三次数学危机作为高等数学第一课的教学探索与实践  

Exploration and Practice of Three Crises in Mathematical Historyas the First Course of Advanced Mathematics

作　　者：董乐[1] 朱亚丽[1] 马迎宾[1] DONG Le;ZHU ya-li;MA Ying-bin(School of Mathematics and Information Sciences,Henan Normal University,Xinxiang Henan 453007,China)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453000

出　　处：《大学数学》2021年第3期72-77,共6页College Mathematics

基　　金：河南省高等教育教学改革研究与实践项目(2019SJGLX255);河南省教师教育课程改革研究重点项目(2019JSJYZD-010)。

摘　　要：三次数学危机是数学史上的重要事件,与高等数学的教学内容联系密切,但通常在教学中不被重视.通过分析给出了三次数学危机作为高等数学第一课的设计思路、实施方案和实践效果.实践证明,这一课打开了学生了解微积分脉络的窗口,培养了学生的质疑精神,在数学史观的熏陶下,使学生学好高等数学的同时,成为数学文化的承载者和传播者.Three crises of mathematics are important events in the history of mathematics,which is closely related to the teaching content of advances mathematics,but it is usually ignored in teaching.In this paper,we analyze and give the idea,steps,and practical effect of the three crises as the first course of advanced mathematics.It is proved that this course opens a window for students to understand the context of calculus and cultivates students’questioning spirit.Under the influence of the historical view of mathematics,students can learn higher mathematics well and become the bearers and disseminators of mathematics culture.

关 键 词：数学危机 高等数学 无穷小量 集合论 

分 类 号：O13[理学—数学] G642[理学—基础数学]