摘要
文章从微积分发展史的角度考察了“无穷”概念的发展并讨论了其对数学教育的启示:微积分的教学中,相对于公式和计算技巧的教学,数学思想的教学应当加以突出与强调;记住概念和定理发展阶段的次序对教学实践具有指导意义;一开始就教授学生极限的严密化定义,从逻辑上讲是具有建构性的,但从教学上讲是毁灭性的;教师应当至少意识到非标准分析的基本思想和方法,并在合适的场合向学生传达这些信息。
The development of infinite concept is discussed from the history of calculus,so is the enlightenment to mathematical education.The study shows:the teaching of mathematical ideas should stand out compared to the formulas and techniques in teaching of calculus;It can guide the teaching to keep the order of the development stages in mind in discussing any concept or theory;To begin a calculus course with a rigorous definition of limit may be logically constructive,but pedagogically destructive;Teacher should at least aware of the elementary ideas and techniques of nonstandard calculus,and convey these to students at some point in mathematical education.
作者
王彩芬
傅海伦
WANG Cai-fen;FU Hai-lun(School of Mathematics and Statistics,Shandong Normal University,Jinan,370100,China;School of Mathematics and Statistics,Qingdao University,Qingdao,266071,China)
出处
《高等理科教育》
2019年第4期72-77,共6页
Higher Education of Sciences
基金
2017年教育部人文社会科学研究项目“数学质疑式教学模式创新与实效研究”(项目编号:17JA880020)
山东省教育科学“十二五”规划“高等教育数学教学专项”一般资助项目(项目编号:YBS15021)
关键词
无穷概念
微积分
极限
数学教育
数学史
infinite concept
calculus
limit
mathematics education
mathematics history
