教评融合的双阶建模教学框架建构与实践——旨在缓解中学数学建模教学的“过程断层”

Construction and Practice of a Two-Stage Modeling Instructional Framework Integrating Teaching and Evaluation—Addressing the “Process Gap” in Secondary School Mathematical Modeling Instruction

摘要: 基于弗赖登塔尔数学化理论，本研究构建“教评融合的双阶建模教学框架”，通过双阶教学与双轨评价的同步实施实现教评融合。以人教A版《三角函数》为载体，设计摩天轮、二十四节气日影变化两个案例，验证框架实施路径。相较于传统建模教学将建模窄化为应用题训练的不足，本框架在新知阶段设置建模锚点以激活概念需求，章节阶段构建建模单元以强化决策能力；双轨评价创新开发概念需求发生与建模决策能力两套量化评估体系，将内隐思维过程转化为可观测、可诊断的行为指标。该框架并非对现有教学的零散修补，而是针对“过程断层”这一核心缺陷的一种系统性的教学路径，可为中学数学建模教学改革与实践提供参考。

Abstract: Based on Freudenthal’s mathematization theory, this study constructs a two-stage mathematical modeling teaching framework with integrated teaching and evaluation. The integration of teaching and evaluation is realized through the synchronous implementation of two-stage teaching and dual-track evaluation. Taking the Trigonometry volume of People’s Education Press Version A as the carrier, two teaching cases regarding the Ferris wheel and the solar shadow variation of the Twenty-four Solar Terms are designed to verify the implementation path of the framework. Conventional modeling teaching tends to simplify mathematical modeling into applied problem training, while the proposed framework sets modeling anchor points in the new knowledge learning stage to stimulate conceptual demand, and builds modeling units at the chapter level to enhance students’ modeling decision-making competence. The dual-track evaluation innovatively develops two quantitative evaluation systems for the generation of conceptual demand and mathematical modeling decision-making ability, converting implicit thinking processes into observable and diagnosable behavioral indicators. Rather than a fragmented revision of existing teaching practices, this framework provides a systematic teaching approach targeting the core problem of “process discontinuity” in middle school mathematical modeling teaching, which can provide a reference for the reform and practical implementation of middle school mathematics modeling instruction.