Monday, July 16, 2012

Just the Facts, Ma'am

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?


dcamardo said...

As someone who does math for a living, I always say, "You don't actually need to know that 5 + 5 is 10. You need to understand why 5 + 5 is significant."

However, if you were born before the abacus, I guess you would need to know that 5 + 5 is 10...

Mike Lewis said...

Then there's my favorite situation: Students who know their multiplication facts, but have to count it out to add or subtract.

Yes, there is clearly some kind of problem there... 5 x 2 = 10, yet we're not quite sure about 5 + 5?

I never understood why "12 times tables" were pushed so much in 3rd and 4th grade, until I realized how much of our world revolves around 12... a dozen eggs, 12 hours in half a day, 12 inches to the foot, lumber in 12 foot lengths, etc. Now I'm in graphic design, and I find out that its 12 points to a pica, and 72 points to an inch (or, 6 picas to an inch).

R.C. Lewis said...

True enough, Derrick. Of course, not every situation has a computer with Excel at the ready. ;-) But yes, as the rate of technology development continues to increase, critical thinking skills and problem solving ability are so much more important than being able to carry out particular algorithms.

Mike, well, those kids generally know doubles, like 5+5. It's things like 9+7 or 8+6 that they count out (or reach for the calculator). And yes, 12 is definitely significant in our society ... but I didn't really have a lot of those facts memorized until I started teaching and saw them over and over every day.

E.B. Black said...

I was very thankful to my fifth grade math teacher. She had us take tests once a week that were timed and had all the multiplication tables 1-12. If we could fill it out in less than a few minutes, we'd get a piece of candy and our name on the board. It was great motivation and I still have all of them memorized.

stagecoach said...
This comment has been removed by the author.
stagecoach said...

As I am a math-knuckle-head, I figure equations out until I have to go to the effort of taking my socks off to count -- if I have to do that -- it is not my problem but is the problem of someone who is capable of doing so.