Research On Knowledge Cohesion Of Mathematics Textbooks In Primary And Secondary Schools

The problem of mathematical cohesion in primary and secondary schools has always been the concern of mathematical researchers and mathematical teaching workers.With the difference between the educational reform and the mathematics achievement of primary and secondary school students,and the basic cancellation of the system of repeating grades and entrance examination in the sixth grade of primary school in the relevant educational system,the connection between primary and secondary school mathematics becomes particularly important.And bridging education is a very large research object.Through the literature review,it is found that most researchers study the connection between teachers’ teaching and students’ learning.Teaching materials,teachers and students are the three elements of a lesson.The cohesion of teaching materials is directly related to teachers’ teaching and students’ learning,and the cohesion of teaching materials explores the essence of mathematics.This paper takes "number and algebra" as the research object.Through literature method,text analysis method,data processing method,comparative analysis method to analyze the research object.First of all,the paper makes a cohesive analysis of the curriculum objectives,knowledge requirements,curriculum contents and teaching Suggestions of mathematics curriculum standards for compulsory education(2011),and takes them as the standards for the cohesion of textbooks.From the cohesion analysis of course objectives and knowledge point requirements,it can be seen that as the level of course objectives and knowledge point requirements increases,the difficulty of knowledge point increases gradually.It can be concluded from the cohesion analysis of textbook compilation Suggestions that the difficulty of knowledge points should follow the scientific premise and adopt the principle of gradual progression and spiral,which further indicates that the difficulty of knowledge points should be gradually deepened in textbook compilation.From macroscopic and microscopic analysis of the course content,macroscopic analysis divides "number and algebra" into seven dimensions:the knowledge of number,the calculation of number,the understanding of formula,the calculation of formula,common quantities,equations and inequalities,and functions.On the micro level,the concrete connection point of "number and algebra" is:from arithmetic number to rational number,from number to formula,from formula to equation,inequality and function.Secondly,the connection between "number and algebra" is analyzed macroscopically and microscopically.The macroscopic quantitative analysis adopts the course difficulty model of shi ningzhong and kong fanzhe:N=αS/T+(1-α)G/T,and carries on the difficulty cohesion analysis from all grades and dimensions.Micro qualitative analysis of the overall knowledge structure of elementary and middle school mathematics cohesion analysis.And the "function" case analysis summary "number and algebra"convergence status:(1)In the human education edition "the number and the algebra" grade between the knowledge point comparable difficulty’s connection is good.Basically in line with the physical and mental development of students.According to the data analysis of knowledge difficulty in Beijing normal university edition,the difficulty fluctuates greatly among grades.The difficulty of the first learning paragraph increases gradually,the difficulty of the second learning paragraph decreases gradually,and the difficulty of the third learning paragraph increases gradually.As for the part of "number and algebra",there are some problems in the connection of the difficulty of knowledge points.(2)In the connection of the difficulty of knowledge points in all dimensions,the connection of the difficulty of "function" knowledge points in the human education edition needs to be strengthened,and the difficulty of "knowledge of Numbers" in the first learning paragraph is too large.In the edition of Beijing normal university,the difficulty connection of knowledge points among the small dimensions needs to be strengthened.(3)The sequence of knowledge points in textbooks needs to be considered.The order of knowledge structure of mathematics teaching materials in primary and secondary schools should be integrated,hierarchical and adaptive,which is the natural representation of scientific cohesion.Wholeness is the system of knowledge itself;Hierarchy is the principle of textbook compilation in the curriculum standard—spiral thinking is needed;Adaptability indicates that it is necessary to adapt to the law of students’ physical and mental development,so that students can better understand knowledge.(4)The absolutization of the spiral of cohesion of textbooks and knowledge.(5)The human education edition is more compact in the arrangement of knowledge in each dimension,while the Beijing normal university edition is relatively loose.Finally,the paper analyzes the causes and puts forward corresponding Suggestions according to the connection status.The reasons are summarized as follows:it is difficult to grasp the development of students’ mind,body and thinking,the lack of emphasis on the concept of "cohesion" in the curriculum standards,and the different emphases in the compilation of teaching materials.According to the current situation and reasons,the author puts forward corresponding Suggestions for textbook compilation and teachers:Suggestions for textbook compilation:(1)in accordance with students’ physical and mental development,the difficulty of "number and algebra" part of the math textbooks in primary and secondary schools spirals and Narrows the difficulty difference between the textbooks.(2)Study primary and secondary mathematics textbooks,in-depth analysis of knowledge structure cohesion.(3)In-depth classroom survey,reasonable and improve and optimize the knowledge structure of teaching materials.(4)We should pay attention to the introduction of mathematical culture and strengthen the cohesion of knowledge points.Suggestions for teacher:(1)study course standards and textbooks.(2)organize thematic teaching and review.