Kids should understand the multiplication tables, but memorizing is also useful, and in certain cases, we memorize math facts before we understand them. What about calculating the area of a circle? I think we all memorized this one before we understood it...at least I didn't understand the Calculus behind the area formula when I was 10 or 11.

I'm sure no one here actually figures out multiplication for each and every problem they encounter with the understanding method, though I agree that understanding is key to building on math knowledge.