The Study Of Curricular Progression For Number And Operation Content In School Mathematics Curriculum

In recent years,various countries around the world have begun to set off a wave of curriculum reform,and curriculum standards have been constantly revised.This paper is a research achievement of a major project of Shanghai Education Science Research in 2015: Effective Design of Mathematics Textbooks for Primary and Secondary Schools(Project No.D1508).Subproject 1-"Top-level Design of the Main Line of Content Development of Mathematics Courses for Primary and Secondary Schools".Because the content of number and operation is very important in mathematics learning of primary and secondary schools,this paper studies the main line of curriculum development of "number and operation" in mathematics curriculum of primary and secondary schools.The research questions in this paper are as follows:(1)What are the core contents of mathematics and operation in primary and secondary schools?(2)How does the core content of number and operation develop in the curriculum of primary and secondary schools?The research method of this paper belongs to qualitative research.There are two main research methods involved: text comparative analysis and expert interviews.The comparative analysis of the texts mainly includes six curriculum standards of China(China and Shanghai),the United Kingdom,the United States,Singapore and Australia.After comparing and analyzing the curriculum standards of these countries,we find out their similarities and differences.Then we preliminarily determine the quasi-core content of number and operation and the main line of Quasi-development of number and operation.After that,we set up interview questions in valuable places and consult experts for their opinions.A total of three experts were interviewed.They are associate professors of algebraic geometry in the School of Mathematical Sciences,East China Normal University,teachers and researchers in a district of Shanghai,and professors of elementary mathematics education in East China Normal University.After expert interviews,the core content of number and operation has been redefined and the development thread of number and operation has been revised.The conclusions of this paper are as follows:(1)The core contents of number and median include integer,fraction,decimal,rational number,real number and complex number.The core content of operation mainly includes four operations,multiplication operation and square operation.See Table 17 for details.(2)The main line of development of number and computation includes bright and dark lines.Among them,the open lines are mainly sorted out according to the actual content of number and operation,and presented in the form of hexagonal graphs,as detailed in Figure 11.Dark line 1 is based on the combination of number and shape.It is arranged according to the number and actual figure,number and plane figure and the ascending trajectory of number and coordinate system.It reflects the important role of the combination of number and shape in the learning of number and operation.See Figure 12 for details.Dark line 2 is presented from the development of arithmetic thinking level,and the four arithmetic thinking levels are arranged in order from low to high.Combining the actual content of number and arithmetic and the specific expression of different arithmetic thinking,this paper illustrates the corresponding level of different expression,as shown in Figures 13 and 19.This paper mainly summarizes and presents the core content and the main line of development of mathematics curriculum in primary and secondary schools,hoping to provide some design ideas for the compilation of mathematics curriculum standards and textbooks in primary and secondary schools,at the same time,it can also help mathematics teachers to understand this part of the content more comprehensively.