Research On The Teaching Of High School Mathematics Concepts Based On APOS Theory

"Clear concept" is the primary and basic factor to determine the effect of mathematics teaching.In the 1980s,American educator Dubinski put forward APOS education theory,which was generally accepted by mathematics education circles.Based on this point of view,this paper applies APOS educational theory to senior high school mathematics,and carries out teaching practice research on mathematical concepts.One hundred years ago,German mathematician F.Klein advocated that "function" should enter middle school mathematics.The position of "function" in middle school mathematics curriculum is well known.Vector,as a quantity of controlling space,can not only express the static phenomena of the objective world,but also accurately depict the dynamic phenomena of the objective world.At the beginning of this century,after the reform of basic education curriculum in our country,"vector" entered the senior high school mathematics curriculum,and became a tool to learn many senior high school mathematics knowledge.In the process of research,we rely on the two mathematical concepts of "function" and "vector".In the process of research,firstly,through searching and reading literature,we can further understand APOS education theory and its application knowledge in teaching.Based on the four stages of action,process,object and schema of mathematical concepts understanding,a test paper on the concept of "function" was compiled.A questionnaire survey was conducted among two different classes of senior two in Xinghua Wenzheng Experimental School to understand the current situation of ordinary senior high school students'understanding of functional concepts.The study found that:3.16%of the students are in the active stage,only a few students are still in the junior middle school understanding of the concept of function;87.37%of the students are in the object stage,although most of the students have some corresponding or mapping principles in their minds,there are still great difficulties in answering function questions in some situations;9.47%of the students are in the object stage,only a small part.The students with score can treat function as an independent object;none of them are in the graphic stage and can treat function as an independent object,so all of them are unable to have a comprehensive thinking ability to solve function problems.The overwhelming majority of students do not have a deep understanding of the essence of the concept of function;several commonly used methods of function representation deal with each other in an independent state;the reading,understanding and application of the symbolic language of function are poor;accurate information can not be collected from set language and functional language;and objective phenomena can not be accurately explained from the perspective of function.Then,according to the analysis of the reasons for the current situation,thinking about how to carry out the teaching design of mathematical concepts based on APOS educational theory.This paper attempts to study the two basic concepts of "the concept of vector" and "the quantity product of vectors" in the chapter of vector,and gives their instructional design.This paper is a survey and teaching design of mathematical concept teaching under the guidance of APOS theory.It explores how to apply teaching theory to teaching practice,and provides teaching reference for finding more suitable mathematical concept for students' development.