Those Times Tables
By Dr. Eugene Maier |
I was in the stands at a middle-school basketball game. The mother of one of my grandson's teammates had noticed my "Math and The Mind's Eye" sweatshirt and, during a lull in the game, commented about it. We chatted briefly about math until the game resumed. In our conversation she mentioned that her son was having trouble in math. I gave her our web address and a couple of days later I got an e-mail from her elaborating on her son's difficulties.
Her son, a sixth-grader, she wrote, had never "mastered" the timed tests in elementary school. Recently he had scored in the seventies on a three-minute timed multiplication test and the teacher had announced that all those who didn't score 85% on the next one--in two weeks--would have to go to "homework club" until they did.
She told her son, in true Nike-town fashion, it was time to "just do it." So, they devoted Monday of a three-day weekend to the task and her son passed the tests. "It's great to be past that hurdle," she wrote. Meanwhile, her 4th grade daughter was struggling to up her score on a 5 minute, 100 problems test from 68% to the teacher-mandated 95%. Mom looked for the "mental stumbling blocks" getting in her daughter's way. Finding those--the nines--she "showed her some relationships" and daughter did fine.
Mom also recounted some of her own experiences. "With four kids," she wrote, "I just haven't devoted my life to this drilling." She was also reluctant to have her children experience what she went through in fifth grade to pass "those tests," the scores of which "were posted on the wall for everyone to know where every student stood at any point in time"; creating, she added with a bit of wryness, " another nurturing exposure to Math smile." She went on, "I've never been good at the pure 'memorization' game but succeeded with seeing or constructing relationships with material at hand as a way of latching it to the memory fibers of my brain."
I was reminded of my own family's stories about timed tests and multiplication facts. I remember a child in tears at the breakfast table because he got so nervous during timed tests on arithmetic facts he couldn't think, he said, even though he knew the answers.
I recall my youngest sister, after a game-playing session with her nephews, wishing she could do arithmetic as fast as they did and confessing that she had never learned to multiply. When I inquired what she meant, she told me that there were certain products she never could remember, like 8 x 7. She said she had to start with something she did remember, like 4 x 7 and count on by sevens until she got what she wanted. I told her she knew how to multiply; her system might take longer than her nephews but that was fine as long as it worked for her. Unfortunately, she finished school with the belief that she has very little math ability.
From what I gather, educators who insist that students have instant recall of the times tables believe that it's an essential basic skill, without which students will be hampered in their later mathematical development--especially when it comes to learning paper-and-pencil multiplication and division algorithms. But this confuses acquiring non-essential algorithmic skills with what is basic to all mathematics education: drawing out and developing the mathematical abilities that exist in every child, including the ability to devise one's own arithmetical procedures.
There is no question that being able to instantaneously recall arithmetical facts can be a convenience. However, one must weigh this convenience against the price paid in forcing rote memorization of facts and giving timed tests, especially when there are so many other ways of arriving at these facts, be it by counting, reading a chart, or punching a cal