Automaticity

Last Wednesday during math class, our table had some discussion about the value of memorizing algorithms: Aren't there formulas and operations that are simply worth memorizing, the value of knowing number sense and alternative approaches notwithstanding? I have come to appreciate the value in understanding the concept behind a given procedure, along with the various strategies a student (or our cohort-mates) might employ to solve a problem. But I also think that memorizing some basic math facts (discussion of the Crespo "Basic Facts" article forthcoming) simply makes sense.

I was thinking about this point in light of both the Crespo article, which focused on fourth-graders, and my first-grade daughter's math homework, which recently featured "double-plus-one" problems. At the same time, she takes periodic timed tests on addition and subtraction facts, and as I read the Crespo article, I kept thinking about how the "varied practice" strategy could, for some students, bog down the process of recall--not just for a timed test but for everyday needs. My daughter's teacher said, echoing advice that my master teacher gives to her fourth-graders, that practicing math facts in the car is a good way to kill time in traffic and develop automaticity at the same time. I haven't tried it yet with my daughter, because it's often so hard to get a word in edgewise.

In my fourth-grade placement, I encounter students who haven't yet mastered their multiplication facts, and now that we've moved onto two-digit multiplication and beginning division, students who haven't memorized anything above 5s continue to struggle because they're so busy counting 6 x 7. Multiplication tables are a gateway to so many concepts that to me, they are an example of something that should be memorized. Alternative approaches? Varied practice? Crespo made a compelling case, and I'm not dismissing that case, but memorization is sometimes the practical strategy. Am I being too stubborn?