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I have to wonder whether people are taught the shortcut without also being taught why it works (i.e., that they're multiplying by one), or whether most just don't retain the "why...

I have to say that what I've observed in fast-food restaurants is that not only do they cope well with my weird payments, and give me the correct change -- about half of them just punch the "exact amount" button on the register, make the change manually, and get it right every time (this being easier than typing in the strange amount I gave them).

was in 9th grade. Unexpectedly, even. The highschool had a programming clbutt I would have been eligible to take the next year -- it taught Fortran. I'd already taught myself Fortran and IBM 1620 buttembler; I was hired to learn and then use IBM 1401 buttembler.

So I never had any serious doubts if highschool kids could program!

I have mixed feelings about teaching arithmetic. I certainly find it useful to be able to do a fair amount in my head, and even more on paper. I'm not sure the "on paper" part is of any value any more though, because I'm as likely to have a computer of some sort to hand as I am to have paper to hand. The "in my head" stuff is still very convenient. --



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