A Comparative Study Of The Complex Number Of Senior High Schools In China,Britain And Australia Based On ISM

International exchange is becoming more and more extensive,and the exchange of mathematics education among countries has become an important part of the internationalization of mathematics education.The selection and adjustment of mathematics content is an important part of curriculum reform in various countries.Since the curriculum reform,the content of complex number in senior high school mathematics in China has changed greatly,which has aroused great controversy from all walks of life.As the carrier of curriculum standard,textbook's teaching content arrangement sequence,core content selection and system structure setting are all very important aspects to measure the quality of textbook.Britain and Australia are countries with characteristics in the field of basic education.Therefore,the comparative study of Chinese,English and Australian mathematics textbooks in this paper has a high theoretical value and practical significance.This paper introduces the interpretive structural model(ISM).Based on “ISM” method,this paper takes the knowledge of “complex number” in Chinese senior high school mathematics textbook elective 2-2,British senior high school mathematics textbook CIE and Australian senior high school mathematics textbook IB as the research object,and uses literature analysis,comparative research,statistical analysis and other methods to carry out a comparative study on the content of "complex number" in Chinese English and Australian mathematics textbooks.First of all,the literature review method is used to analyze the research status of applying ism in textbook comparison at home and abroad;Secondly,the paper uses ISM to compare and analyze the actual arrangement order of the “plural”content in the PEP edition,the CIE edition in the UK and the IB edition in Australia;Then,based on ISM,construct the element level directed graph of “complex” content,and analyze the characteristics of the three editions of textbook content from the aspects of core element selection,basic element arrangement,the highest goal selection and the formation of relationship between elements;Finally,according to the element level directed graph,the improvement of teaching method and the guidance of learning method are carried out.The results show that there are some differences in the content of plural in the three editions of textbooks:(1)In terms of the selection of core elements: the number of core elements of the people'seducation version is less,the content is relatively simple,the number of CIE and IB versions is more,and the content is more substantial;(2)In terms of the arrangement of basic elements: the three editions of textbooks are introduced with the concept of “complex number” as the basic element,but they have their own characteristics in the way of introduction.Both human education edition and IB are introduced from mathematics itself as the concept of complex number,but CIE edition attaches great importance to the formation process of students' knowledge,and guides students to understand the expanded mathematical knowledge of number department from the perspective of mathematical history;(3)In the aspect of the selection of the highest goal: the PEP version is more basic,the CIE version is located at the geometric application level of “complex number”,while the IB version is more in-depth,which is mainly located at the application of “complex number”and “Euler's theorem of complex number”;(4)In the aspect of the relationship between the elements: the relationship between the elements of the people's education version is more in line with the students' recent development area,and the relationship between the elements of CIE and IB version is relatively jumping,so the arrangement of elements is more difficult.The teaching method and learning method improved by using element level directed graph are better improved,and effective enlightenment is put forward.