Analysis Of Inequality Problems In High School Mathematics Competitions And Research On Competition Teaching

In 1956,under the initiative of mathematician Hua Luogeng,Su Buqing,Jiang Zehan and others,the middle school mathematics competition was held for the first time in Beijing.Since then,because of its important role in selecting excellent mathematics talents,the middle school mathematics competition has been paid more and more attention,and the number of people participating in it has gradually increased.So far,there are three main types of mathematical competitions: the international mathematical competitions,national and regional mathematics competitions.Its content is based on the teaching content of middle school mathematics,is also an extension and expansion of the classroom teaching content.The competition teaching plays an irreplaceable role in improving students' ability of solving problems.Inequality problem is one of the hot topics in mathematics contest questions.Inequality is favored by contest proponents because of its flexibility of solution and wide application.Therefore,this paper takes inequality problem as the starting point of research,including five aspects,its background,theoretical basis and proposition analysis,problem-solving method and analysis,contest Teaching practice investigation,and combines the above research content to give teaching suggestions and teaching case designs.The main content of this paper includes the following five parts.The first part is the first chapter of it,which is the introduction part.It mainly describes the development process of mathematical competition,summarizes the research status of inequality problem solving methods,and explains the research purpose and significance of this paper.The second part is the second chapter of it,which takes the concepts and properties of inequalities in high school mathematics competition as analysis basis of the questions,sums up the proposition principles and methods of inequality problems,and uses statistical analysis method to analyze the inequality problems in the International Mathematics Olympiad,China Mathematics Olympiad and National Senior High School Mathematics League in the past ten years,andanalyzes its development trend in the math contest.The third part is the third chapter of it,combining with the competition examples,starting from solving inequalities and proving inequalities to analyze inequalities solution method,which provides some reference for students to choose the solution methods properly in solving problems practice.The fourth part is the fourth chapter of it,on the basis of the first two parts,based on the theory of "basic skills of solving problems" put forward by Luo Zengru of Shaanxi Normal University and "how to solve problems" put forward by Polya,an American mathematician.Taking all the students who come from the mathematics competition class of the first senior high school in Mudanjiang city as the research object,to investigate the basic situation of senior high school competition students' solving inequality problems by the method of questionnaire and test paper,and to make statistical analysis on the questionnaire and test paper by using SPSS software.The fifth part is based on the problems found in the investigation.With the help of front-line teachers,this paper puts forward corresponding suggestions for the contest teaching and learning of inequality content from three aspects,including knowledge structure,thinking ability and experience.Combined with the teaching suggestions,this paper takes Cauchy inequality as an example to design the teaching,hoping to provide useful supplement to competition teaching research and could give some practical suggestions to the competition teaching teachers.