The Level Definition Of Symbolic-graphic Combination And Its Study Of Teaching Cases

The symbolic-graphic combination concept plays an important part in high school teaching.It connects abstract mathematical language with intuitive images.Through the observation of images,it is easier for students to understand the nature of algebra.The problem can be simplified by using symbolic-graphic combination method when we deal with many problems,and it is easier to find the entry point of the problem and solve the problem flexibly.It is a long process to learn symbolic-graphic combination,which is seeped into the knowledge points during the interpretation of new lessons.Students are required to develop an awareness of solving problems by drawing consciously,thus forming the thought and method of applying conversion between numbers and forms to problem solving.According to the author's teaching experience for many years,this paper was written by investigating the situation of symbolic-graphic combination idea among high school teachers and students on the basis of the requirement of symbolic-graphic combination in the mathematics teaching outline,combining the research achievements of predecessors' for symbolic-graphic combination ideas.This paper is divided into five chapters.The first chapter elaborates the origin of the combination of several forms,the research status,the purpose and the significance of the research.The second chapter is to know the situation and problems of the teachers and students' awareness of symbolic-graphic combination.According to the outline requirements,level classification of mathematics learning,evaluation in mathematics teaching process,symbolic-graphic combination idea is defined in level in order to solve the problems found.The third chapter is about teaching designs of the representative sections based on the level definition of the symbolic-graphic combination,combined with the contents of the high school mathematics teaching material.The teaching designs which reflect the development stage of symbolic-graphic combination contain the teaching of monotonicity of function,exponential function and the teaching of sine function respectively.The nature of the function is revealed from the perspective of the interpretation of the concept of function,by observing the image,and students' symbolic-graphic combination thought level is developed by the connection between the image as well as graphic transformation and flexible solutions.The fourth chapter states the effects the level definition of symbolic-graphic combination has on teachers' teaching according to the teaching design in the previous chapter.It expounds the three aspects: setting up the teaching consciousness of symbolic-graphic combination among teachers,how to cultivate the students' symbolic-graphic combination idea in the teaching procedures,the methods of guiding the student to utilize the symbolic-graphic combination.The fifth chapter analyses and summarizes the advantages of the level definition of symbolic-graphic combination,according to the author's own teaching practice,investigation and study.It also shows the effects the use of symbolic-graphic combination in teaching designs has on the formation of student's thinking form.In the end,the author make a summary and puts emphasis on the infiltration of symbolic-graphic combination in mathematical teaching.Students' application of symbolic-graphic combination is strengthened to improve students' ability to solve high school math problems.