Research On The Teaching Of Auxiliary Lines For The Construction Of Plane Geometry Problems In Junior High Schools

Geometry is an important branch of mathematics,which contains many important mathematical ideas.The teaching of plane geometry runs through the whole junior middle school stage.With the deepening of knowledge learning,the gradual expansion of knowledge level and the continuous improvement of difficulty,students will encounter a lot of difficulties in the process of learning plane geometry.The proper construction of auxiliary lines is an effective means to solve geometric problems.How to construct auxiliary lines correctly and properly is the key and difficult point in learning plane geometry.The research on the teaching of constructing auxiliary lines in junior middle school plane geometry can provide a theoretical basis for improving teaching and has important reference significance.This study is based on Bruner's cognitive discovery learning theory,Polya's problem-solving theory,reduction thought and related theories of reasoning ability,and draws lessons from the research results of academic literature at home and abroad.By using the method of literature research,this paper discusses the views of scholars at home and abroad on auxiliary line teaching,analyzes students' ability to solve problems by using auxiliary lines through questionnaire survey and in-class testing,and understands the current situation of teachers' teaching of auxiliary lines.This paper discusses the role of auxiliary lines in plane geometry from three aspects: knowledge,problem solving and education.First of all,from the construction of the knowledge system of plane geometry,this paper sums up the construction rules of the auxiliary lines of several kinds of graphics which are common in plane geometry in junior middle school.Secondly,it investigates the present situation of auxiliary line teaching and students' learning of plane geometry,analyzes and summarizes the problems encountered in auxiliary line teaching and learning,and gradually explores the feasible strategies of constructing auxiliary line teaching for plane geometry problems in junior middle school.And in view of the specific problems in teaching and the current situation of the teaching process put forward the corresponding countermeasures:emphasize standardized drawing,pay attention to geometric language professors;delve into teaching materials,scientific arrangement of teaching content;heuristic teaching leaves students room for full thinking;mastering the method of auxiliary line drawing,guiding students to find the method of constructing auxiliary lines and sorting them out;establishing students' confidence in mathematics;combining multimedia technology with the teaching of constructing auxiliary lines.Finally,taking the "circle" in junior high school mathematics as an example,combined with the contents of teaching materials and exercises to carry out demonstration teaching,to explore the educational value of auxiliary line teaching,and put forward suggestions on how to cultivate students' core literacy.