Problem Solving Strategies And Deformation Exploration Of CGMO Planar Geometry Problems

The research on the Chinese Girls' mathematical Olympics in China has made great achievements in the new level of mathematics.It is a branch of the mathematics competition.It has become an internationally recognized educational activity.It occupies a very important position in high school mathematics competition.As an important way to discover and cultivate outstanding mathematics talents,the Chinese Girls' mathematics Olympics has attracted much attention.The main purpose of this paper is to sort out the plane geometry test questions in the Chinese Girls' Mathematics Olympics.Based on the dialectical relationship between the whole and the part,the plane geometry test questions are separated from the Chinese Girls' Mathematics Olympics.As the previous studies on this contest are few,this paper not only provides some reference value for the future research of the contest,but also has some reference and guidance for the teaching guidance of plane geometry and students' learning in mathematics contest.This paper mainly uses the literature analysis method,taking the plane geometry test questions in the Chinese Girls' Mathematics Olympics in recent years as the research object,sorting out the related test questions in previous years,analyzing and researching the problem-solving process of the test questions.This paper probes into the thinking characteristics of solving related questions.It classifies the questions with similar thinking process and summarizes the solving strategies contained in them.The strategies proposed in this paper include construction method,identical method,special and general method,classification discussion,area method,whole and part method.On the basis of the existing results of the test questions,other conclusions implied in the test questions are analyzed,studied and found,and even the conditions provided in the test questions are replaced.A simple geometric deformation of the combination figures of the test questions is explored by using the Geometer Sketchpad,so as to obtain similar results or the same results as the original test questions,and prove them.Finally,this paper puts forward a summary and prospect.