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**topsquark** Okay, I took a Unisom last night and woke up pondering the following. (I take it when I have trouble sleeping but I've also found it induces a bit of extra free-association.)

In the current education system in the US, when teaching the concept of multiplication, we have the following argument: n x m is defined as n groups of m. So, for example, 3 x 4 = three groups of four which is, according to the curriculum, not the same as 4 x 3 = four groups of three. I am not happy with this teaching method, which supposedly helps the student "later on" in their Math education. (Where I cannot say.)

But I woke up thinking about just how they are going to teach factoring? Clearly 12 = 3 x 4 and 4 x 3. But supposedly the two expressions are not the same. And how can they also relate that 12 = 2 x 6? And, God forbid, factoring a number into it's prime factors.

Does anyone know how they teach this?

-Dan