[Roccus]

I use several different 'short-cuts' when doing math in my head. These are tricks I learned, on my own, long after finishing school. I do not think I would have been able to do so had I not learned, and understood the old (early 50s) way. The fact that we were schooled to 'prove' our answers went a long way toward understanding the machinations of numbers.

My .02

[Alia]

You are right!

CA schools still demand students PROVE their answers. It has to be essays, based upon the type of rainforest math that is taught. Essays. I remember learning to PROVE my answers.

And, unfortunately, many of the newer math means require essay answers because the newer means are based upon assumptions of provable math. True, these newer means are quicker; but require a tome to prove. My argument with the new math agents in schools is that unless the students have had TRADITIONAL math, they are and will be unable to explain/PROVE the newer math!

It's like writing macro's. Macros employ an interface (compressed translator) which shortens the verbiage required to write a routine in long-hand programming.

New math provides the macro language, making things move fast. But to fully prove a "macro", one is at a loss unless they also understand the initial, primary programming language(s).