In article <ehrebeniuk-9D4DF2.22183130042008@[EMAIL PROTECTED]
>,
Chookie <ehrebeniuk@[EMAIL PROTECTED]
> wrote:
>In article <fv3agm$3m8q@[EMAIL PROTECTED]
>,
> hrubin@[EMAIL PROTECTED]
(Herman Rubin) wrote:
>> As the children grow older, and get taught mainly by
>> memorization and routine, this ability gets smothered,
>> and it is difficult to reawaken later.
>Which is why children shouldn't be taught maths by memorisation.
>Of course, I *would* say that; it was never my strong point!
It was always a strong point with me, and yet I did not see
the im****tance of thinking conceptually, instead of about
the mechanics or proofs, until quite late. Not all good
mathematicians develop this; it is quite possible to be a
good theorem prover, even of im****tant theorems, without
it, but most develop some sort of conceptual understanding.
One version of this is the so-called "geometric intuition",
at which I was never very strong, while I was at what could
be called "proof intuition". But for the person using
mathematics for other purposes, the various intuitions are
im****tant, and the "counting numbers" have MANY conceptual
intuitions. The conceptual intuitions, which are close to
being formal, CAN be taught, and the manipulations and
proofs based on them.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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