“问题驱动–案例贯穿–模型迭代”模式在农林高校高等数学教学中的实践——以一阶线性微分方程为例

Practice of the “Problem-Driven, Case-Integrated, Model-Iterative” Model in Higher Mathematics Teaching at Agricultural and Forestry Universities—Taking First-Order Linear Differential Equations as an Example

摘要: 针对农林高校高等数学教学理论脱离实际、学生应用能力薄弱的问题，文章基于认知冲突理论，提出“问题驱动–案例贯穿–模型迭代”教学模式。以一阶线性微分方程为核心，构建从马尔萨斯模型到逻辑斯谛模型再到松毛虫种群防控的递进案例链，将解析求解与数值模拟有机融合，引导学生实现从常量思维到变量思维、从经验直觉到数据驱动、从解题者到决策者的三重思维跃迁。实践表明，该模式有效激发了学生的学习兴趣，提升了其解决农林实际问题的数学建模能力。

Abstract: Addressing the issues of theory being detached from practice and students’ weak application abilities in higher mathematics teaching at agricultural and forestry universities, this paper proposes a “Problem-Driven, Case-Integrated, Model-Iterative” teaching model based on cognitive conflict theory. Focusing on first-order linear differential equations, it constructs a progressive case chain from the Malthusian model to the Logistic model and then to the prevention and control of pine caterpillar populations. By organically integrating analytical solutions with numerical simulations, the model guides students to achieve a triple mindset shift: from constant thinking to variable thinking, from empirical intuition to data-driven approaches, and from problem-solvers to decision-makers. Practice has shown that this model effectively stimulates students’ learning interest and enhances their mathematical modeling ability to solve practical agricultural and forestry problems.