韦伯–费希纳定律在初中数学教学难度梯度设计中的应用研究

Study on Application of Weber-Fechner Law in the Design of Teaching Difficulty Gradient in Junior High School Mathematics

摘要: 双减背景下，教学难度梯度设计是精准教学的核心，传统经验范式缺乏量化依据。本研究引入韦伯–费希纳定律，构建“教学刺激–认知感知–学习效度”三维模型，假设教学难度与学生感知强度呈对数线性关系。基于福建省32,945名九年级学生监测数据，采用多层线性模型验证了量化关联，估算初中数学学科感知系数。学校资源配置存在显著调节效应，城、镇、乡村学校最优年度难度增幅差异明显。所构建的“三维四阶”梯度框架经实证检验，能提升教学效果、缩小城乡学业差距、缓解学习焦虑，为数据驱动精准教学提供量化范式与实践参考。

Abstract: Against the background of the Double Reduction policy, the design of teaching difficulty gradient lies at the core of precision teaching, while the traditional empirical paradigm lacks quantitative basis. This study introduces the Weber-Fechner Law to construct a three-dimensional model of “teaching stimulus - cognitive perception - learning validity”, and hypothesizes a logarithmic linear relationship between teaching difficulty and students’ perceptual intensity. Based on the educational monitoring data of 32,945 ninth-grade students in Fujian Province, the hierarchical linear model is adopted to verify the quantitative correlation and estimate the perceptual coefficient of junior high school mathematics. School resource allocation presents a significant moderating effect, with distinct optimal annual growth rates of teaching difficulty among urban, town and rural schools. Empirical tests confirm that the constructed “three-dimensional and four-stage” gradient framework can improve teaching effectiveness, narrow the urban-rural academic gap and alleviate learning anxiety, providing a quantitative paradigm and practical reference for data-driven precision teaching.