Research On Auxiliary Line Method Of Plane Geometry In Junior Middle School Based On Reverse Thinking

Elementary geometry often borrows the intuition of graphics,and the common sense of mathematics.The basic way to solve the problem of plane geometry in junior high school is to construct a support between the known conditions and the verification conclusion.As a very systematic plate,the many theorems in plane geometry derive many ways to make auxiliary lines.Geometry questions are ever-changing,and auxiliary lines are also ever-changing,which makes the problem of auxiliary lines a difficult point in plane geometry learning.Therefore,it is of great significance for junior high school mathematics teachers who are in the front line to teach effectively and learn simply and quickly to explore effective auxiliary line teaching methods that are in line with the conditions of junior high school.It will not only help improve the related teaching theory of auxiliary lines,but also help.For students to master the internal laws of mathematical knowledge,establish a cognitive structure,and improve the level of mathematical thinking and mathematical learning ability.This research uses reverse thinking as a foothold to explore the practice of plane geometry auxiliary lines.Firstly,the chapter is clear,to clarify the purpose and significance of the research;Secondly,the literature research method is used to discuss the relevant research status and theoretical basis,and on the basis of the junior high school students' thinking level and obstacle analysis,the difficulties in the process of adding auxiliary lines to the students in the plane geometry study are discussed.Investigate and analyze the links and their reasons.At the same time,use interviews to discuss the auxiliary line teaching methods with junior high school mathematics teachers;On the basis of literature research and investigation and analysis,introduce the practice of junior high school plane geometry auxiliary lines led by reverse thinking,mainly including Make the basis of auxiliary lines(graphic public method and basic charting)and basic methods,basic auxiliary lines,analytical methods,ingenious auxiliary lines and analysis tree models;Then,a specific teaching case analysis is used to show the important role of reverse thinking in improving students' ability to add auxiliary lines.The following conclusions are obtained through research: In the current situation of auxiliary line teaching,students' knowledge structure is weak,thinking is limited and reasoning ability is weak,teachers' teaching of auxiliary line is only on the surface,and does not go deep into the intricate knowledge of geometry.Therefore,combined with the overall knowledge structure of junior high school mathematics,the relationship between the various parts of plane geometry is ingeniously analyzed,the basic graphics are analyzed in the form of partitioned blocks,and the auxiliary lines of different graphics are drawn.Use reverse thinking to help students sort out the ways in which suitable auxiliary lines appear,and use the analysis tree model to clearly and intuitively show the thinking process,help teachers' teaching and students' learning build a strong engine,and broaden the sunshine avenue.It is found that teachers need to improve students' ability to add auxiliary lines from two aspects of geometrically intuitive and reverse thinking.As the leader of teaching,on the basis of "secondary development of teaching materials",teachers should reduce the slope,build a reasonable bridge,set up special training of auxiliary lines,guide students to analyze and review problems,and guide students to summarize the methods of auxiliary lines in time.