Tuesday, July 22, 2008

How things have changed

"You say you don't find it difficult to multiply one number by another," Miss Honey said. "Could you try to explain that a little bit?"
"Oh dear," [Five-year-old] Matilda said. "I'm not really sure."
"For instance," Miss Honey said, "if I asked you to multiply fourteen by nineteen...No, that's too difficult..."
"It's two hundred and sixty-six," Matilda said softly.
Miss Honey stared at her. Then she picked up a piece of paper. "What did you say it was?" she said, looking up.
"Two hundred and sixty-six," Matilda said.
Miss Honey put down her pencil and removed her spectacles and began to polish the lenses with a piece of tissue. The class remained quiet, watching her and waiting for what was coming next. Matilda was still standing up beside her desk.
"Now tell me, Matilda," Miss Honey said, still polishing, "try to tell me exactly what goes on inside your head when you get a multiplication like that to do. You obviously have to work it out in some way, but you seem able to arrive at the answer almost instantly. Take the one you've just done, multiplied by nineteen."
"I..I...I simply but the fourteen down in my head and multiply it by nineteen," Matilda said. "I'm afraid I don't know how else to explain it. I've always said to myself that if a little pocket calculator can do it why shouldn't I?"
"Why not indeed," Miss Honey said. "The human brain is an amazing thing."
"I think it's a lot better than a lump of metal," Matilda said. "That's all a calculator is."
"How right you are," Miss Honey said. "Pocket calculators are not allowed in this school anyway." Miss Honey was feeling quite shivering. There was no doubt in her mind that she had met a truly extraordinary mathematical brain...
From Matilda, by Roald Dahl, published in 1988.

Today's schools, far from banishing calculators, have made them an integral part of their curricula.

And today's Matildas, far from being appreciated for their extraordinary mathematical brains, are marked down for not satisfactorily explaining how they got their answers.


W.M. Irwin said...

The late science-fiction writer Robert Heinlein openly deplored today's state of mathematics education. He recalled that, in his own youth, being able to multiply two two-digit numbers in one's head was more the expected rule than the exception.

lefty said...

Any arbitrary pair of two digit numbers? I'm not sure I know anyone, of any generation, who can do that easily. Though I agree it is a nontrivial math skill.

W.M. Irwin said...

I believe that Heinlein's assertion referred to his experience that multiplication used to be so strongly drilled into the students that they could automatically break up such a problem into its component parts and arrive at an answerer without having to depend on pencil and paper. Naturally, five-year Matilda's special ability with this seems to be quite a different matter.