Research On The Current Situation Of Junior High School Students In Learning The Method Of Adding Auxiliary Lines To Plane Geometry Problems

Auxiliary line is an important tool to break through and solve geometric problems,and it is an effective way to solve problems.Adding some auxiliary lines properly is helpful to solve geometric problems,and the teaching of adding auxiliary lines in class must understand the adding methods adopted by students.Through literature research,it is found that researchers mainly focus on discussing the teaching of auxiliary lines from the perspective of teachers,and Research on the methods of adding some auxiliary lines.Few researchers investigate the current situation of students' adding auxiliary lines from the perspective of students.This study from the perspective of students to explore the current situation of junior high school students to master the method of plane geometry to add auxiliary lines and research,analysis of students' psychological development process of problem-solving to add auxiliary lines,is of great significance to both teachers and students.On the one hand,it can enrich the teaching research of adding auxiliary lines,on the other hand,it can provide research basis for the method of adding auxiliary lines from the psychological perspective.This paper mainly uses questionnaire research method,test paper research method,literature research method and oral report research method to investigate the current situation of junior high school students' mastery of the method of adding auxiliary lines to plane geometry.Based on Li Ping's student questionnaire,the paper revised and compiled the survey on the current situation of adding auxiliary lines to junior high school students' solving plane geometry problems,Referring to SANA's master's thesis "plane geometry add auxiliary line test",the questionnaire and test paper are investigated,and the data are analyzed to get the status quo;On this basis,three top students,three middle students and three students with learning difficulties were selected from the students who took part in the survey.Based on the above two studies,the main conclusions are as follows:1.In plane geometry problems,students generally find it difficult to recognize the basic graphics.Only a few students who are excellent in class can abstract the basic graphics and understand the nature and relationship between the basic graphics when facing the graphics of plane geometry problems.2.In plane geometry problems,nearly half of the students can't tell whether they need to add auxiliary lines,that is,they don't have a high awareness of adding auxiliary lines to solve plane geometry problems;The eighth grade students think that the learning of the auxiliary line is to cope with the examination more than the ninth grade students.3.In the plane geometry problem,the students lack the guidance of the auxiliary line learning behavior,nearly half of the students usually do not take the initiative to summarize the auxiliary line.Teachers have induction and special training for the learning of auxiliary lines.4.It is easy for students to recognize the basic graphics of triangles,so it is easy to add "connecting two points" auxiliary lines.Most of the students deal with polygons by adding auxiliary lines to convert polygons into triangles.For the problems that can be solved without or with auxiliary lines,most students do not add auxiliary lines to solve problems.Junior high school students in mastering plane geometry problems to add auxiliary line level is general,especially in mastering the plane geometry quadrilateral part of the auxiliary line level is poor,mastering the plane geometry triangle part to add auxiliary line level is better.5.When students need to add auxiliary lines to solve plane geometry problems,the attention process of top students and middle students to add auxiliary lines is the process of resource limitation,while the attention process of students with learning difficulties to add auxiliary lines is the process of material limitation of basic geometric figures.Top students' perceptual processing psychology is a top-down process,while middle students and students with learning difficulties are a bottom-up process.The thinking of excellent students is mainly the organic interaction of image thinking,logic thinking and inspiration thinking,and most of them use inspiration thinking to construct auxiliary line.When using logic thinking to construct inappropriate auxiliary line,they can quickly negate it,and then choose another idea to construct auxiliary line;Middle school students' thinking of adding auxiliary lines is mainly logical thinking and image thinking,and few students can have inspiration thinking;Students with learning difficulties mainly use logical thinking.The suggestions in this paper are as follows: pay attention to the teaching of geometric theorems of basic figures;Strengthen students' attention to geometry teaching;Strengthen students' thinking flexible teaching.