[akikuchi]

The crux of the issue as I see it is an extension of what mathematics educators call "number sense." (http://en.wikipedia.org/wiki/Number_sense)

It seems from many of the other comments is that people recognize that performing exact mental-arithmetic calculations is rarely necessary; however, the more intuitive understanding of how numbers relate in magnitude etc. is critically important. Estimation is something that I think many of us take for granted, but that has some significant mental pre-requisites.

Interestingly, a growing branch of mathematics education has been working to explore whether the traditional rote memorization is the most effective way of instilling this more hollistic understanding of numbers. If people were interested, I could ask some educator friends for more up-to-date links/citations on this topic.