初中一次函数概念教学策略

Teaching Strategy of the Concept of Linear Function in Junior High School

摘要: 一次函数是初中数学函数体系的入门内容，是学生实现从“常量数学”到“变量数学”思维跨越的关键载体，其概念理解直接影响后续反比例函数、二次函数等知识的学习。本文基于初中生具象思维为主的认知特点，结合变异理论/HPM数学史与数学教育等数学教育理论，从认知障碍的理论溯源出发，结合课堂教学实践，系统梳理一次函数概念教学的核心策略，为提升初中数学函数教学质量提供实践参考。

Abstract: Linear functions, as the foundational component of junior high school mathematics, serve as a pivotal bridge for students to transition from “constant mathematics” to “variable mathematics” thinking. Their conceptual mastery directly impacts subsequent learning of inverse proportion functions, quadratic functions, and related concepts. This study, grounded in the concrete thinking characteristics of junior high students and incorporating theories such as variation theory, HPM (History of Mathematics) in mathematics education, and cognitive impairment theory, systematically examines core teaching strategies for linear functions. By tracing the theoretical origins of cognitive barriers and integrating classroom teaching practices, this research provides actionable insights to enhance the quality of function instruction in junior high mathematics education.