| The consciousness of "Elementary Mathematics from a High Point of View" advocated by mathematician Felix Klein has had a wide-ranging and far-reaching impact on the mathematics education community.Middle school mathematics and advanced mathematics are interdependent and intertwined.Middle school mathematics is the elementary and generalization of many concepts,propositions and theorems in advanced mathematics,and advanced mathematics is the deepening and expansion of middle school mathematics.The curriculum standards clearly point out that mathematics teachers need to master advanced mathematics knowledge closely related to middle school mathematics,establish a complete mathematical knowledge system,clarify the occurrence and development process of knowledge and the mathematical thinking methods behind it,and be able to infiltrate it into the teaching process,which is in order to implement the core literacy of students in mathematics.It can be seen the importance and necessity of high point of view for mathematics teachers.Mathematics normal students are the main force of future mathematics teachers,therefore,high viewpoint knowledge and ability are also crucial for mathematics normal students.Function is an important part of middle school mathematics curriculum.It runs through the whole process of mathematics learning,contains rich mathematical thinking methods,and has a wide range of practical applications.Based on the above analysis,this research takes "The Main Line of Function Development from the High Point of View" as the research theme,selects mathematics normal students as the research object,and mainly studies the following two issues:(1)What is the main development line of functions in the content of mathematics curriculum in primary school?secondary school?university? How to reflect a high point of view in mathematics?(2)Can mathematics normal students use high viewpoints to view and deal with function content and problems? What are the deficiencies?This study uses text analysis,testing and interview methods to conduct research.The text includes textbooks and curriculum standards for primary and secondary schools,textbooks and training programs for college mathematics majors,and books related to high viewpoints.The test paper is designed on the basis of text analysis,and mainly examines normal students' functional high point of view ability and related mathematics core literacy.The interview outline is compiled based on text analysis and testing.Semi-structured interviews are used to further understand the current situation and deficiencies of normal students' ability to function high opinion.The final conclusions of this paper are as follows:For question 1,this study uses text analysis to obtain the main line of function development under high viewpoints,which is divided into bright lines and dark lines.The bright line is the order of development of function knowledge teaching,and the dark line refers to the process of infiltration and development of the four core literacy of mathematical abstraction,logical reasoning,intuitive imagination and mathematical modeling that are closely related to the function teaching process.Each line of development follows the timeline of primary school ? middle school ?university.Functions appear in the form of "patterns" in primary school,including graphic patterns and digital patterns.The learning of functions in middle school follows "function concept ? specific function ? image and properties ?application" path.The study of university functions is divided into two perspectives:theoretical and applied.Theoretical study mainly involves macroscopic and microscopic analysis of the internal knowledge and structure of functions,and explores the relationship between functions and other branches of mathematics and other disciplines.Applied learning mainly includes mathematical modeling activities and the learning of drawing software such as Geo Gebra.For question 2,this study adopts the test method and interview method.The study found that mathematics normal students have improved and developed in three aspects: subject higher knowledge,subject structure knowledge and subject application knowledge,and there are certain differences in the four core literacy of mathematical abstraction,intuitive imagination,logical reasoning and mathematical modeling.Among them,the literacy of intuitive imagination and mathematical modeling are relatively good,while the literacy of logical reasoning and mathematical abstraction are still lacking.The study found the following deficiencies in the function content of normal students linking advanced mathematics and middle school mathematics:(1)The foundation of university mathematics is not solid,and it is impossible to establish a complete mathematical knowledge system;(2)Inability to integrate abstract university function knowledge and concrete middle school function knowledge within the cognitive scope of students;(3)It is impossible to achieve a high degree of coordination between the teaching of high-level mathematical thinking methods and the teaching of problem-solving applications.On this basis,this study puts forward several suggestions that can improve normal students' high-perspective ability:(1)Lay a solid theoretical foundation for college mathematics;(2)Read more mathematics journals,mathematics books,mathematics history,and broaden your perspective;(3)More communicating and learning with mathematics experts,mathematics education experts,and front-line mathematics teachers;(4)Consciously combine university theoretical knowledge with middle school teaching examples in the learning process.This study sorts out the main development lines of function content in the three stages of primary school?secondary school?university from the perspective of high point of view,and through tests and interviews to study the current situation of mathematics normal students' high point of view of function,analyze its existing problems,in order to provide reference for the improvement of functional high perspective ability and the development of mathematics core literacy of mathematics normal students. |
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