> 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.* 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.