The Study Of The Consistency Of Concept Of Numbers And The Consistency Of Operation Of Numbers In Primary Schools Mathematics

In 2022,the Ministry of Education issued the Mathematics Curriculum Standards for Compulsory Education(2022 Edition),in which the two themes of “Number Understanding”and “Numbers’ Operation” were integrated into one theme of “Number and Operation”in the field of “Number and Algebra”,and the “consistency” was first proposed in the curriculum standards which essentially refer to the consistency of the number concept and the consistency number operation.What is the necessity of “the consistency of number concept” and “the consistency of number operation” in the content of mathematics curriculum of compulsory education? What is the truth of “the consistency”? How to explain the rationality of “the consistency” ? Is it feasible to implement “the consistency”? How to implement the consistency teaching? The research on the consistency is of great significance for the reform of primary school mathematics curriculum,textbooks and teaching.This study mainly focus on “the consistency of number concept” and “the consistency of number operation”.First part,this study analyses the necessity of proposing “consistency”through the research of the comparison of primary school mathematics textbooks at home and abroad in various countries,and the teaching practice of mathematics classroom in Chinese primary school.Theoretically,this study explains the connotation of “the consistency of number concept” and “the consistency of number operation” and the secondary indicators in primary school mathematics,and analyses the rationality of “the consistency” through expert consultation and teacher questionnaire.And on the basis of the analysis of the connotation of consistency,this study constructs the evaluation framework of students’ understanding of the consistency in primary school.The hierarchical level of the evaluation is carried out on the students in grade 6 of primary schools in a municipal school,a county-level school and a township school,and the appropriate teaching suggestions are put forward in combination with the students’ understanding.Practically,this study puts forward long-term modification idea and designs the teaching plan of the general stage,and carried out two teaching experiment research on the consistency in Beijing and Changchun,to study the acceptance of consistency teaching by primary school students,and give suggestions on the implementation of textbook revision.The main conclusions of this study are the following:First,“the consistency of number concept” and “the consistency of number operation”are the path to make mathematics curriculum structured and mathematical.It is found that the number and operation content of courses of integer,decimal and fraction in various countries are scattered,and the truth of number and the algorithm of operation of integer,decimals and fractions shows its own meanings,and the students’ understanding of math is fragmented without the systematic,mathematical and consistent understanding of math.This study believes that it is necessary to reform the content structure and teaching process which means to establish a reasonable teaching process to realize mathematization,so it is necessary to put forward “the consistency of number concept” and“the consistency of number operation” in primary school mathematics.Second,it is reasonable to put forward “the consistency of number concept” and “the consistency of number operation” of integers,fractions and decimals in primary school mathematics.This study clarifies the connotation of “the consistency of number concept” and“the consistency of number operation” of integers,fractions and decimals,and dimensions dividing:“the consistency of number concept” includes the consistency of the expressions form of numbers and the consistency of the size comparison;“the consistency of number operation” includes the consistency of addition and subtraction operations,the consistency of multiplication and division operation and the consistency of the law of operation.Mathematics education experts identifies the dimensions division and indicator description of “the consistency of number concept” and “the consistency of number operation”.Front-line teachers have a high degree of recognition and implementation of “the consistency ” which is in the promotion stage.Third,the study constructs the understanding evaluation framework of “the consistency”,including the content dimension and the level of understanding dimension.The content dimension includes “the consistency of number concept” and “the consistency of number operation”.The level of students’ understanding of “the consistency” is divided into three levels,namely,the representation level,the understanding level and the essence level.The results of student evaluation show that the three levels is basically reasonable.And the sixth grade students understand the consistency: the overall situation is common,the understanding of the number concept is better than the number operation.Fourth,the implement of “the consistency of number concept” and “the consistency of number operation” teaching is feasible.According to the principle of consistency,we can implement the consistent teaching of integer division and fractional division.The students in fifth grade can accept the consistent teaching,and can accept the conclusions obtained by logically reasoning and use them flexibly;In the general review stage of primary school mathematics,the consistency teaching can be carried out.Most students in sixth grade can understand and express the consistent expression of mathematical number and operation.Practice has proved the feasibility of the consistency teaching,and explored the path of the consistency teaching in primary school mathematics.