照组，结合前后测量化数据、课堂观察、半结构化学生访谈开展混合研究。研究表明，该教学模式能够有效打破高等数学与农科专业之间的壁垒，帮助学生理解数学理论的农业应用价值，在夯实学生数理基础的同时，实现知识传授、能力培养与价值引领的协同育人目标。

Abstract: Higher Mathematics is a compulsory general-basic course for undergraduates in agriculture-related universities. As the core fundamental knowledge of calculus, the continuity and discontinuity points of functions serve not only as an essential prerequisite for the subsequent study of differentiation, integration and differential equations, but also as a vital bridge linking mathematical theories with agricultural production practice. Taking the teaching content of function continuity and discontinuity points as the carrier and based on the talent-training objectives of agriculture-forestry majors, this paper integrates agricultural cases together with ideological-political qualities of seeking truth from facts, perseverance and dialectical unity into classroom teaching. By exploring the internal correlations between the mathematical connotations of continuity and discontinuity points, agricultural production laws and the mission of rural revitalization, a trinity teaching mode of “mathematical knowledge + agricultural application + ideological-political education” is constructed. To objectively verify the educational effect of this teaching mode, a quasiexperimental research design is adopted in this paper. An experimental group and a control group are set up, and a mixed-method research is carried out combining pre-exist quantitative test data, classroom observation and semi-structured student interviews. The study shows that the proposed teaching mode can effectively break down the barriers between Higher Mathematics and agronomyrelated majors. It helps students understand the application value of mathematical theories in agriculture. While consolidating students mathematical foundation, it realizes the collaborative educational goal of knowledge imparting, ability cultivation and value guidance.