This has been an interesting thread, although those of us who would
be happy to see calculators banned from early education are clearly
engaging in wishful thinking.
Nevertheless, I think that something important has been lost now that
students can use calculators to do even the most simple calculations,
and that is what I call "a feel for the numbers." There is simply no
appreciation for finding a correct answer when all you have to do is
punch in the numbers and read the answer off the calculator. As a
result, the students really have no clue when they might have gotten
a wrong answer. Many time I have seen students submit answers to
problems that are clearly nonsense (speeds of 10^21 m/s, terrestrial
distances of 10^15 m, ordinary times of 10^20 s, etc.) without ever
questioning them. The thinking seems to be, "if I got it from the
calculator, it must be right." Since they have no idea how to do
rough calculations in their heads, they have no sense of what the
order of magnitude of the answer must be, so they are incapable of
telling when an answer is unreasonable.
I have never been much of a stickler on significant figures (I leave
that to the chemists), but I do get upset when I see a number written
to 12 or 13 s.f. that should have no more than 2 or 3. Of course
these numbers are there because the calculator doesn't know s.f. for
beans, and so the students simply copy the numbers they read without
thinking about what they mean.
I don't want to do away with calculators. They can do some wonderful
things, and they are valuable tools for the classroom, but I do think
that we could use some help from the math teachers here. I suspect
that much of the problem comes from them. They also, by their nature
are not very interested in numbers as they relate to the real world,
and so they don't emphasize the GIGO aspect of calculators when they
teach them. I have never known a math teacher who has any kind of
intuitive feel for sig. figs. or for order of magnitude calculations
and, as they teach about calculators, I suspect they pass that lack
on to the students, who, for their part, are quite happy to not have
to worry about something. Undoing that has been difficult, if not
impossible, in most cases.
The advantage of a slide rule for pedagogical purposes was that to
use it you *had* to have a feel for both sig. figs. and order of
magnitude, and I have found that appreciation to have been invaluable
over the years. It has kept me out of trouble more than once.
Although I am far from an expert at "Fermi problems," I have been
able to develop that ability to estimate answers because for most of
my educational years, the most advanced device we had for calculating
was a 10-inch slide rule. Now, when I bring out my slide rule to show
a class, they look upon it as some sort of museum exhibit.