摘要
关于微分的教学,从认知心理学角度建议作如下调整：（1）将教材上＂函数的微分＂这一节放到下一章＂微分中值定理与导数的应用＂的＂泰勒公式＂这一节之后.导数一章专讲导数概念和求导法则.（2）将微分和泰勒公式在近似计算中的应用综合在一起,单独立一节,放在＂函数的微分＂这一节之后,突出近似计算的实际意义,便于比较.关于微分概念,要把握如下3个要点：（1）是函数增量的一级近似;（2）用导数和自变量增量的乘积表示;（3）局域性.一般说来,只有在自变量增量很小的情况下,函数的微分才是函数增量的主部,△y ≈dy,才有实际意义.
Based on the relevant laws of cognitive psychology, we suggest adjusting the traditional differential teaching method as follows： （1） Move the section of ＂differential of functions＂ to the position behind the section of ＂Taylor＇s formula＂ in the next chapter of ＂differential mean value theorem and applications of derivative＂ and only preserve the concept of derivative and derivation rules in the chapter of derivative. （2）Integrate the contents of differential and Taylor＇s formula with the applications of approximate calculation as an independent section and put this new section to the position behind the section of ＂differential of function＂. This adjustment highlights the practical significance of approximate calculation. In the process of teaching the differential concept, we should pay more attention to three key points： （1） The differential is the first-order approximation of a functional increment; （2） The differential can be described as the product of derivative and the independent variable＇s increment; （3） The differential＇s property of locality. In general, only on the condition of a small increment of an independent variable occurred, the differential of a function is the main part of the increment of this function, namely △y ≈dy.
出处
《数学教育学报》
北大核心
2012年第4期76-78,共3页
Journal of Mathematics Education
基金
教育部、财政部第四批高等学校特色专业建设点项目——物理学特色专业建设点(TS11635)
关键词
认知心理学
微分概念
教学
cognitive psychology
differential concept
teaching
