The Comparative Research On The Content Of Calculus In High School Mathematics Textbooks Between China And America

An international comparative study of mathematics textbooks is the hotspot of comparative education research. In this paper, I intend to compare the textbooks of two countries and find out how students’ innovation was cultivated by American education. Therefore, I would be able to give some advices of textbook compilation.The content of this study is calculus. Study selected high school mathematics textbooks developed by the university of Chiago school mathematics project—Integrated Mathematics (UCSMP textbooks), published by People’s Educatfon Press (PEP textbooks) and published by Beijing Normal University Press (BNU textbooks) as the object. Through a static comparative study, we could discover the differences and characteristics between these three editions, providing useful suggestions of textbook compilation on calculus.The findings are as follows:(1) The quantity of knowledge relating to calculus in American textbooks is more than that of China. The America textbooks emphasize a "wide" feature of knowledge points, while Chinese textbooks tend to be "narrow". In addition, the core knowledge points are "derivative" and "intergral", while the core konwledge points of Chinese textbooks are "limit" and "derivative."(2) From the external presentation on calculus, American textbooks distribute it in discrete sections, while Chinese textbooks arrange them in a section or continuous sections. As for the differences on internal structure of the calculus presented in the teaching materials between China and America is American textbooks describe the concept of the derivative after the meaning of derivatives but Chinese textbooks will introduce the concept of the derivative first and then come to the meaning of derivative. Also, American textbooks would like to technical term, such as "difference quotient", "Riemann Sum"etc. Only basic content were given in Chinese textbooks, and there are no use of technical term.(3) China and the America have their own characteristics on high school mathematics textbooks column settings. But the biggest disparity is that the America textbooks put "information technology" into mathematics learning and examination, while the "Information technology" of Chinese textbooks does not fully penetrate in calculus class.(4) We can see the high school mathematics textbook exercise in calculus difficulty settings from the America and the China, the level of exercises’ difficulty of latter is higher than former. Also, in setting the exericise of inquiry level, the two materials are mainly based on application and inquiry-based exercises, but the proportion of exploratory exercises in American textbooks is higher than that in Chinese textbooks.Based on the comparison above, it is recommended that our Chinese teaching materials should cover more on knowledges points of calculus reasonablely and the use of technical terms. Focusing on the combination of content and information technology and increasing the number of background exercises and inquiry exercises rationally.