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I'm really not sure how you could arrive at an understanding of multiplication without first going through the exercise of adding up X groups of Y to yield X *

I'm really not sure how you could arrive at an understanding of multiplication without first going through the exercise of adding up X groups of Y to yield X * Y. We don't need to declare to children that the precise definition of multiplication is repeated addition. If that's what you're arguing, we agree. If it's that 3*5 shouldn't be explained as 5+5+5, I'm not sure how kids would be expected to learn the subject. We can't transactionally insert comprehensive math knowledge, so it's got to be incomplete along the way.

pdonis 6y ago
> I'm really not sure how you could arrive at an understanding of multiplication without first going through the exercise of adding up X groups of Y to yield X Y.* Arriving at an understanding of one particular special case of multiplication might indeed be a necessary step towards arriving at an understanding of multiplication in general, but that doesn't mean the two are the same.