On Sep 4, 2012, at 11:56 AM, kirby urner <firstname.lastname@example.org> wrote:
> Adding 1/2 of length or volume pi to 0 is the same as multiplying pi > by 1/2. The use of the preposition "of" is important. "Add 1/2 a cup > to the mixing bowl" -- ideas about volume enter in (no reason to just > stay with length).
You realize that this is circular, right?
It is funny how the discussion of "Is it appropriate to introduce multiplication to 8 year olds as repeated addition?" turns into "Is multiplication repeated addition?" You know what a neat study would be? Take a group of active elementary math teachers and a group of mathematicians and ask them those two questions.
1. Is it appropriate to introduce multiplication to 8 year olds as repeated addition? 2. Is multiplication repeated addition?
I would not be surprised if the group of elementary math teachers earn a higher score overall than the mathematicians. Of course, it is easy to define an active elementary math teacher, not so easy to define a "mathematician".
Btw, the answers to those two questions are Yes and No respectively.