Research On Trigonometric Function Periodicity Teaching Based On APOS Theory

An important manifestation of mathematical abstraction is the formation of mathematical concepts.Dubinsky’s APOS theoretical model is a classic theory of concept formation.There are many problems in the current mathematics concept teaching.By taking the periodic teaching of trigonometric functions as an example,the author provides an empirical study for the application of APOS theory to concept teaching.First of all,the author thoroughly studied the four stages of APOS through a large amount of literature reading,namely the specific meaning of activities,processes,objects,and schemes,laying a theoretical foundation for the application of APOS theory in the teaching of trigonometric functions;the author found that although these four stages have Hierarchical structure,but it is cyclic;the author made specific interpretations of the mathematical concept teaching formula based on the periodicity of trigonometric functions.Secondly,the author analyzes the development of trigonometric functions and the duality of the periodic concept of trigonometric functions,and makes a certain sorting analysis of the periodic arrangement of trigonometric functions in the current textbooks,paving the way for subsequent teaching design.Next,based on the four stages of APOS,the author did a textbook analysis and academic analysis of the periodic concept of trigonometric functions,and determined the teaching objectives and core qualities,major and difficult points and teaching procedures,and specifically designed two and triangle functions.A teaching plan for concepts related to the periodicity of functions.Finally,in order to verify the effect of the model,the author took the first-year high school students of a middle school as the experimental object,carefully designed questions representing different stages of APOS,and quantitatively tested the level of students.At the same time,the author uses interviews to qualitatively evaluate teachers’ understanding of teaching materials and control of teaching,as well as students’ difficult questions.From this,find out the students’ thinking misunderstandings,and put forward practical teaching suggestions to teachers.