This is a little tangent to the discussion in another thread about "abstraction".

A lot of us old farts were educated in the '50s and '60s, before there was any such thing as a hand held calculator. So, we learned how to do long division because that was about the only way to get the job done (well, aside from the slide rule, sort of, if you didn't care about precision or that pesky remainder).

Now everybody has a calculator in every drawer in their house and you can buy a new one for less than it costs to replace the batteries in the old one. Given that modern state of affairs, does it make sense any more to teach long division to kids? Does knowledge of that arithmetic ritual somehow help their understanding the concept of division, or is the abstraction of division provided by the magic "divide" button on the calculator all they need? Are there "caught on a desert island without a calculator" situations where long division would somehow manifest itself as a survival skill?

One of the voices in my head says, "Yes, dammit! What's the matter with kids today? Of course they should learn long division in school just like you did fifty years ago."

On the other hand, I vaguely recall a similar arithmetic ritual for manually extracting square roots. I never did learn that particular process, and have managed nevertheless to live a full and productive life because by the time I matured enough to develop a passionate interest in square roots, I also had an HP-35 to do the dirty work.

Who has kids (I don't)? Do they teach 'em long division any more? Is it a good idea to do that, or just a waste of time that they should be using to teach other things? Now that I'm in babbling mode, I guess the same question actually applies to manual arithmetic in general. Is it enough these days to know what it means to add or subtract or multiply two numbers, without actually knowing how to do it by hand on paper?

-- Russ