Research On Teaching Practice Of Cauchy Inequality

Cauchy inequality has a very extensive application in the mathematics in high school,it is closely related to other knowledge,such as functions,series,geometry and so on.It also has a big value in education.As the elective part of the learning content in high school,Cauchy inequality is quite difficult.Because teachers and students pay different emphasis on it,teaching research is too scattered,the pertinence is not strong,so the study of Cauchy inequality is not deep enough.And all these above make the teaching of Cauchy inequality become relatively thin and rigid,without the value it was supposed to be.Therefore,what difficulties will the teachers and students encounter in the process of Cauchy inequality teaching and how to teach Cauchy inequality,these two aspects is exactly what this thesis expects to solve.In view of the above phenomenon,this thesis has consulted a large amount of relevant literature,it includes the aggregation of examination questions about Cauchy inequality from the college entrance examination and some competitions in recent years,and it analyses and explores problem-solving ideas and methods on it.At the same time,in the process of summarizing and analyzing the questions,this thesis ponders the teaching difficulties and teaching blind spots in the teaching process,and according to the teaching requirements,compiles three examinationquestions about the Cauchy inequality referencing the compiling principle and some excellent examination questions at home and abroad.In the end,in order to solve the problems that the understanding and application of Cauchy inequality for student are generally surface,it is easy to ignore the condition of equal sign,the method of proving is deficient,and the ability of using of Cauchy inequality to solve the relatively question is relatively weak and so on,this thesis explores the application of undetermined coefficient method with parameters in Cauchy inequality from the perspective of the problem solving,deeply understands the historical background of Cauchy inequality,and shows the importance of the condition the equals sign on the side.It provides a teaching design for two aspects,optimizing the CPFS structure of students and improving the students' solution ability.Some teaching suggestions about Cauchy inequality are put forward,which is based on my teaching experience.The innovative point of this thesis is to make a deep inquiry into how to construct Cauchy inequality in the process of solving problems and provide corresponding teaching design for analyzing the method of to construct by introducing parameters and using undetermined coefficient.Meanwhile,three innovative questions of Cauchy inequality are compiled,hoping to provide a new idea for the teaching of Cauchy inequality.