Research On The Practice Of High School Mathematics Concept Teaching Based On APOS Theory

Mathematical concepts are the foundation of mathematical knowledge and the most essential content in mathematics,and mastering mathematical concepts is the key for students to learn mathematic well.Trigonometric function is the most important content in high school mathematics.According to the requirements of the new teaching reform,this paper takes the concept of trigonometric function in the new version of the text book as an example,and uses APOS theory to carry out practical research on the teaching of high school mathematics concepts.APOS theory is a kind of conceptual learning theory proposed on the basis of constructivism combined with educational research practice,which believes that the learning of mathematical concepts should go through four stages: operation,process,object and schema.First of all,this paper uses the literature analysis method to fully excavate the domestic and foreign literature on APOS theory and understand its essence and characteristics.Secondly,by using the questionnaire survey method,this paper investigates the situation of students learning concepts and the current situation of teachers in concept teaching,and makes descriptive statistical analysis and correlation analysis with SPSS statistical software.It is learned that teachers often only pay attention to concept assimilation and do not pay attention to the formation process of concepts in concept teaching,and students only stay on the surface of concepts when learning mathematical concepts without deep understanding.Aiming at the problems of teachers and students,this paper takes the "concept of trigonometric functions" as an example to apply APOS theory to concept teaching.The specific contents are as follows:(1)Theoretical analysis is carried out on the four stages of APOS theory,and how it is integrated into the conceptual teaching of trigonometric functions is studied in depth.(2)Teaching the design of trigonometric function concept under the guidance of APOS theory.(3)According to the teaching design under the guidance of APOS theory,the experimental class is taught and practiced,compared with the traditional teaching class.(4)After class,the evaluation of teaching effect was analyzed by an independent sample t-test,and the results showed that there was a significant difference between traditional teaching and teaching under APOS theory.Comprehensive statistical data analysis shows that in the concept teaching of new textbooks,the teaching effect based on APOS theory is significantly better than that of traditional teaching,which is conducive to students’ understanding and mastery of concepts.At the same time,in the teaching process,it will be found that the application of APOS theory for teaching can enhance students’ learning interest and improve students’ learning performance.According to the research results,the APOS theory is suitable for the teaching of high school mathematics concepts,and has a guiding effect on the teaching of other concepts in new textbooks.