
06134879
j
2013a.00206
Zeng, Jiuhong
Research on teaching the differential concept from the viewpoints of cognitive psychology.
J. Math. Educ. (Tianjin) 21, No. 4, 7678 (2012).
2012
Editorial Department of Journal of Mathematics Education c/o Tianjin Normal University, Tianjin
ZH
C30
I40
cognitive psychology
differential concept
teaching
Summary: 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 derivatives" and only preserve the concept of derivatives and derivation rules in the chapter of derivatives. (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 firstorder approximation of a functional increment. (2) The differential can be described as the product of a derivative and the independent variable's increment. (3) The differential's property of locality should be considered. 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 $\Delta y\approx dy$.