A Comparative Study Of Univariate Function Integration And Related Contents In Chinese And American Calculus Textbooks

With the development of science and technology,the popularization rate of higher education has increased,and the reform and innovation of calculus as a basic course has received widespread attention.The compilation of teaching materials is the foundation of calculus reform.The author compares the calculus textbooks of China and the United States and hopes to have a clearer understanding of the strengths and weaknesses of the textbooks compiled by the two countries.This article selects "Calculus" edited by Zhu Laiyi(published by China Higher Education Press)and "Calculus"(published by John Wiley & Sons,Inc.)edited by Deborah Hughes-Hallett,Andrew M Gleason,etc.Functional integration and related content have been compared and studied from the macro and micro levels.This article raises two research questions: Macroscopically,what are the similarities and differences in the order and structure of the two editions of textbooks?On the micro level,what are the similarities and differences between the two editions of the teaching materials,the presentation of knowledge,the relevance of example questions,and the setting of question types? conclusion as below:(1)Macroscopically,the arrangement of "calculus" is linear;"Calculus" is spiral;the course width of the two editions of textbooks is about the same.The arrangement of "calculus" is compact and emphasizes the completeness of the nature theorem.The layout is loose;in the depth of the course,the contents of the two editions of the textbook have their own characteristics."Calculus" is mainly based on formal definitions,and the concepts,properties,and theorems of definite integrals are highly abstract,with special emphasis on the rigor and precision of mathematical language.Through the orderly arrangement of concepts such as definition,lemma,theorem,and inference,a complete theoretical framework is constructed,which reflects the rigor and integrity of the textbook theoretical system."Calculus" is mainly based on descriptive definitions.The goal is to allow students to understand the nature of therelevant theorem of the nature of the concept.It attaches more importance to the introduction of mathematical ideas,rather than being rigorous in logic.(2)On the micro level,there is no obvious difference between the two editions of textbooks in the way of concept introduction;the use of "calculus" charts is more abundant,which is conducive to the students' understanding of the image of basic mathematical concepts;for the relevance of example exercises,"calculus" attaches great importance to the students' procedural memory of the process of solving problems,and the degree of understanding and training of the inherent nature of mathematics is weak,while "calculus" attaches great importance to the rigor of logic It pays attention to the cultivation of students' logical thinking and the internal nature of knowledge points;in the setting of questions,calculus pays more attention to the memory and understanding of concepts,and the number of training exercises for the ability of logical reasoning is less,while calculus pays more attention to the cultivation of students' ability of calculation and logical reasoning,and understands the internal nature of mathematics,and the number of exercises related to the understanding of concepts is less.