On 6/27/09, Juliana wrote:
> On 6/25/09, Rich/CA/Math wrote:
>
>>
>> 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.
>>
> By seeing it as two multiplication problems, one in the numerator and
> one in the denominator.
>
> 1 x 1 = 1 = 1
> _ _ _____ _
> 2 x 3 = 2+2+2 = 6

But where does the repeated addition concept lead to a multiplication as
2 multiplications and a division? In other words, how do you get from a
definition of multiplication is repeated addition to this is what you do
with fractions. You kind of need to know how to multiply 2 fractions and
*then* you can see the repeated addition. But the concept of
multiplication has to be explained in a way that when you get to 1/2 *
1/3 that concept can be used to explain how we get to the algorithm for
multiplying fractions.

The repeated addition concept fails because how do you explain
conceptually (not computationally) that we are adding 1/3 to itself a
half of a time. We need to see how the concept leads to the algorithm,
not just how the concept is enfolded within the algorithm. Otherwise it
is just trickery to the students.

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