The Studies Of High School Geometry And Teaching About High Viewpoint

In recent years,with constantly updated modern mathematics teaching views,geometry questions with "high viewpoint" as the carrier,higher mathematics knowledge as the background,frequently appeared in the college entrance examination papers.As it can effectively test the students' creative thinking ability and the potential to continue the study of mathematics,it's gaining more and more favour from education scholars.And thus the geometry and teaching methods in high school are making continuous improvement accordingly: some preliminary knowledge of higher geometry has been compiled into high school teaching materials,and the teaching process has penetrated into many higher mathematics thinking methods.This thesis focuses on the study of high school geometry problems and teaching with "high viewpoint" in the following six chapters:The first chapter is the introduction,which elaborates the high school geometry research under the background of "high viewpoint",the reason of the topic selection,and based on the current relevant research results,proposes the problem to be researched and solved in this thesis.The second chapter expounds the necessity of "high viewpoint" in high school geometry,mainly from the following four aspects: the limitations of high school geometry,the guiding function of "high viewpoint" on high school geometry teaching,the necessity of geometric "high viewpoint" under the new trend of autonomous enrolment and competition,and the cultivation of students' geometry thinking based on lifelong learning.Chapter three,four,five are the main body part: the third chapter is about the relationship between higher mathematics and high school geometry,overview the theoretical consistency on thinking methods between them,with symbolic-graphic combination as an example,and furthers the study on the related knowledge of general curve similarity through the analogy of the similar triangles.The fourth chapter illustrates the infusion of higher geometry knowledge into high school geometry,and that the space vector content has its own system in the high school textbooks,which greatly reduces the difficulty of the solid geometry problem solving and thus has an very important function.In addition,the application of affine coordinate system in problem solving can be seen everywhere,simplifying the steps and also the thinking process.In the fifth chapter,the author uses the advanced geometric knowledge solve the problem of high school analytic geometry,and mainly uses coordinate expansion transformation and polar pole theory to solve the difficult conic curve problems simply and quickly.The sixthchapter is the high school geometry teaching inquiry under the "high viewpoint";research on the "high viewpoint" teaching of several class types: designing novel and efficient new lesson teaching under the "high viewpoint",expounding the integration function of "high viewpoint" on high school knowledge scattered system,and designing review lessons teaching plans that embody the effectiveness of high school geometry knowledge review under "high viewpoint";then some simple and feasible suggestions given to the geometric teaching under "high viewpoint".Finally,the thesis summarizes and reflects the whole thesis based on the analysis and research of the problem.