The Teaching Reconstruction Of The Concept Of Function In Senior High School

The curriculum standards for general high school mathematics?2017 edition?highlights four main lines that run through the high school mathematics curriculum,namely,functions,geometry and algebra,statistics and probability,as well as mathematical modeling activities and mathematical inquiry activities that emphasize application.As one of the four main lines,this is unprecedented.The concept of function is the core content of function and also the core concept in high school mathematics curriculum.In particular,the Standard?2017 edition?added“the case 2 of the concept of function”in Appendix 2 to facilitate people's understanding of why high schools emphasize the correspondence between functions that are real Numbers.For a long time,high school function definition is one of the concepts that is difficult to teach and difficult to learn because of its high degree of abstraction,which is not easy to be understood by students and recognized by teachers and students.This paper starts from the current high school mathematics teaching materials,and finds that there is no clear definition of the word"Corresponding relations f"in the definition of the function in the current teaching materials,and few scholars have defined it.Moreover,due to different understandings of"Corresponding relations f",some people think that the corresponding relations between function y=x,x?{0,1}is the same as that between function y=x²⁰¹⁹,x?{0,1},while others think that the corresponding relations between the two functions is different.Then how to correctly understand the concept of function,especially the corresponding relations f,so as to avoid such teaching chaos caused by different understanding of"Corresponding relations f",this is the research problem of this paper.Based on the above problems,this paper mainly adopts the methods of literature,investigation and statistical analysis,and takes"high school function concept"as the object to carry out the research.Starting from the function definition,through to the sorting of literature and materials,analysis of scholars and textbook writers'understanding of"high school function definition,found no unified definition of nowadays high school function definition,also does not have the unification,the nature of function and function definition of the word"corresponding relationship"is easy to make the person produces ambiguity and function relation definition avoids easy to cause ambiguity of the relationship between"is completely consistent",and more to highlight the nature of function.Therefore,based on the existing problems of"the concept of function"in the current high school mathematics textbook,this paper explores the teaching reconstruction of the concept of function in high school from two perspectives.Secondly,based on the definition of"relationship",the concept of function is reconstructed.The findings:?1?the main problem with the concept of function in the current textbook of people's education A is that“function f:A?B”is confused with“correspondence f”,which leads to ambiguity of“two functions are equal”or“correspondence is completely consistent”in the definition of“the same function”.In order to distinguish the difference between “function f:A?B”and“correspondence f”,the following Suggestions are made:1)change the“correspondence”in“correspondence emphasizes the corresponding result,not the corresponding process”in the standard?2017 edition?to“function”;2)delete the statement of“correspondence is exactly the same”in the current textbook,and modify the definition of “two functions are equal”to“if the domain of two functions is the same,and the value of the function corresponding to the same independent variable is the same,then this is Two functions are equal”;3)for two functions with different analytic expressions,their corresponding f relations are not the same;4)“two functions are equal”is more appropriate than“the same function”.?2?In this paper,the necessity and feasibility of introducing function relation definition from high school,from two angles of theory and practice to expound function relationships define the necessity and feasibility of introducing high school teaching,and from the perspective of empirical description:there are 72.69%of the students are able to understand function relation defined,96.77%of the pre-service teachers are able to grasp the good function defined content,can teach good function is defined.Therefore,on the basis of not canceling the current function definition in high school,the content of function relation definition can be added appropriately in the teaching of high school.Based on the above contents,the following Suggestions are made:1)appropriately reduce the length of the current high school“concept of function”textbook,and add a section“definition of function relationship”;2)permeate the content of"definition of function relation",do not appear cartesian product,that is,increase the set notation of function;3)add“functional relationship definition”reading material.