The Study Of Main Line For Function Content In School Mathematics Curriculum

Many countries have stepped up the pace of curriculum reform in the 21 century.National curriculum standards and Shanghai curriculum standard in China are being revised.This paper is the periodicity research result of the subtopics-one "the top design of main line of mathematics curriculum content in primary and secondary schools",which belongs to the major research project of educational science filed in Shanghai 2015 "effective design of mathematics textbooks in primary and secondary schools(No.D1508)".This paper focuses on the main line of "function" for the importance of function in primary and secondary schools especially in the secondary stage.The research question overall in this paper is:how does the function happen and develop in primary and secondary schools?In detail,there are two research questions:(1)what are the core content of function in school mathematics education?(2)How spread the core contents of function in school mathematics curriculum?This paper employed the qualitative research method,including text analysis,comparison and interview.The texts include the United States,the UK,Singapore,Australia,the national of China and Shanghai,a total of six countries curriculum standards.This paper interviewed 11 experts,whose identity covering the professors in Department of Mathematics(different research direction:analysis,algebra,geometry),the professors researching mathematics education,the textbook writers and high school mathematics research staff.The interview was used to revise the main line of function with semi-structured interview outline.The construction of the main line is based on the students' cognition,curriculum theory,mathematical logic and a series of empirical researches;it can become more and more consummate.The results of this study are as follows:question(1)the core content of function in school mathematics education is:the concept of function,the property of function,the application and modeling of function,and this three core content spread with function.The answer to question(2):Function in school mathematics education is spread as "the foundation of function?the variable view of function definition?function(1)?its propety?its application?function(2)?its propety ? its application?……the corresponding view of function definition?the basic properties?function(3)?its propety?its application?function(4)?its propety?its application?……" based on the question(1),the mathematical logic and the students' cognition.And the main line contains the unit"six basic elementary functions?its propety?its application".For the detail information please see the graph 19 "the main line for function content in school mathematics curriculum",from which we can see that the change in the content of the function from left to right,from the bottom to top represents the development of the function from simple to complex over time.At the same time,this study also explores the content needed before learning the.function and the mathematical competencies and ideas in fuction content.This study clarifies the content main line of function in the basic education and provides the design ideas for writing the mathematics curriculum standard and the textbooks.The research findings in this paper can help math teachers stand in a high perspective to grasp the main design of the function in textbook,find the emphasis of the function and give reasonable arrangements for function content.