People are too dependent on pencil and paper :-)}

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People are too dependent on pencil and paper :-)}

If you need to calculate 7 times 13, do you reach for:

        a) a calculator
        b) a pencil and a scrap of paper
        c) a swallow of water after coming up with the answer in your head?

How about 1200(8 - 3) ?  I find it very hard to convince anyone (my students
in particular) that this is really the sort of calculation that should
be performed "by inspection", and that a great many of the calculations
that we need to perform on a daily basis fall into this category.

The problem is that most people in today's society have been "poisoned" by
steady messages that the "right" way to perform a calculation is to follow
certain assigned computational procedures to grind out the answer.  The story
is really that one should always choose an appropriate tool (and method)
for carrying out a prescribed calculation or series of calculations, rather
than just reaching for your chain saw (or your trusty old crosscut saw).
How could one learn this?  Very rarely do I run into any person or text
that _teaches_ this point!

Part of the problem we are experiencing today in choosing appropriate
mathematical tools for our everyday work is that it is only recently that our
current set of new, magically-powerful, tools have appeared and we don't quite
know what to do with them yet.  It is silly to use these tools only to carry
out the practice work that was developed to help us learn to use the old tools.

 I am sure that this sort of problem came up back when the powerful new
methods of calculating with digital algorithms (pencil and paper) first
were introduced, and upset the balance that existed at that time.  Over
time it was realized that new computational domains could be reached
with the new techniques, and students were taught to carry out as a
matter of course computations that had not been formerly possible.  But
in the beginning there must have been a feeling of loss of the level of
skills developed in the old ways of computing (a lot of metal work, for
example).  And it remained true that you shouldn't have to scratch out
everything on paper!

Again today we are suddenly able to reach new computational domains,
and student should be learning to carry out as a matter of course
computations that were not formerly possible.  I can't see that it is
worth agonizing a great amount about whether students should be able
to use the old ways to the same degree of skill as previous generations
did (probably not) when tackling problems matched in difficulty level
to the old ways.  I think we ought to move on to focus on newer classes
of problems and understandings.  But it does remain true that one
shouldn't have to push every calculation through a keyboard!!

How many people on this list have run into (or collect, like I do) problems
that are _harder_ to carry out with a calculator than without?


          RWW Taylor
          National Technical Institute for the Deaf
          Rochester Institute of Technology
          Rochester NY 14623

          >>>> The plural of mongoose begins with p. <<<<
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