一、引言“函数”是数学中最基木也是最重要的概念之一.它反映和刻划了客观物质世界中各种事物的“运动”过程及其相互依赖关系。它的形成和发展经历了漫长的历史过程,是从特殊到一般,从具体到抽象,一步一步地抽象概括得来的。由于函数概念比较抽象,长期以来,为便于教学,把它分为三个阶段,在初中阶段,采用对应关系描述性的函数定义;在高中阶段,则采取映射方式的函数定义;直到大学阶段才给出一般集合上的函数定义。整个过程,战线冗长,占据了大量的教学时间,而且学生对函数概念的认识相当模糊,知其然而不知其所以然,没有真正理解函数的概念。因此.很有必要对中学数学中函数的传统定义方式以及教村结构进行反思。能否另辟捷径,采取另一种方式来给函数下定义,使函数概念更精确、更简洁、更便于教学呢? I. INTRODUCTION “Function” is one of the most basic and most important concepts in mathematics. It reflects and sculpts the “movement” process and interdependence of various things in the objective material world. Its formation and development have gone through a long historical process. It has been abstractly summed up from specific to general, from concrete to abstract, step by step. Because the concept of the function is relatively abstract, for a long time, it has been divided into three stages to facilitate teaching. In the junior high school stage, the descriptive function definition of the corresponding relationship is adopted; in the high school stage, the function definition of the mapping mode is adopted; it is not until the university stage. Give the definition of a function on a generic set. Throughout the process, the battle lines were lengthy and occupied a lot of teaching time, and students’ knowledge of the concept of functions was rather obscure. However, they did not know why they did not understand the concept of functions. Therefore, it is necessary to reflect on the traditional way of defining the function of middle school mathematics and the structure of teaching villages. Can you give a shortcut and adopt another way to define the function so that the concept of the function is more precise, more concise and easier to teach?