Mama Says

The other day I was talking with some of my fellow tutors at the Seeds of Literacy GED prep program. I learn a lot this way. Several of Seeds’ tutors are retired teachers, business people, scientists, or experienced parents, so there’s a wealth of knowledge handy and ready to be tapped, completely free of charge.

Some of what I hear in tutor talk is eye-opening, as when another tutor demonstrated “partial quotient division,” a method of doing long division that is especially useful when you have divisors that are more than a single digit. I rarely use any other method for long-division any more.

But of course, some tutor talk is, if not complete hooey, at least debatable.

Such was the nature of the aforementioned discussion. A former math teacher — a swell, soft-spoken guy — was commenting with much regret on the inability of modern children to do math in their heads. I begged to differ.

This is a topic that pops up at our house regularly. My husband, John, is a mental mathematician. And although I’m sure he doesn’t mean to, he occasionally reacts just a little scornfully when he observes me demonstrating to our kids how to write out, in detail, a math process. “Just do it in your head!” he cries. “Break it down! Do the hundreds place first, then the tens, put it all together in your brain!

Show off.

Now, I’m not debating that mental math is impressive. For people who can’t do it, mental math seems magical. I’ve gotten books out of the library, to see if I could teach myself to do what John can do without apparent effort. And I’ll even concede that if each and every American could find square roots without relying on fingers and toes, ours would be a stronger, more productive nation.

But I do contest the suggestion that mental math is more important than math done “by hand.” Moreover, based on the people I’ve met who are working toward a GED, I am increasingly of the opinion that an emphasis on “doing it in your head” can interfere with the much more valuable process of helping students get cozy with math.

That coziness — a comfort with math that is similar to the pleasure we get from doing a word search, a crossword puzzle, or a Sudoku — strikes me as much more important than skill at mental computation, or even speed. In observing both adults and children doing math, I’ve seen that the students most likely to quit in frustration were the ones who were trying to skip steps, rush through the problem, hide their hand-counting, or jump to conclusions.

Meanwhile, another student who copies out the whole equation, neatly stacks her numbers one above the other, uses counters or other visuals — that student may spend twice as much time on the lesson. Of course, she may also attempt half as many problems, but more of them are correct at the end. Through the writing, even the counting on her hands, she gets to watch the problem unfold in some physical way before her eyes, revealing what Nobel laureate Richard Feynman meant when he spoke of the beauty of the language of nature.

There is, I concede, one aspect of mental math whose value is pretty clear. Mastery of the basic, single-digit arithmetic facts is essential if the rest of math’s beauties are to be experienced. I have encouraged our kids to get the single-digit facts for addition, subtraction, multiplication and division cemented into their heads as quickly as possible. While some mnemonics and hand-counting rituals are themselves impressive and interesting (such as the “nines trick” Edward James Olmos demonstrated in “Stand and Deliver), spending too much time on basic computation puts the student off track, and slows his approach to the really fun stuff.

Who knows how many would-be mathematicians where nipped in the bud when they were shamed by their reliance on hands and pencil? I am no math whiz, myself, though I have come to love algebra and especially geometry. I dropped out of high school math classes in trigonometry and calculus in order to protect my GPA. Part of my math fear had to do with my embarrassment that a few of my classmates seemed to be able to skip large chunks of the problems, apparently pulling correct conclusions from thin air. Even if I could eventually produce the same answer, I understood that there was something inferior about my method.

It’s that assumption of superiority that I think has no place in math instruction at either the elementary or high school level. In fact, it should probably be the other way around. “Just knowing” is very nice, but being able to prove your knowledge — in writing — is more important, and much more scientific.

This entry was posted on Wednesday, February 15th, 2006 at Feb 15, 06 | 1:05 pm and is filed under . You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.