On 6/25/09, Cullen wrote:
> On 6/25/09, Elementary Teacher wrote:
>> I teach elementary school, and I have always thought
>> multiplication was just repeated addition. Can you explain
>> to me why it's not?
>
> According to my state standards it is

Lots of state standards are bad.

Operations should be extensible. And they are. We can not only
multiply 2*3 we can multiply (1/2)*(1/3). Now explain how the
latter can ever make sense if multiplication is repeated addition.

I would recommend that anyone who is interested in the
mathematical foundations of basic arithmetic consult the draft
chapters of a teacher training manual put together by Hung-Hsi Wu
at Berkely. The link will take you to his home page where a lot
of his writings are listed. The ones I am referring to are:

Professional Development and Curriculum Chapter 1: Whole
Numbers (Draft) (July 15, 2000; REVISED September 1, 2002)

Professional Development and Curriculum Chapter 2: Fractions
(Draft) (June 20, 2001; REVISED September 3, 2002)

Link

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