How important is it to memorize multiplication facts?
There is an article by Daniel T. Willingham entitled "Is It True That some People Just Can't do Math?" that answers this particular question well for me. D.T.W. references many others in his Endnotes.
http://www.aft.org/pdfs/americaneducator/winter2009/willingham.pdf
I see your point and I agree with your answer. When you multiply enough times, you memorize the numbers, so you just need to calculate often, right?
Some kids like drilling and some kids don't. There's nothing wrong with asking them hey what's 7x8, in the car, once in awhile . The best way I think is to have them do math in the service of a greater goal... so they don't even realize that they are learning. For example: games that involve multiplication, like counting points in card games, or figuring out costs at the supermarket, or counting money etc.
Games are super powerful, because the kids want to play over and over again, and real life situations may not come up that often If they can build that skill, multiplication or whatever in multiple contexts/domains, it'll be much stronger skill. Rather than, hey I can only do math on worksheets, but anywhere else I can't. (which I've seen in some kids). The worse I've seen is when kids just drill for a test, and then forget soon after. Math skill has to be incorporated in life.
The way we do it, you don't memorize individual "facts" about particular numbers, but whole patterns. And yes, as you say, this happens when children work with patterns enough times - represent them in math art, prove they work algebraically, modify one pattern to make another, build hands-on models, write computer programs for them and so on.
For example, you don't memorize 2x10, 3x10,... 10x10 separately. You learn how multiplying by ten works in general, and why, and then you can apply it to every number. Surprise: there are general patterns like that for the rest of the times table!
I think memorize is the wrong word. You don't memorize where to put your foot when you ride a bike. When you drive, you don't memorize whether the right foot or left foot is the break. Well.... maybe when you first start driving you do, but my point is, calculation is a skill, that you learn by using. Memorizing is for facts.
