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Guess-n-Check in AlgPoW
Posted:
Dec 17, 2000 11:51 AM
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As coordinator of the AlgPoW service, I am happy to inform all
teachers who are using my problems with their students, that I have
just add some significant new material to my Guidelines for Writing
PoW Answers page. The most important item concerns my policy
regarding the use of guess-and-check as the primary strategy for
solving the problems. It says:
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Use of Guess-and-Check Procedure
In general, the method of "guess-and-check" is not allowed in AlgPoW
as your primary strategy to solve the problem. This is not saying
guess-and-check is not a good way to solve problems. In fact, it is
often a good way to start to understand a problem, and therefore
recommended for that. But for most of our problems, you must define
variables or unknowns, then form equations to solve by logical steps.
Historically, it was the main way that problems were solved. But as
advances were made in symbolic notation, mathematicians moved away
from it and toward the more efficient and time-saving methods of
step-by-step manipulations on equations.
One of my mentors told me that he advises students in the following
way:
"Guess and check is a valid problem-solving approach. However, it
also one of the most difficult to explain. If you are going to use
guess and check, you must list every guess, along with the reason that
you know the answer is incorrect. You also must explain why you know
your final answer is the only possible answer. In all, a pretty long
process; however, since this is the Algebra Problem of the Week, you
might want to try algebra. Please read the "Guidelines for Writing POW
Answers." The link is at the bottom of the problem."
So, unless otherwise indicated, please do not use guess-and-check as
your principal solving procedure.
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I hope this makes things more clear for everybody. I would like to
recommend that copies of the "new and improved" Guidelines page be
made for distribution to students. Some teachers have already done
this, but now there is more information than originally.
Comments are also welcomed.
Thank you.
P.S. The URL is http://mathforum.com/algpow/writing_answers.html
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