> >Paradoxically I believe that when pencil and paper arithmetic goes away >much of the older mental math will return. When we eliminate the paper >and pencil algorithms in favor of calculators and computers, then there >will be more time and more need to perform approximate calculations >mentally. This is all to the good. Currently many kids blindly follow >their paper and pencil algorithms without thinking about the plausability >of their results. When the paper and pencil crutch is removed, they will >need to return to checking plausibility.
While I would very much agree that the pencil and paper can get in the way of doing a number of interesting problems, I would tend to disagree that calculators encourage checking plausability. I will go even so far to say that when pencil and paper was about it (I know this dates me :-)) that I really tended to spend a lot of time checking plausibility (I was never that fond of algorithms :-)). I will even go so far to say that many of my brightest students seem not to have developed the ability of checking plausibility and unquestionably use a calculator as a crutch.
Okay, after saying all this. I feel that a calculator will become a common tool in the classroom and I would like to see students taught to question their answers in an appropriate fashion. This is not happening as much as one might hope, but that doesn't mean that it isn't possible.