A Comparative Study On The Contents Of "Ratio And Proportion" In Mathematics Textbooks For Primary Schools In China And The United States

The concept of "ratio and proportion" is the basis of mathematics and is also very important in many other fields of knowledge.Understanding these concepts and using their skills and abilities contribute to the development of mathematical awareness.Mathematics textbooks are one of the important components of the mathematics curriculum.They are the main educational tools and materials for the implementation of mathematics curriculum and are of vital importance throughout the education system.Therefore,through the comparative study of mathematics textbooks,especially the international comparative study of mathematics textbooks,drawing lessons from the excellence of other countries’ mathematics textbooks,it has important practical significance for the development of mathematics curriculum in China.This study selects the Chinese People’s Education Press and the American California version of the primary school mathematics textbooks for a static comparative study.This study analyzes and contrasts the content of "ratio and proportion" of the two versions of the textbook: it consists of two parts: The first part is the comparison of the ratio and proportion of the two editions of textbooks,including the comparison and analysis of the compilation basis,content arrangement,organizational structure,knowledge point presentation and text characteristics of the textbooks of the two countries.The purpose is to fundamentally analyze the design concepts of ratio and proportion in the teaching materials and study the comparison of teaching materials in the two countries and the presentation of the content of "ratio and proportional".The second part is the comparison of the examples and exercises of the "ratio and proportion".The purpose is to analyze whether the examples and exercises in the textbooks in both countries are helpful to stimulate students’ interest and whether they can help improve the students’ cognitive ability.The research results of this paper show that:(1)In the preparation of teaching materials for the two countries,the comparison of Chinese mathematics curriculum standards and the processing of proportional content requirements is relatively simple,while the American curriculum standards are more detailed.However,in terms of design concepts,the curriculum standards in both countries are both focused on improving the students’ level of mathematics thinking,and also focusing on the use of ratios and proportions to solve practical problems in real life.(2)In terms of the content of "ratio and proportion" in the textbooks of the two countries,for the concept of ratio,the California version of the textbook gives a more appropriate concept;for the application of ratio,the California version of the textbook is more comprehensive than the type of application;for the basic nature of the proportion,thetwo versions of the textbook use different methods of reasoning.(3)With regard to the writing features of examples,the situation of examples in the two countries is relatively simple.The compilation of examples of Chinese textbooks focuses on the assignment and inspiration of students.(4)In terms of the cognitive complexity of exercises,the breadth and depth of cognitive complexity in Chinese textbooks is higher than in the United States.It can be said that Chinese textbooks are more challenging for students.Based on the results of the comparative study,the author made the following suggestions:(1)The content and requirements of the curriculum standards can be further elaborated.(2)Clear the concept of ratio and reveals the mathematical nature of ratio.(3)increase the types of questions in the application of ratio to enhance students’ understanding of the relationship expressed by "ratio".(4)Pay attention to the logic and rigor of reasoning about the basic properties of proportion.(5)The organization of the content can be appropriately carried out in a spiral manner.(6)enhance the diversity of example situations.(7)The design of textbook exercises should focus on the development of students’ high cognitive level.