From: Grover.Partee@f58.n343.z1.fidonet.org (Grover Partee)
Newsgroups: k12.ed.math
Subject: Arbitrary Techniques?
Date: Wed, 07 Oct 92 17:18:09 PST
Organization: FidoNet node 1:343/58 - Silver Lake, Everett WA

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 BBS: Silver Lake BBS
Date: 10-03-92 (11:21)             Number: 12740
From: BRIAN HARVEY                 Refer#: NONE
  To: ALL                           Recvd: NO
Subj: Arbitrary Techniques?          Conf: (65) K12_MATH_E
BH>From: bh@anarres.CS.Berkeley.EDU (Brian Harvey)
BH>Date: 3 Oct 1992 15:40:48 GMT
BH>Organization: University of California at Berkeley
BH>Message-ID: <1akeu0INN30t@agate.berkeley.edu>
BH>Newsgroups: k12.ed.math

BH>Grover.Partee@f58.n343.z1.fidonet.org (Grover Partee) writes:
 >I seem to recall that my students quit offering that particular
 >complaint as soon as we started "word problems."  Then, it was just
 >"Ugh!  I hate word problems!"  "REAL life," of course, consists of
 >word problems!

BH>This reminds me of a funny passage from _Letter to a Teacher_ by the
BH>Schoolboys of Barbiana, a great book written by students at a small
BH>parochial school in Italy.

BH>        The geometry problem on the exam brought to mind a sculpture
BH>        in one of the modern-art exhibitions: "A solid is formed by
BH>        a hemisphere superimposed on a cylinder who surface is
BH>        three-sevnths of that ..."

BH>....

BH>        And so Carla was tested on a modern problem on her exam this
BH>        year, based on boilers:  "A boiler has the shape of a
BH>        hemisphere superimposed..."  Back to surfaces again.

There is, however, a potential difference.  Instead of simply laying
out the various shapes and dimensions and then asking what the surface
are would be, suppose we give the students the picture and ask them
how much paint they will need to paint it?  That's a REAL problem,
since some people do have to paint boilers as well as other odd
shapes.  Possible similarly real extensions abound.  For example:
Paint A covers 22% more surface per gallon but costs 8% more than
Paint B.  Morover, the boiler would need to be repainted in 15% less
time.  Which is the cheaper paint?  Would that answer change if you
had 3 such boilers?  What if Paint A covered 30% more surface per
gallon.  What if the price of paint B falls by 5% or you get a
quantity discount of 10% if you buy 50 gallons of A but only if you
buy 100 gallons of B?  If you only need 92 gallons, would you be
better off buying 100 gallons any way?

I am, of course, just pulling numbers out of the air here and we need
a lot more data to actually solve this problem, but I hope you can see
that this sort of approach lends itself very well to the "real world."
Decisions along these line make the difference between profit and
bankruptcy for painting contractors all the time!

I also see some real potential for "team problem solving" on these
kinds of more complex problems.  Teamwork is utilized rarely in
science classes and almost never in math classes.  (At least that was
the case in the ancient past - when I was in school!)  It seems to me
to be a shame.  Many of our scientists and mathmaticians have poor
interpersonal skills, yet the best work is often done by teams rather
than by individuals.  Granted that it may seem like more work.  No; IS
more work.  But, you probably will find you have several extra
"teachers" to help.  Certainly, IMHO, you will have far more learners!


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