人教A版函数定义的三个引例的问题探析  

Discussion on the Three Quotations Related to the Definition of Function in the Textbook by People's Education Press (Edition A)

作　　者：赵思林[1] 王佩[1] 李秀萍[1] ZHAO Silin;WANG Pei;LI Xiuping(College of Mathematics and Information Science,Neijiang Normal University,Neijiang,Sichuan 641199,China)

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641199

出　　处：《内江师范学院学报》2018年第4期33-37,共5页Journal of Neijiang Normal University

基　　金：教育部"本科教学工程"四川省地方属高校本科专业综合改革试点项目(ZG0464);四川省"西部卓越中学数学教师协同培养计划"项目(ZY16001);内江师范学院2016年度校级学科建设特色培育项目(T160009;T160010;T160011)

摘　　要：对人教A版函数定义的三个引例的问题进行了分析.这三个引例的知识背景涉及斜抛运动、臭氧层、恩格尔系数等,这些知识学生不熟悉,会给学生理解造成困难.在引入函数概念时,容易混淆"数量"和"数"的概念,把数量集(其元素为数量)当成数集,把映射当成函数.在教学中,从映射到函数一般应展现抽象过程.提出了用数学运算引出函数定义的教学建议,指出了函数这种特殊对应关系的本质,即自变量在定义域内的每一个数都对应并且只对应一个函数值,用反例强化了对函数定义的理解.An analysis is given to the three quotations concerning the definition of function in the textbook published by People’s Education Press(Edition A).The three quotations involve background knowledge like projectile motion,ozone layer and Engel coefficient,etc.,the lack of sufficient knowledge of which would result in their difficulty in understanding.When introducing the concept of function,the students are apt to confuse the concept of“quantity”and“number”,to mistake quantity set(whose elements are quantities)for number set,or mistake a mapping for a function.In teaching,in general,from the mapping to the function,the change should be displayed as the process of abstraction.A teaching suggestion that mathematical operation be used as the introductory step for the learning of the functional definition is put forth.It points out the essence of the special correspondence relation of function-each value of the independent variable in the domain shall correspond to one and only one function value.And counter examples are quoted to strengthen the understanding of the function definition.

关 键 词：函数定义 映射 数量集 教学建议 

分 类 号：G633.6[文化科学—教育学]