Re: The unimportance of decimal arithmetic ability

On 21 Dec 2006 12:23:45 -0500, hrubin@xxxxxxxxxxxxxxxxxxxx (Herman
Rubin) fed this fish to the penguins:

In article <1166718352.507422.89310@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Pubkeybreaker <Robert_silverman@xxxxxxxxxxxx> wrote:

john wrote:
Thanks to those who have posted helpful informatin.

And, yes, GRE is for entry into graduate school and this is from
exercise section of general GRE which is required for all grad school.


In my case, I haven't done that level of arithematics since I was 12.

The "level of arithematics (sic)" is elementary school.
If someone can not do elementary school arithmetic, then that person
does not belong in grad school regardless of the field of study.

Nonsense. Being able to do arithmetic is a convenience,
and not an indication of any understanding of mathematics.
While arithmetic is part of mathematics, the ability to
carry out the manipulations with decimal strings is not.

How many good mathematicians and scientists do we lose
because they are poor at decimal arithmetic? And
conversely, how many who have no understanding get into
our advanced college classes because they are good at
computation and have no understanding of concepts?
At least the old algebra course (before it was watered
down) and the old "Euclid" course weeded some of them
out, but these courses often are not even available.

I always remember a lesson I learned from the introduction to Spivak's
calculus text. He had a sentence there, apropos the Stokes theorem and
its proof, to the effect that what matters are the concepts. The
concepts should be complex while the proofs should be "trivial". The
cognitive load shifts from the theorems to the definitions. Once one
masters the concepts, the proofs should become obvious (exagerating
somewhat, but you get the idea).

This is somewhat akin to the general thumbrule in programming, where
the complexity is shifted from the code to the data: compare a switch
statement (or an if-elif) with an array of function pointers or the OO
programming elaboration of this idea.

Best regards,
G. Rodrigues
.

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