Teaching Research On "Expansion Of Number System And Introduction Of Complex Numbers" Under APOS Theory

Under the continuous promotion of the new curriculum reform of mathematics,senior high school mathematics teachers in the new era need to stick closely to the new curriculum standards and grasp the essence of mathematics content in their mathematics teaching activities.Senior high school mathematics teachers should carefully design appropriate teaching plan programs,and adopt appropriate teaching mode,so as to cultivate students’ core accomplishments of Mathematics and improve their comprehensive ability.In recent years,many scholars’ research on APOS theory shows that applying APOS theory to mathematics teaching in senior high school is helpful to the cultivation of students’ ability.In addition,the chapter "The Expansion of Number System and The Introduction of Complex Number" is the last expansion of Number System experienced by senior high school students,which has great significance to the mastery of knowledge and skills,the application of ideological methods and the infiltration of mathematical culture.Therefore,under the guidance of APOS theory,the author conducts a practical research on teaching of the chapter of "The Expansion of Number System and The Introduction of Complex Number".The author uses the methods of literature,interview and questionnaire to conduct the research in this paper.The research contents of this paper are divided into the following parts:(1)Comprehensive analysis and research on the relevant literatures of APOS theory,make the theory more specific,can be better applied to the classroom teaching of high school mathematics.(2)Through questionnaires and interviews,this paper investigates the teaching and learning of "The Expansion of Number System and The Introduction of Complex Numbers".The subjects of the survey are four classes of senior high school students and two experienced mathematics teachers in a four-star high school in Wuxi.To figure out the existing problems,the author analyzed the current teaching and learning according to the combination of the students’learning status,teachers’ teaching status,the requirements of textbooks and new curriculum standards for this chapter.(3)On the basis of the present investigation,this study first expounds the feasibility and necessity of APOS theory in the teaching of "The Expansion of Number System and The Introduction of Complex Numbers".Under the guidance of teaching strategies and principles,the teaching design of "The Expansion of Number System and The Introduction of Complex Numbers" under APOS theory is preliminarily designed.Those teaching designs are applied to the class with the author.After the whole unit teaching,the test paper is made to test the students in the experimental class and the control class and the results are analyzed and summarized.At the same time,the cognitive and non-cognitive barriers often occur in students’ learning are analyzed in teaching practice,and teaching suggestions are given.(4)Point out the problems after summarization and reflection.Such as the limitations of APOS theory in teaching practice,etc.The analysis of the test results shows that the application of APOS theory to the introduction of the plural teaching has a significant effect on students’academic achievement and attitude towards leaming.The innovation of this paper lies in the application of APOS theory to the chapter of "The Expansion of Number System and The Introduction of Complex Number",which provides a new theory and method for the teaching of Complex Number in senior high school.