Josna Rege

42. The Times Tables

In 1930s, 1960s, 1990s, Childhood, Education, Family, history, India, Inter/Transnational, postcolonial, Stories, United States on May 7, 2010 at 11:00 am

As a child, like most of my generation, I had to memorize and recite the multiplication tables. The singsong recitation of the times tables was a not-unpleasant soundtrack to my early schooldays. We recited them as a group, we recited them at home under our breath, we recited them in our dreams, until, on cue in the classroom—or indeed anywhere, and for the rest of our lives—we were able to retrieve the product of any given combination of numbers from our memory banks effortlessly, and at lightning speed. Three elevens? Easy: thirty-three. Eight sixes? No problem, the same as six eights: forty-eight. Twelve twelves? A hundred and forty-four (or a gross—since the old British measures still lingered).

In India we were officially responsible for knowing the answer to the multiplication of any two numbers between one and sixteen (although I never mastered any beyond twelve). It was rote learning, no doubt, but rote learning employed where it worked best. Through repetition, in a reassuring rhythm, these basic computations became second-nature to us. And in any case, there was not to reason why: it was simply what we did.

Thirty years on, Nikhil’s schooldays had a different soundtrack. By the time he was in elementary school, requiring a student to memorize numbers or words was considered something akin to child abuse, and recitation of the times tables was retrograde. In fact, they were no longer even called multiplication tables, but were now simply Math Facts. Rather than being required to memorize them in logically ascending patterns of numbers, the children were now given worksheets to take home with lists of assorted math facts on them, in no discernible order. They were expected to practice filling out these sheets faster and faster, using higher and higher numbers, until they attained their personal best in speed and accuracy.

As a parent, I was at a loss to understand how Nikhil could be expected to memorize the products of seemingly random combinations of numbers without their being organized into tables by number, and without reciting them. (Kids have marvellous memories, and before Nikhil and Eric even went to school, reciting numbers was a game for them, their minds naturally creating their own order. I remember three or four-year-old Nikhil counting by tens up to a hundred: “…seven-ty, eight-ty, nine-ty—ten-ty!”) But somehow, without recourse to recitation, he did manage to master his Math Facts; and in any case, he now has the computations at his fingertips at all times, thanks to the calculator function in his iPhone.

If the educators of the nineties considered it borderline-abusive to require memorization of the multiplication tables from one to twelve, I wonder what they would have thought of  the system in my father’s boyhood? He had to memorize the tables not only for whole numbers, but for fractions: a quarter, a half, three-quarters, one and a quarter, one and a half. As my father recited out loud—in Marathi, of course—his father monitored him from a distance, while reading in the next room. Whenever he slipped or faltered, his father simply marked his mistake with a questioning grunt, and he had to start over. Before long, the answer to six three-quarters came as easily to him as the answer to six sixes does to me.

It is easy to mock today’s concern for children’s tender sensibilities from the perspective of old-school “common sense,” and I have been guilty of it above. But I can’t help thinking of an exchange I had with a classmate one day when I was eight, and we were being called on one at a time to recite a memorized poem in class. Like the times tables, the recitation of canonical poems or passages from Shakespeare plays was a regular requirement, but the experience was dramatically different for every child. Words came easy to me and, when called on, I loved showing off in front of the class. (In fact, I was no doubt one of those irritating kids who has her hand up insistently, early and often. “Please miss, please, ask me!”) On this one particular day, as I swaggered back to my desk after my performance, the hapless classmate who had been called upon next muttered to me, “It’s all very well for you—you love it.”

At the time I didn’t understand what he meant, and merely dismissed his bitter tone as sour grapes. It was not until many years later that it dawned on me that what had been positively pleasurable for me had probably been torture to him. While for me, memories of “Daffodils” and “The quality of mercy” are like Portia’s gentle rain from heaven, for many they are associated with the lingering hell of childhood failure, punishment, and humiliation. I could not identify with that schoolboy from Shakespeare’s “All the World’s a Stage” speech, “creeping like snail/ unwillingly to school”: I loved school. Still, socialization, while certainly preparing us for the world, took its toll. As Nikhil used to say of elementary school, “It’s okay. But it takes up too much time.”

