Okay, the whole thing makes more sense to me now that I've looked at
the Keith Devlin article It Ain't No Repeated Addition
(http://www.maa.org/devlin/devlin_06_08.html) and read the discussion
at
http://scienceblogs.com/goodmath/2008/07/teaching_multiplication_is_it.php.
I think Devlin goes overboard and comes to some false conclusions,
but his basic position makes more sense than I thought it did at
first. But he seems to be putting repeated addition in the same
category as telling children that a square is not a rectangle, or
that you can't subtract seven from five, and that kind of thing, and
I really don't think it's as dumb as that: it's more like a Newtonian
understanding that's enhanced, but not completely supplanted, by
Einsteinian physics.

On 6/28/09, Juliana wrote:
> On 6/26/09, Burt wrote:
>
>> I think the first thing you need to differentiate is between
>> the computational procedure and the concept. There is nothing
>> wrong with repeated addition as a computational procedure to
>> calculate the product of whole number multiplication. It is a
>> useful computational strategy, and it works with whole
>> numbers, but it is not the concept of multiplication.
>
> I see repeated addition quite the opposite way: nearly useless in
> computation, except in very simple examples, but extremely
> powerful for conceptual understanding.

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