中美高等数学教材内容的比较研究——以美国宾夕法尼亚九版和中国同济七版为例

Comparative Study on Advanced Mathematics Textbook’ Content between China and America ——Taking America Pennsylvania Ninth Edition Textbook and China Tongji Seventh Edition Textbook as Examples

采用定性和定量研究相结合的方法,对宾夕法尼亚九版和同济七版高等数学教材进行比较分析.研究发现：两版教材内容体系编排及难度差别较大.同济七版注重数学知识体系的系统性和数学理论的严密性,习题侧重纯数学问题;宾夕法尼亚九版注重数学直观、现实应用和学习指导,习题侧重有真实数据来源的实际问题.同济七版的总体难度高于宾夕法尼亚九版.在共有内容中,同济七版的知识点数量是宾夕法尼亚九版的1.3倍;同济七版在基础性知识、微分和积分3个知识团的内容深度与习题难度均高于宾夕法尼亚九版.建议在教材的编写中,体现高等数学在学科中的应用价值、适当增加直观呈现、注重数学知识的生成过程、融入学习指导.

Adopting the combination of qualitative and quantitative research methods, this article compared China advanced mathematics textbook with America. The study found that： there was a greater difference of the content system arrangement and difficulty between the two version textbooks. Tongji seventh edition paid attention to the system of mathematics knowledge and the rigor of mathematics theories, and the exercises focused on pure mathematics problem; Pennsylvania ninth edition paid attention to the mathematical intuition, realistic application and study guiding, and the exercises focused on the practical problems with real data source. Tongji seventh edition was higher than Pennsylvania ninth edition on the whole difficulty. The number of Tongji seventh edition＇s knowledge point was 1.3 times of Pennsylvania ninth edition in the common content. The contents depth and problems＇ difficulty of Tongji seventh edition was higher than Pennsylvania ninth edition in the knowledge groups of＂basic knowledge＂, ＂differential＂, and ＂integral＂. Based on the above analysis, it was suggested that we should pay attention to the embodiment of the advanced mathematics application value in different subjects, increase intuitive present appropriately, paid attention to the generation process of mathematics knowledge, and the learning guidance when compiling advanced mathematics teaching textbook.