A Practical Study On The Function Teaching In Senior High School Based On APOS Theory

The development of mathematics teaching has been deepening and has entered the new stage of establishing the idea of people-oriented moral education and core competence teaching.The high school mathematics curriculum has a lot of concepts,which is the basis of mathematics learning.It is more abstract and more difficult to understand than other disciplines.Therefore,the teaching of mathematical concepts is extremely important.At present,it is still a common problem that most teachers pay more attention to solving problems but less attention to the concepts itself.In addition,the teaching of concepts should be equally emphasized and in-depth research.From the nine-year compulsory education to high school,the biggest challenge for students in high school will be the study the chapters of function.The compact of function is the core content of high school mathematics,occupying an important position,and the level of ion is high.Based on the cognitive basis of students,it will be difficult to learn.The learning process of the function not only learns knowledge,but also the ability to infiltrate and cultivate the core literacy of mathematics.How to better apply the teaching theory to deepen the research,optimize the teaching design of the function chapter concept,and infiltrate the cultivation of core competence,which is the problem we need to think and study.Based on the APOS theory of Dubinsky's mathematical concept teaching theory,this paper explores and practices the teaching of the function chapter concept with the students' psychological activities.Let students actively participate in the whole process of conceptual construction in the study of functions,clarify the ins and outs of concepts,and grasp the mathematical essence of concepts.The first part of this paper puts forward the issue.There are still many shortcomings in the teaching of the function chapter concept,the teaching design using APOS theory to optimize the concept will be discussed.The second part summarizes the teaching of APOS theory and high school function from the perspective of APOS theory,and introduces the status quo of related researches at home and abroad.The third part,using questionnaires and interviews investigates and analyzes the current situation of students learning and teachers teaching in the function chapters of our school.Analyze the questionnaires and interview results by using APOS theory to explore the factors affecting students' concept learning of the function chapters,analyzing the deficiencies in the teaching links,and proposing improvements to the existing problems.In this process,the author listened to a large number of classes teaching by our school teachers about functions chapter,observed the provincial level and city level teaching competitions and open classes,learned the advantages from the teachers,and found out the students'doubts.Select some of the conceptual teaching segments that are heard and use APOS theory to compare and analyze.In the fourth part,the author try to use the APOS theory as a guide to teach and design the function chapter in Book One.For the two classes taught by the author in 2018,the APOS theory-guided experimental class and the regular teaching class served as the control group were set up.After about three months of teaching,the statistical data were used to analyze the experimental situation and effects.There was no significant difference in the scores of the two classes before the experiment while the experimental class achieved remarkable results after the experiment.In the fifth part,the author combines the actual situation of the students taught,and reflects on the teaching of the concept of the function chapter,and clarify the deficiencies and place needs improvement.The author hopes that this study can help teaching,and the author can understand the APOS theory more deeply and use it better in the future teaching.Learn the theoretical and research results of teachers and experts,integrate their own teaching experience,and put forward some ideas and suggestions.The author hope more teachers and experts will join the research.APOS theory will become a favorable tool to optimize the teaching design of high school mathematics concepts,help students better understand concepts and cultivate students' core competence.