Study On Cohesion Problems Of Elementary And Advanced Mathematics

High school education which belongs to the continuation of compulsory education focuses on all students,moreover to undertaking the task of sending and selecting talents for colleges and universities.The university focuses on building builders and successors for the socialist,ensuring that students can master basic professional knowledge and professional ability before entering society.Although there are great differences between the two in terms of teaching goals,content,ideas,methods,and level of thinking of the educated,but from the perspective of systems theory,education is a complete system.Different subsystems are interconnected and affect each other.In view of the great changes in teaching methods and student learning methods in high schools and colleges,students may not be able to adapt to the study environment in university.Therefore,the connection between primary and higher education has become increasingly prominent.The knowledge about trigonometric functions is not only one of the basic elementary functions,but also one of the channels that communicate between elementary mathematics and advanced mathematics.As an inverse trigonometric function,which is an inverse function with a trigonometric function,it plays an important role in understanding the knowledge of trigonometric functions,furthermore it can be used to cultivate students' logical reasoning ability and rigorous mathematical thinking.Therefore,this article uses trigonometric functions and inverse trigonometric functions as the starting point to study the connection between elementary and advanced mathematics,wishing to contribute to the integration of China's education.First of all,clear topic research background and significance of this study.Based on this,relevant literature was sorted out and analyzed to understand the research status of trigonometric functions and inverse trigonometric functions,and to analyze the teaching contents and key points of trigonometric functions and inverse trigonometric functions in the elementary mathematics stage.At the same time,it summarizes the domestic and foreign research on educational cohesion.Next,it is promoted gradually with the mainline of "proposing questions-analyzing problems-solving problems".Among them,the part of "proposing questions" is the analysis of the teaching and application of trigonometric and inverse trigonometric functions.In elementary mathematics,using the mathematics curriculum standards and the national college entrance exam questions as the starting point,analyze the teaching status of trigonometric and anti-trigonometric functions.At the same time,use the fourth edition of "Mathematical Analysis" as a reference to analyze the applications of trigonometric and anti-trigonometric functions in higher mathematics."Analyzing problems " is mainly based on the analysis of the above situation,to summarize the cohesion problems of triangle and inverse trigonometric functions,from the two dimensions of elementary mathematics and advanced mathematics,to dig into the causes of the formation of cohesion problems.In the part of "solving problems",the author proposes corresponding cohesive suggestions for different subjects according to the problems raised and the reasons for their formation,and gives some teaching fragments and case designs of two specific cohesive contents.Finally,it is the generalization of the research results.In combination with the suggestion of "paying attention to improving students' discipline core quality",the research results of this paper are extended to the application of definite integral in a lesson,and a detailed teaching design is given.