*[Photo by dsb nola via flickr.]*

The most effective and powerful way I’ve found to commit math facts to memory is to try to understand why they’re true in as many ways as possible. It’s a very slow process, but the fact becomes permanently lodged, and I usually learn a lot of surrounding information as well that helps me use it more effectively.

…

Actually, a close friend of mine describes this same experience: he couldn’t learn his times tables in elementary school and used to think he was dumb. Meanwhile, he was forced to rely on actually thinking about number relationships and properties of operations in order to do his schoolwork. (E.g. I can’t remember 9×5, but I know 8×5 is half of 8×10, which is 80, so 8×5 must be 40, and 9×5 is one more 5, so 45. This is how he got through school.) Later, he figured out that all this hard work had actually given him a leg up because he understood numbers better than other folks. He majored in math in college and is now a cancer researcher who deals with a lot of statistics.— Ben Blum-Smith

Comment on Math Mama’s post What must be memorized?

The entire discussion (article and comments) is well worth reading:

You may also enjoy:

May I add my favorite take on math facts–I like the balance between thinking/understanding strategies and practice:

http://www.thinkingwithnumbers.com/QuestionsAnswers/index.html

That is interesting, especially his goals page, though I would put a much higher emphasis on goal #2 (understanding, demonstrated in the ability to explain one’s reasoning) than on #1 (speed). And I can’t imagine any math facts product that I would be willing to pay those prices for.