高中生函数建模中“选模困难”的成因分析与教学突破——以“函数模型选择”教学为例

Analysis of the Causes and Teaching Breakthrough of “Model Selection Difficulty” in High School Function Modeling—Taking the Teaching of “Function Model Selection” as an Example

摘要: 当前高中函数建模教学中，学生普遍存在“选模困难”——面对现实问题时能够逐一计算函数值，却不知如何选择适配的函数模型。本文从函数认知发展的层次论视角出发，分析“选模困难”的认知成因，指出传统教学停留在函数认知的“操作层”与“过程层”，未能帮助学生达到建模所需的“对象层”认知。基于此，提出以“函数性质对比”为核心的建模教学策略，并以“共享单车用户增长趋势分析”为案例，完整呈现教学设计与实施过程，为一线的函数建模教学提供可复制的实践参考。

Abstract: In current high school function modeling teaching, students commonly face “model selection difficulty”—they can compute function values individually when facing real-world problems, but cannot determine which function model to apply. This paper analyzes the cognitive causes of “model selection difficulty” from the perspective of function cognition development hierarchy theory, pointing out that traditional teaching remains at the “operational level” and “process level” of function cognition, failing to help students reach the “object level” cognition required for modeling. Based on this, a modeling teaching strategy centered on “function property comparison” is proposed, and a complete teaching design and implementation process is presented using the case of “shared bicycle user growth trend analysis”, providing replicable practical reference for frontline function modeling teaching.