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  1. Josna, when I was in grade school, I too absolutely loved it and always was the first to have my hand up to be called on. I also added to the answer to show everyone the extant of my superior knowledge. But one day my best fifth grade friend called me a know it all and a showoff because the teacher told him he should be smart like me if he was going to jump up and down to be called on. I never raised my hand again in class until I was in college. I decided that it was better to have friends than to show my studiousness.

    • Jimii, I can just imagine you as a bright, eager 10-year old. It seems a shame, doesn’t it, that the educational system pits children against each other, so that they are forced to choose between being good students and being loyal to their friends?

  2. When I was a program evaluation consultant in Cambridge, I was amazed to see how poorly kids did on simple math, still counting on their fingers in fourth grade. I taught one boy about the times table and the nifty trick to the 9’s: 9×9=81 and 8+1=9; 9×8=72 and 7+2=9, etc. He was amazed and excited, thought it very cool.

    The mentality that regards all rote learning as “drill and kill” is missing something important. Sometimes teaching “for meaning” leaves kids in an undifferentiated sea, where they have to filter too much by themselves to find something they don’t even know they’re looking for. It isn’t a thrill that 6×4=24, but it’s handy to know, and I enjoyed the sing-song recitations, too.

    The same thinking often overemphasizes individuality. Yes, we’re all individuals, but there is a place for the collective. I distinctly remember being told in kindergarten to draw something “original,” not what everyone else was doing. I was stumped. What should I draw? I erased and crossed things out a lot. Five years old and worried about being derivative! And think of thousands of years of Chinese schoolchildren painting lovely goldfish.

    7th Grade in Canada:

    In Flanders’ fields the poppies blow
    between the crosses, row on row,
    that mark our place. And in the skies
    the lark, still bravely singing, flies,
    scarce heard amid the guns below.

    We are the dead! Short days ago
    we lived, felt dawn, saw sunset glow.
    Loved, and were loved.
    And now we lie in Flanders Fields.

    Take up our quarrel with the foe!
    To you from failing hands we throw the torch!
    Be yours to hold it high.
    If ye break faith with us who die
    we shall not sleep,
    though poppies blow
    in Flanders’ fields.

    And now to google and see how much I’ve forgotten since 1967 . . . hardly missed a word! “Lark” should have been plural, which I had at first but then changed. Middle-aged memory, another story . . .

    • Wow–not bad!! 40+ years on and only one letter off!
      Yes–once memorized, it’s there for good (or ill)! And why not? As long as it’s not torture but fun. I agree with you entirely about the rote learning–although of course it’s nice to know why it works as well as just knowing it by heart. I remember starting to learn calculus in England by just memorizing the formulae for integration and differentiation, but not having any idea what they were and what you used them for, When I got to America and we started Calculus here I was ahead for about a week, and then I fell hopelessly behind, because they everyone else was learning the principle behind the formula.
      Still its scary to think that a 4th-grader today wouldn’t have any tricks yet for multiplication besides counting on his fingers.

      • P.S. I’ve been re-reading this sentence of yours, and I love it: “Sometimes teaching “for meaning” leaves kids in an undifferentiated sea, where they have to filter too much by themselves to find something they don’t even know they’re looking for.”

  3. I remember the sense of accomplishment I had when I had so clearly, so definitively learned something: all the times tables up to 12×12. It was a surety that I could do something that was hard. And, I could use this knowledge as a I moved through the real world of running errands for my mother.

    • Hi Claudia! I love your comment; it made me remember, too, that thrill that comes not only with having memorized something, but with actually being able to use it. It’s sweet to imagine you using the times tables on errands for your mother.

  4. I was one of those poor unfortunates who had a difficult time with math and still do to some extent.
    Those times tables were my saving grace! I could never have grown up without them!
    I think it is a real shame that children are not taught to learn poetry by heart nowadays. They lose
    so much!

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