One of the fun little debates in math education is over the importance of "knowing your math facts." By this, people generally mean having your times tables memorized, that kind of thing.
How important is this? I admit, it's a little frustrating when I'm trying to get a student to understand a complex higher-math problem (algebra, maybe), and they get slowed down trying to remember what nine-times-six equals.
On the other hand, I find it more worrisome when a student has their multiplication facts down pat, but can't problem-solve enough to figure out that multiplying is what they're supposed to do in the first place.
Then there's my favorite situation: Students who know their multiplication facts, but have to count it out to add or subtract.
Instead of memorizing math facts, I'm more a fan of developing math fluency. When I was in elementary school, I had most of my times tables down, but struggled with the twelves. It didn't matter, though, because I knew I could just multiply by eleven then add the number I wanted to multiply by twelve. I could do it quickly enough that my teachers never knew I hadn't memorized those facts.
And it didn't matter.
That's math fluency. It requires having some math facts under your belt, but more importantly, a fundamental understanding of operations and how they work.
What do you think? What are the benefits of memorizing math facts? How did you handle learning those facts in school? Would you do it differently if you could go back?