Case Study On The Application Of APOS Theory In Function Concept Teaching In High School

The function knowledge runs through the entire high school mathematics knowledge,the function concept understanding directly relates to the student to the function foundation knowledge grasp and the application,but because the high school function concept highly abstractness,the student often cannot very well understand thefunction concept essence.As the guiding theory of concept teaching,APOS theory has been widely applied in concept teaching of high school mathematics in China in recent years,and some good teaching results have been achieved.What are the advantages and limitations of applying APOS theory to function concept teaching?How to carry out function concept teaching in high school based on APOS theory and improve the teaching effect is a problem worth studying.In order to study the above two problems,first of all,literature analysis method was adopted to sort out the application of APOS theory in the teaching of high school mathematical concepts and the enlightenment of APOS theory on concept teachingaccording to relevant literatures.Secondly,by using the comparative research method,the author observed the practical teaching activities of the concept of function,observed the specific practical teaching situation using APOS theory,and compared the advantages and disadvantages of using APOS theory for the concept of function teaching and not using APOS theory for teaching.Finally,the paper adopts the case analysis method to discuss and analyze the advantages and limitations of using APOS theory in concept teaching by analyzing students' response to the same example in different teaching modes and their test scores after learning.Through the above comparative analysis,the following conclusions are drawn:the advantages of concept teaching under APOS theory;The limitation of using APOS theory in concept teaching is explored.Based on the advantages and limitations mentioned above,Suggestions for the design of concept teaching using APOS theory are given:(1)during the activity stage,attention should be paid to the use of mathematical history or mathematical culture creation activities to stimulate students' interest;(2)teaching in the process stage should respect the order of knowledge;(3)in the object stage,students are given exercises in the form of quizzes to form conceptual prototypes;(4)in the schematic stage,attention should be paid to the concept map method for teaching,so as to help students sort out the relationship between concepts for betterapplication.