| Compared with middle school mathematics,higher mathematics courses not only expand and deepen the knowledge structure,but also put forward higher requirements in terms of ability and skill.In terms of mathematical thinking methods,higher mathematics undoubtedly has strong guidance for middle school mathematics.Mr.Wu Daren,a famous math educator,pointed out:"The higher the point of view is,the simpler things seem to be.For example,some things which are difficult to understand in real number field are clear from the point of view of complex number field.Some phenomena which are not easy to explain in Euclidean space are well explained from the point of view of projective space." At the same time,he also highlighted that "The Elementary Mathematics Under the High Viewpoint" lays particular emphasis on "integration",which is the integration of elementary mathematics and advanced mathematics,the integration of various parts of mathematics,the integration of geometric concepts and arithmetic concepts and the integration of perception and rationality,and so on".Thus,the comparative study of the relationship between advanced mathematics and middle school mathematics has a great significance in guiding middle school teachers in their academic field.Under the requirements of the new curriculum reform,the curriculum standards are constantly changing.Although the overall difficulty of the national college entrance examination mathematics papers has not changed much in recent years,innovative topics have received considerable attention.It examines not only the students’basic grasp of the content of the textbook,but also their core mathematical literacy。Some of topics can well and simply solved through advanced mathematical methods.This paper discusses the elementary education of advanced mathematics in middle school by adopting literature research and interaction between teachers and students.Taking the real questions of college entrance examination and mathematics contest questions in some provinces and cities as research templates in recent years,this paper comprehensively analyses and collates some classical topics in order to advocate multiple solutions to one question.And it also tries to overlook the topic from a higher perspective and aims to excavate knowledge,methods and mathematical ideas contained in the topic.This thesis is divided into two parts:the introduction and the main text.In the introduction,it explores the elementary application of advanced mathematics with reference of relevant researches at home and abroad.Through the analysis of some knowledge points of high school mathematics and common test questions,it establishes the research status and the significance of this thesis.As for the main part,it can be divided into four parts.In the first part,the elementary equalization of mathematical analysis in elementary mathematics is discussed by analyzing examples from the relationship between sequence and function,Cauchy inequality,Abel formula and other knowledge points.The second part discusses the elementary equalization of probability and statistics method in elementary mathematics and the inequality proved from the perspective of probability and variance.At the same time,two probability models are exemplified.In the third part,the knowledge points in elementary number theory are discussed.The last part discusses the elementary application of radiation transformation in plane vector,linear programming and conic curve and reveals the leading role of affine transformation in solving some senior high school questions with practical examples.All in all,this thesis compares the general method with the special method,and it analyzes the mathematical background of the topic by exploring the application of knowledge points in the elementary education mentioned above.It hopes to provide theoretical support and guidance.for future teaching and research. |
