函数概念的演变及其对高中函数教学的启示

The Evolution of Function Concept and Some Implications for Classroom Teaching in Senior High Schools

函数是数学中最基本的概念，也是高中数学的核心内容，函数的思想方法贯穿高中数学课程的始终。根据历史发生原理，数学教育取向的数学史研究的主要目的之一就是获取相关知识点（概念、公式、定理）的教学启示。基于函数概念演变阶段与发展动力的分析，高中函数教学给我们的启示是：从丰富的现实背景及具体的函数入手抽象概括函数的本质；注重从不同角度认识函数概念；注重对运动、变化的体现与分析；从数学史料中精选函数教学材料。

Function is a basic concept in mathematics and also is the core content of mathematics for senior high schools, and its thought and method go through mathematics curriculum of senior high schools. It is one of the aims to obtain some implications for teaching relevant knowledge in studying history of mathematics based on the historical-genetic principle. By analyzing the phase as well as the impetus of the evolution of function concept, we get some suggestions from the teaching of function in senior high schools： abstracting intrinsic quality of function concept from abundant real backgrounds and some concrete functions; understanding function concept from different perspectives; paying attention to the presentation and analysis for movement and change; selecting teaching materials from the history of mathematics.