A Comparative Study Of AP Calculus Teaching Materials Between China And America

The reform of the high school mathematics curriculum standard brings the Advanced Placement(AP)course into the secondary course of high school mathematics elective course,which makes "the compulsory + elective 1 +AP course" as an integrated curriculum.The AP course materials in China are in the embryonic stage,and the lack of teaching materials is one of the important factors that restrict the promotion and implementation of the AP course in China.As a hot course in the AP course system,the research and development of the supporting materials are the important topics of the subject research.The domestic related research content mainly focuses on the University calculus teaching materials,the calculus content of high school mathematics textbooks and the comparison of the high school calculus curriculum.At present,there is no study on comparative analysis of calculus textbooks between China and foreign country.Through the comparison of the AP Calculus teaching materials between China and America,we can understand the characteristics and advantages of the American AP calculus teaching materials,also can absorb the experience and advantages of foreign excellent textbooks more quickly,and provide valuable reference for the in-depth study and development of the AP Calculus teaching materials in our country.This paper is based on the CAP series of Chinese Higher Education Publishing House "calculus" and "Rogawski's Calculus for AP: Early Transcendentals and Second Edition" compiled by Professor Jon Rogawski in the United States.The specific research problems are as follows:(1)Compared with the overall structure,content setting of the teaching materials,arrange the sequence,then analyze its similarities and differences.(2)To compare the presentation styles of textbooks,including the presentation of concepts and the form of integration of mathematical history and culture.(3)To compare the layout of teaching materials,and excavate the different styles and characteristics of two versions of textbooks in visual presentation.Through comparative analysis,the following conclusions can be drawn:(1)the overall knowledge structure: the knowledge of Chinese and American two edition textbooks is the same.The Chinese version focuses on "function preparation knowledge","limit and continuity","derivative and differential".The American version focuses on "integration and its application" and "other expanding knowledge".(2)content setting and arrangement sequence: Chinese version linear arrangement,American version of spiral up arrangement;The Chinese version pays attention to the integrity of the concept system;the American edition pays attention to the application of knowledge;The organization and arrangement of the contents of the Chinese version is high,the organization and arrangement in the American edition chapters are meticulously distributed;the American Edition More attention is paid to the combination of information technology.(3)column style: the Chinese version of the section column is single,the American version of the column is rich and diverse and humanized.It attaches great importance to the permeation of the history and culture of mathematics and the stratified design of the exercises.(4)concept presentation: the Chinese version pays attention to the objectivity of mathematical knowledge,the American edition pays attention to the cognitive understanding of the students,emphasizes the application of the "numerical" and "graphical" methods;the Chinese version has a high degree of formalization,and the United States is based on descriptive definition;the concept organization of the Chinese edition is classified by parallel type,the core concepts of American edition are arranged in a linear type.(5)mathematics culture: the number,content distribution and application level of American edition of mathematical culture are all higher than that of Chinese edition.(4)layout style: the Chinese version is mainly written in characters,and the American version is equally important.The American version has the ingenious design and the number is much higher than the Chinese version.According to the conclusion of the study,the following suggestions are put forward to improve the Chinese edition of AP calculus teaching materials:(1)enrich the setting of the column style;(2)strengthen the application of the calculus knowledge,pay attention to the infiltration of mathematical culture;(3)concept processing pay attention to the concept of understanding;(4)enhance the layout and illustration design level;(5)to strengthen the integration of information technology and calculus...