A Comparative Study Of Calculus Textbooks Between Chinese And American Universities

According to the report of the 19 th National Congress of the Communist Party of China,"accelerate the construction of first-class universities and disciplines,and realize the connotative development of higher education",which means that the reform of higher education has reached the stage of "comprehensive construction and internal decoration".As a wide range of basic courses in the university stage,the reform and development of calculus naturally has a significant impact on higher education.The purpose of this paper is to understand the characteristics and shortcomings of the two textbooks through the comparison of calculus textbooks between China and the United States,so as to provide some references for the compilation and reform of calculus textbooks in China.This article selects "Calculus"(third edition)("Higher Education 3rd Edition")edited by Professor Zhu Laiyi of Renmin University of China and "calculus"(Fifth Edition)("Hughes-Hallett 5th Edition")edited by Hughes-Hallett et al.as the research object,and make a comparative study of the content of the univariate between the two textbooks from the macro and micro perspectives: on the macro level,it compares the similarities and differences between the two textbooks in terms of compilation style,layout design,main content,arrangement order,content breadth and content depth;on the micro level,it compares the similarities and differences between the mathematical concepts and propositions contained in the two textbooks in terms of Import method,representation mode and application,it also compares the similarities and differences between the two textbooks in terms of the number of example exercises,the setting of question types and the relevance of example exercises?Through comparative analysis and quantitative analysis,this paper mainly draws the following conclusions:(1)The third edition of higher education textbook is mainly arranged in a straight line,and pays more attention to the integrity and logicality of knowledge structure,while the fifth edition of Hughes-Hallett textbook is mainly arranged in a spiral way,paying more attention to the cognitive level of students.(2)In terms of content breadth and content depth,the third edition of higher education textbook presents the characteristics of "wide and deep",while the fifth edition of Hughes-Hallett textbook presents the characteristics of "fine and shallow";(3)the introduction of the concept of the third edition of higher education textbook is simple,which requires high abstract thinking ability of students,Hughes-Hallett The concept of the 5th edition of textbooks is introduced in detail and well expressed by "four rules";(4)most of the mathematical propositions in the 3rd edition of higher education textbooks are directly given,while the 5th edition of Hughes-Hallett textbooks focuses on exploration and analysis;(5)the 3rd edition of Higher Education textbooks focuses on logical proof of propositions,Hughes-Hallett In the fifth edition,most of the textbooks are explained reasonably and appear in the form of exercises after class;(6)Hughes-Hallett The number of exercises in the fifth edition of the textbook is the most,and mainly focuses on concept understanding,calculation and practical operation,while the exercises in the third edition of the textbook of higher education are mainly about calculation and reasoning;(7)the LPR and GPR are the most and is the least in the third edition of the textbook of higher education,which focuses on cultivating students' ability to think independently;the is and LPR are the most and GPR is the least in the fifth edition of Hughes-Hallett textbook,which focuses on cultivating students' confidence in learning mathematics.