Mueen Nawaz <m.n### [at] ieeeorg> wrote:
> What she referred to as the new way of
> teaching it weren't simply heuristics - they always work

  I didn't claim the methods don't work. What I said that the methods
are only easily applicable to a small subset of all possible operations,
while the "classical" method can be equally easily applied to any operation
(only the length of the calculation varies, not its difficulty).

  If you want to calculate "223882819200394832*4802993291324" on paper,
the "old-fashioned" way is equally easy as calculating "244*25" (it just
takes longer, which is understandable, but is in no way harder). It would
be completely hopeless to calculate that with the "new methods".

  I don't disagree in teaching alternative methods for easy cases, such
as for example "25*9" (which can be thought of as, for example, "25 times
10 is 250, minus one time 25, which is 225"). However, I completely disagree
in not teaching the "mechanical" way of calculating multiplications (or
other operations), for the case when you really need to do so.

> I didn't really understand her complaints. She seemed to just have this 
> opinion that the old ways were better. For me, it's best to teach both.

  The old way is better in the sense that it allows you to calculate *any*
summation, multiplication and division (and even things like square roots),
regardless of the size of the operands. The "new methods" are very limited
and become very complex in many situations. Not teaching the classical way
is really stupid, IMO.

-- 
                                                          - Warp

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