Teaching Research On Construction Of Auxiliary Lines For Plane Geometry In Junior High School

Plane geometry has always been a difficult problem for students to learn mathematics knowledge in junior middle school mathematics learning,and the use of auxiliary lines to solve plane geometry problems is the most effective method at present,so how to determine whether the auxiliary line is reasonable and effective is an important problem worth thinking and studying at present.Therefore,in the teaching process,it is necessary for teachers to discuss and study this problem and try their best to provide practical solutions for students.This study is based on the research status of constructing auxiliary lines to solve plane geometry problems at home and abroad,based on discovery learning theory and mastery learning theory,using questionnaire survey method,testing method and teaching case design method.First of all,understand the current situation of applying auxiliary lines to solve plane geometry problems in junior high school,and then analyze the existing problems,and conduct an in-depth exploration of the feasibility strategy of constructing auxiliary lines in junior high school teaching.Secondly,the questionnaire is used to investigate the cognitive attitude,emotional attitude and behavioral habits of students.Combined with the obtained data,it is shown that there are significant differences in each variable in mathematics achievement and significant differences in cognitive attitude in grade variables.Then,through the study of the answers to the test paper,it is found that junior high school students are weak in answering auxiliary lines in plane geometry questions,and they are not strong in the consciousness of skillfully using auxiliary lines to solve problems.Most students are difficult to clarify the relationship between graphs in complex plane geometry problems and make auxiliary lines correctly.Finally,this study takes the triangle as an example to design a teaching case of constructing auxiliary lines by using the hand-in-hand model and the half-Angle model.Through this study,on the one hand,we hope to cultivate students’ understanding ability of geometric language,improve students’ grasp of the internal connection of graphics,pay attention to the guidance of students’ thinking process of model construction,and enhance teachers’ awareness of inquiry teaching.On the other hand,it is also hoped that students can be guided to correctly construct auxiliary lines,so that students can pay attention to hidden clues in graphs and use them in series in solving problems,so as to enhance their confidence in solving problems.