Research On The Teaching Of Functional Concept Variants In High School Based On The APOS Theory

Function is a very important module content in the high school math curriculum.It runs through the entire high school math curriculum.If students can master and understand the concept of function it has a great impact on students' careers in high school.In feedback from actual teaching,we found that students generally feel that the concept of function is abstract and complex,and it is difficult to understand and accurately grasp its essence and connotation.Therefore,functional content has become a difficult point for high school students to learn,and it is also a key point in teacher teaching research.In recent years there have been continuous teaching and research results on the functional concepts of the baccalaureate,among which APOS theory and variant teaching are very good representative theories.The APOS theory aims to guide how to build concepts in the teaching or learning process,and to provide a series of powerful theoretical supports for teaching in the teachers' classroom;Variable teaching is a high-quality teaching experience accumulated in a long teaching career,which guides teachers Resolve the problem in a flexible way and change the conditions or conclusions of the problem change the non-essential characteristics of the problem,intelligently helping students students to master its essential attributes.These theories are basically self-centered.This article is based on the APOS theory development process.This process organizes the teaching of functional concepts vertically and adds variable teaching at each stage of APOS theory to expand the depth of teaching horizontally to better integrate the advantages of the two theories.Guiding classroom teaching of functional concepts in high school.This article first collects and finds the literature to classify APOS theory concepts and variant teaching and their respective domestic and foreign research results.At the same time,it summarizes the research results of some scholars on the concept of secondary school teaching function in recent years.Then,through the explanation of the "duality" of the mathematical concept,the feasibility of integrating APOS theory and variant teaching is explained,and then combined with questionnaires of students' attitudes,learning methods and methods.of teaching secondary school functions,the concept of secondary school functions based on APOS theory is further proposed.Variable teaching strategy,analyze how to organize variable teaching in the four stages of APOS activities,process,object and scheme.Finally,the teaching design is represented by exponential function,logarithmic function and power function in secondary school functions.Finally,the didactic design of these three functions is used as a template for didactic experiments.Through quantitative front-to-back screening,it is concluded that teaching the secondary school function variant based on APOS theory improves student performance and helps to deepen the essence and connotation of the concept of functions.Understanding and grasping the function can better build the knowledge system of the concept of function in the mind.