You will never guess what I’ve been doing the past two weeks. I, an Ivy League graduate, at the ripe age of 44, have been learning my times tables. That’s right, multiplication. Now, before you write me off as a failure of American higher education, let me stress that I’ve been doing this in Japanese. I’m memorizing the kuku, Japan’s distinctly rhythmic way of chanting the times tables.
You see, my 8-year-old started multiplication in school this month. Like every other second-grader in Japan, he is expected to learn his times tables so thoroughly that recall is automatic and reflexive. He’ll get lots of practice at school, but parents are expected to drill at home. It won’t do him much good if I drill him in English, so I’m trying to learn the Japanese way.
I figure the kuku method must work, since Japanese children do so well in international comparisons of mathematical ability. Curious about its history, I discovered the kuku was brought to Japan from China more than 1,000 years ago. In those days, they started with the largest numbers and moved down, the opposite of how the kuku is recited today. The first fact, 9×9, was chanted as “ku ku,” which is why the times tables came to be called kuku in Japanese.
The Japanese way of reciting the times tables is highly rhythmic, and each multiplication is stated in the shortest way possible. To achieve this rhythm and brevity, the numbers are altered to the point that I didn’t recognize them as Japanese.
Take, for example, the 3’s. The number 3 is pronounced in four different ways in the chant, some of which I’d never heard. 3×3=9 is said aloud as “sa zan ga ku”; 3×6=18 is “sabu roku juhachi“; and 3×8=24 is “san pa nijushi.” So the number 3 is pronounced varyingly as “sa,” “san,” “zan” and “sabu.”
Japanese children start learning multiplication when they are 7 or 8 years old, a little earlier than in some countries. Teachers start by demonstrating the concepts. A common classroom exercise is to make a pile of objects easier to count by placing equal numbers of them on several plates. The kids learn equivalency in number facts by discovering that three oranges on each of two plates is equal to two oranges on each of three plates.
When the kids start memorizing the multiplication facts, they begin with the 5’s and the 2’s because they are easiest to understand. Then they do the 3’s and the 4’s, the 6’s and the 7’s, the 8’s and the 9’s, and finally the 1’s. They don’t go higher than the 9’s, so Japanese are often surprised to hear that students in other countries memorize up to 12×12 or even 20×20.
Like my second-grader, I started with go-no-dan (the 5’s). Frankly, I’m not doing very well, and I don’t think reciting the kuku will ever be automatic for me. Numbers are hard to process in a foreign language, and I still stumble when taking down phone numbers in Japanese.
My friends here are baffled when I complain that the kuku is driving me cuckoo. “Well, how do you do it in the U.S.?” my friend Miyuki wanted to know. American children also recite the times tables, I explained, but we pronounce the numbers in their usual way: Two times three is six. Five times seven is 35. Eight times nine is 72.
“Oh! But that’s so long and difficult,” Miyuki complained. Out of curiosity, we compared how many syllables were required to state each of the 81 multiplication facts, first in Japanese, then in English. In almost every case, the Japanese way was shorter. For example, 5×2=10 is three syllables in Japanese (go ni ju), compared to five syllables in English (five times two is 10). “You see?” Miyuki concluded triumphantly. “That’s why Japanese children are good at math!”
She’s partially right, of course. Yoshishige Sugiyama, professor of mathematics education at Waseda University and former president of the Japan Society of Mathematical Education, says early mastery of multiplication tables is one reason Japanese children tend to score higher in mathematics than American children. The short phrases and rhythm of the kuku make it easier to memorize, he says.
But let’s give credit where credit is due, to the Drill Master Mothers of Japan. We second-grade moms got a big lecture about this at the parents’ meeting last month. Drilling is our job. We are supposed to drill our kids while we’re cooking dinner. Drill ’em in the bath. Drill ’em on the train. My son’s teacher even recommended putting up a chart by the toilet so our kids can practice while they’re . . . well, you get the picture.
It’s not enough to be accurate in multiplication. You also have to be quick. It’s common for teachers and parents to use a stopwatch, pressing kids for ever faster performances.
There are national kuku-reciting meets, like the spelling bees in English-speaking countries. At one competition this summer, a second-grader from Yamaguchi Prefecture recited the entire kuku in two minutes, 56 seconds. A sixth-grader from Kobe did it in two minutes, seven seconds.
My friend Yoshiko scoffs at such times. Her daughter’s second-grade teacher made every student learn to recite the kuku in one minute. “You couldn’t understand a word they said when they said it that fast, so I never saw the point. But we had to drill Anna until she cried.”
So you can see that it’s a handicap for my son to have foreign parents who don’t know the kuku. What’s worse, I’m beginning to think I’m going to have to teach my older son, too. He learned multiplication in the U.S, and started Japanese school in third grade after his classmates had already mastered the kuku. He says he multiplies in English, which I never thought was a problem until last week, when he told me he’s slower at mental calculation than his peers.
My problems are multiplying.