Investigation And Research On Teaching Cohesion Of Trigonometric Function In Basic Education Based On Apos Theory

As an important mathematical concept in middle school mathematics,trigonometric function is not only the key content of the junior middle school mathematics curriculum,but also runs through the entire middle school mathematics curriculum.As a basic basic function with periodicity in high school mathematics curriculum,it contains many important thinking methods.Many practices have shown that high school freshmen after entering elementary school find it difficult to learn.Therefore,high requirements are put forward for the connection between junior high school and high school teaching.This article attempts to analyze and study the teaching of trigonometric functions from the mathematics learning theory and APOS theory proposed by the American mathematics educator Dubinsky.High school.Related issues propose teaching optimization strategies to improve the current situation of high school students’ difficulties in learning mathematics.The research methods and contents of this article mainly include: First,use the literature analysis method.Through the research and analysis of the cohesive teaching of APOS theory,trigonometric functions and related literature,it is found that APOS theory is a learning theory with mathematical characteristics.Second,use the questionnaire survey method.Investigate the mathematics learning habits and the current situation of trigonometric function learning of freshmen in high school;third,use Excel statistics and analyze the survey results to find out the main problems of the poor connection of trigonometric functions between junior and senior high schools and the reasons for this situation;fourth,Using the interview investigation method,the reasons for the poor connection of trigonometric function teaching in junior high school and senior high school and related optimization strategies are analyzed,and two typical teaching cases in trigonometric function teaching in junior high school and senior high school are analyzed in combination with APOS theory.school.Through this research:(1)After entering the first grade of high school,it is difficult for students to learn high school mathematics;(2)Most students believe that high school mathematics has a lot of knowledge,difficulty and thinking ability;(3)Active learning students are among the minority nationalities,Most students still continue to use the passive learning method of junior high school;(4)Do not understand the definition of trigonometric function from any angle;(5)The difficulty of learning trigonometric function for high school freshmen is mainly due to their poor grasp of knowledge and lack of understanding of concepts.The formula is not familiar;(6)The students hope that the teacher can concentrate on teaching trigonometric functions,and the students will practice more and use the relevant teaching aids of multimedia teaching technology.After understanding the current research status,through questionnaire analysis and teacher interviews,the reasons for the difficulty in learning trigonometric functions were discovered:(1)The content,teaching methods and thinking methods of trigonometric functions in junior and senior high schools are out of touch.(2)There are obvious differences between junior high school and senior high school curriculum standards;(3)The negative impact of junior high school trigonometric function knowledge;(4)The passive learning style of students has continued to high school;(5)The overall calculation ability of students is poor.After understanding the current situation and analyzing the reasons,I first proposed an optimization strategy for the teaching of trigonometric function connection.Focus on the connection between junior high school and high school trigonometric function knowledge points;second;focus on the connection between junior high school and high school trigonometric function thinking methods;third;focus on the assistance of educational technology.Fourth,the connection of high school trigonometric functions;strengthen the communication between junior high school and high school teachers,and promote the cohesion of trigonometric function teaching.Finally,based on the APOS theory,a representative cohesive teaching design is designed.