The Comparative Research On The Content Of Probability In High School Mathematics Textbooks Between China And The United States

With the continuous acceleration of the global economic culture and international education process,the exchange and cooperation of mathematics education in the world has become increasingly close,and the comparison between mathematics education in the international are pushed to the new topic of education research.Due to the cultural differences between the eastern and western regions,the direction of mathematics curriculum comparison is also different.As a representative country in Eastern education,China has actively followed the pace of development of the times,and has achieved more research results in the field of comparative education.It is hoped that by drawing on and absorbing the research of other countries,it can enlighten the development of education in our country.The representative of Western education is the United States,and the study of comparative education in the United States is also endless.As the medium of school education and teaching,textbook plays an important role in school education.It is not only the blueprint for teacher teaching,but also an important carrier for student development.It is also an important resource for achieving the goals of mathematics curriculum and implementing classroom teaching.Whether it is the preparation of textbooks or the difficulty of the course materials,it has a great impact on the development of students.To a certain extent,research materials need to rely on curriculum standards,and curriculum standards have a guiding role in the implementation of teaching materials.In recent years,both China and the United States have carried out bold reforms and active attempts in the education curriculum.In December 2017,the "Mathematics Curriculum Standards for Senior High Schools(2017 Edition)" issued by the Ministry of Education of China(hereinafter referred to as the "course standard"),In the curriculum standard,data analysis is regarded as one of the six core qualities of senior high school mathematics.Statistics and probability,as tools of data analysis,play an important role in senior high school mathematics learning.In the comparative study of mathematics textbooks,there are relatively few comparisons between Chinese and American high school mathematicstextbooks.Therefore,this paper selects the probability parts of high school mathematics textbooks in China and the United States to compare them,which shows that the significance is significant.According to this,this article takes China's "Experimental Textbook of Curriculum Standards for Senior High Schools(" A " Edition)"(hereinafter referred to as "People's Education A Edition").And the CPMP(Core-Plus Mathematics Project)high school mathematics textbook for the United States(hereinafter referred to as "CPMP").Combined with China's "Course Standards" and "American Common Core State Standards for Mathematics".The following research contents were determined,(1)The similarities and differences of the curriculum requirements of the Chinese and the United States curriculum standards for the probabilistic part;(2)The similarities and differences between the probabilistic part of the Chinese and the United States knowledge structure and knowledge presentation;(3)Based on the existing textbook comprehensive difficulty model the content breadth,content depth and difficulty of the curriculum of the probability parts of the two textbooks are explored.The difficulty of the exercises in the two countries is compared and analyzed through the difficulty comparison model.Through the research methods of literature analysis,comparative analysis and statistical analysis,the author finally draws the following conclusions:(1)In the teaching requirements of the curriculum standards,the course standard of both countries attach importance to probabilistic literacy,closely combine statistics and probability,and focus on the combination of modern technology;but Chinese course standard emphasizes the understanding of knowledge,while the United States pays more attention to learning.The process of knowledge and the application of knowledge also have their own characteristics in practice and knowledge development.(2)In terms of knowledge structure and knowledge presentation,the order and content of knowledge concepts are not much different,and they all conform to the cognitive level of students according to the principle of spiraling upwards.The content of the textbooks in China is more detailed and the content is gradual.The CPMP textbooks in the United States run through all the time,and the number of exercises is large.(3)In the breadth of course content,China's teaching materials are five more than CPMP textbooks;in terms of content depth,China's textbooks are 29,CPMP textbooks are 23,so the depth of Chinese textbooks is greater;in the overall curriculum difficulty,through model calculation It is 1.055,0.445,which shows that the comprehensive difficulty of the curriculum of Chinese textbooks is higher than that of CPMP textbooks.In terms of problem difficulty,background level and mathematical cognition,CPMP is on Chinese textbooks.In terms of reasoning,the two countries are almost identical.In terms of computing level and knowledge content,Chinese textbooks should exceed CPMP textbooks.The example exercises of probabilistic content are very close in difficulty and are almost the same.Based on the above conclusions,the author proposes the following four points of textbook writing:(1)Strengthen the application of knowledge and the cultivation of probabilistic reasoning ability;(2)The teaching materials and exercises are moderately difficult,teach students in accordance with their aptitude;(3)Focus on the diversity of problem setting;(4)Strengthen integration with information technology.Through comparative analysis,we can find the differences between the Chinese and the United States probabilistic textbooks,learn from others' strong points and close the gap,advance with the times,increase our horizons,and combine their own advantages.To a certain extent,we should provide reasonable suggestions for curriculum reform and textbook writing in China,hoping to prepare for the textbooks in China.