A Comparative Study Of Limits And Derivative In Chinese And American College Calculus Textbooks

Along with the gradually popularization of higher education, the reform and development of calculus, has become the focus of international mathematics educators.How to correctly understand and improve the teaching materials become a big problem in mathematics education.This study aims to in-depth understanding of the present of calculus textbooks,through the comparison of mathematics textbooks between China and the United States.This study selected the Chinese textbook——?Calculus?,published by higher education press,written by Zhu,and the American textbook——?Calculus?,published by the United States John Wiley&Sons,Inc,written by Deborah hughes-hallett, Andrew M Gleason, William G McCallum e.t. as the research objects;The author has carried on the comparative study in limit and derivative part between the two versions ,both from the macroscopic and microscopic angles,and then the author combines Jun Chai's research conclusions about the college calculus and this textbook comparison,aiming to deeply understand the present of calculus textbooks.The aim of this study is to answer the three questions: what is the similarities and differences between the two versions in the macro view?In the micro level,what's the similarities and differences between the two versions?How dose the differences in calculus teaching materials between China and the United States,impact the college students calculus test results?After careful comparison and data analysis,we can get the following conclusions:(1) the macro level, the Chinese textbook arrange teaching material mainly in line,while the American textbook arrange teaching material mainly in spiral;On the breadth of the textbook, the Chinese textbook showed the characteristics of "wide and tight", and the American textbook is "complex and special";On the depth of the course, the depth of American textbook is significantly lower than our country;On the course of time, the calculus course of time is almost no difference;On the difficulty of mathematical problems, problems in calculus teaching material (including examples and exercises) the difficulty of the comprehensive index is higher than the American calculus textbooks.From a specific perspective, the difficulty of the Chinese teaching material in the demand of "cognitive", "inference" and "knowledge level" are higher;While the American textbook's the "background" level is higher than Chinese.(2) the micro level, the edition teaching material is in rigorous logic;the math problems is difficult ;and the cognitive level the demand is higher, concept is given priority to with direct import, the use of graphs and use of information technology are relatively less;The American textbook pay more attention to the concept of memory and comprehension, attach importance to the cultivation of mathematical intuition and basic understanding of students, the difficulty of the relevant mathematical problem is small, various forms, charts, and the use of information technology are rich.(3) by comparing the teaching material differences and test results,we found that students grasp the materials given in the body better;Students master the contents putting longer in the textbooks better;Students contact with the content learned before can make great progress soon.