The Cognitive Analysis Of Senior High School Students' Function Zero Learning Based On The Theory Of APOS

The study of mathematical concepts is a hot issue in the study of mathematics teaching nowadays.Function,as an important part of modern mathematics,the problems related to it of are worthy of pursuing further.The zero of a function is another important content that appeared after learning the concept and nature of the function.It is an important bridge to link the study of functions and equations.Therefore,it is meaningful to analyze the students' cognitive level of the zero of the function.The four stages of APOS theory can reflect the cognitive levels of students' mathematics learning well,and then find out the problems existing in students' learning process,so as to make targeted suggestions for the students' learning status.Through testing the senior high students of a middle school in Zhangzhou City and using APOS theory to analyze,this paper comes to the conclusion that: 82% of the students reach the excellent level of the action stage;21% of the students reach the excellent level of the process stage;16% of the students Achieving the excellent level of the object stage;2% of the students reach the excellent level of the schema stage.It is reflected in the data that most of the high school students in that middle school can reach the level of the action stage,but the number of people who reach the next three stages is not much.Based on this conclusion,the author interviewed 10 senior teachers of the school's senior high and 10 of the test subjects,and analyzed the reasons from the interview results.The reasons are as follows: 1.The knowledge about function zeros in students minds does not form a network structure,that is,the knowledge structure is scattered;2.Students can not smoothly transition from the concept of function zeros to the knowledge related to it,that is,the process of knowledge convergence is difficult;3.Some teachers can not correctly handle the key and difficult points of function zeros in this lesson.That is to say,it can not guide students to understand the formation of concepts correctly.