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函数概念是近、现代数学的基石,数学中的许多概念或由函数派生,或由函数统率,或可归之为函数观点研究.函数也是高中数学教学的主线,函数概念更是高中生感到最难学的数学概念之一.高中阶段把函数看作是刻画变量与变量之间依赖关系的模型;是联结两类对象的桥梁——对应关系;还是描述客观世界变化规律的重要数学模型.运用下面一些数学策略,可以帮助学生更全面地认识函数.1.变量及其联系的策略函数主要是研究变量之间相互联系、相互依赖、相互制约、相互转化的关系,函数概念包含两个本质属性——变量和对应法则(“单值性”和“任意性”),及相关属性(如集合、定义域、值域等),它研究变量及
The concept of function is the cornerstone of modern mathematics, many concepts in mathematics are derived from functions, or the function of the rate, or can be attributed to function point of view. Function is also the main line of high school mathematics teaching, One of the mathematical concepts that is difficult to learn.Secondary school considers the function as a model of describing the dependence between variables and variables.It is a bridge-correspondence relationship that connects two types of objects.It is also an important mathematical model to describe the changing law of the objective world. The following mathematical strategies can help students to understand the function more comprehensively.1.Strategies of variables and their relations Mainly to study the relationship among variables, interdependence, mutual restraint and mutual transformation, the concept of function contains two essential attributes - Variables and Corresponding Laws ( “Unambiguous ” and “Arbitrary ”), and related attributes (such as collections, definitions, ranges, etc.)