I think that too much emphasis is placed on memorizing multiplication tables. Memorization has nothing to do with an ability to do math; it is far more important to understand the concepts of how and why math works.

Gifted children especially have problems with this, as many gifted children hate rote tasks and repetition, which is necessary to memorize the multiplication tables. But there is some advantage to "knowing" math facts; it helps you to be able to do higher math more quickly and efficiently, and it enables you to do math in your head when you are find yourself without a calculator (ie., the grocery store?)

Here is a cool site which explains why you only really have to memorize 13 facts to know the whole multiplication table. Along the way it explores a lot of interesting mathematical concepts.

Related Links

Multiplication: An Adventure in Number Sense