Case Study About Ninth-grade Mathematically Gifted Students' Feature In Solving Geometry Problems

This paper mainly researched the characteristics of the nine grade mathematics gifted students in the process of solving geometric problems.Gifted education in mathematics is a key link in the implementation of the "popular education" in China,and it's also the only way to cultivate outstanding talents for our country.Students in grade nine not only possess systematic knowledge of geometry,but also face the test of life——“middle school entrance exams” for the first time.The paper Analyze and study the characteristics shown in solving the problem of geometric of gifted students in grade nine,and provide the corresponding teaching suggestions to guide the gifted students to get a better development.First of all,the thesis based on volume tool VAMS,this thesis designed a survey questionnaire suitable for this research,including epistemology,self,teaching and learning behavior.Geometry learning attitude of 30 ninth grade mathematics gifted student has made the investigation and analysis.The results showed that:ninth grade gifted student can use most of the geometric knowledge flexibly and have the internal motivation and self-efficacy of geometry learning.Teachers usually show geometric knowledge intuitively;These gifted students always have the persistent belief in solving the geometric problems.Secondly,according to the writing principles of ability test,the meaning of basic geometric problem,the actual situation of students and the advice of several experienced teachers and experts,it covers the important knowledge points that ninth grade students need to master as far as possible.We need to provide as many subject types as possible,and finally choose 10 representative topics as the research material.The research chose five ninth grade students who were study in a key middle school in Zhangzhou,requiring them to do tests by the method of Verbal Protocol,and require them to keep the records of problem solving process.After the test,we interview the tester timely,and then we can have a further understanding of the participants' thoughts throughout the interview,The study stages had been found:(1)understanding the question: the gifted ninth grade students are good at making a symbolic-graphic combination to get subject information comprehensively and systematically,then analyzing and integrating information appropriately.They are also good at pattern recognition of problem solving.(2)the problem solving phase: ninth grade gifted students in mathematics are good at concentrating thinking on the basis of the divergent thinking.When they encounter problems,they have persistent faith of problem solving,so they can insight into the auxiliary line easily.(3)the inspection and summary stage: ninth grade gifted students in mathematics can make good use of mathematical language and they are also good at making induction,summary and reflection.Finally,according to the analysis of the case studies and interviews,geometrical survey of geometry learning attitude,we provide the corresponding teaching suggestions to cultivate ninth grade gifted student in solving geometry problems.And provide some practical references and basis for the development of students' ability to solve geometric problems.