It is a huge advantage to have the basic facts memorized for instant recall--this is a great timesaver. Why have to reinvent the wheel every time you see a multiplication problem? Grammar school kids are made to take in facts and memorize them. Their abstract reasoning skills don't kick into high gear until they near adolescence.
I think you need to know both. It would be a waste of time memorizing huge products like 234767 times 789932 when you can use a general method instead. But of course, in order to apply the method you need to know basic smaller products, like 7x2, 7x3, etc.
Lots of mathematical problem solving strategies work like that--a general method based on fundamentals that just need to be memorized.
I'm old school when it comes to multiplication facts and wish that every child would memorize them. Math becomes so much easier for elementary students when they do. I love your answers, paxwill and kschimmel. I wished more people agreed so that more children would learn their facts. Thanks for sharing your views on this question.