Well, "simplified form" is the mathematical equivalent to "proper
grammar" in a natural language. To the extent that people communicate
well without it, "it" is not needed in the curriculum.
Of course, this varies with the portion of the curriculum being
discussed. In the case of fractions, "simplified form" often improves
communication. (In most settings, saying "forty-eight sixty-fourths"
instead of "three fourths" is not as clear, and might be a little rude
-- unless the specific culture is based on sixty-fourths.) In the case
of radicals, I have not come up with any situation in which "simplified
form" improves communication in a significant manner. In other
situations, such as polynomials, simplifying is basic to good
communication.
Based on this reasoning, I see merit in covering "simplified form" for
fractions -- though I don't think we need to be extremely picky about
always using it. In the case of radicals, very little on "simplified
form" is needed for good communication, so very little should be covered
(based on this reasoning). For polynomials, we should be more demanding
about simplified form.
(Hopefully it's obvious, but I'll say it anyway: The curriculum can not
be built on one factor -- such as "good communication". A rich
curriculum deals with several factors, including understanding -- and
mathematical beauty -- as well as application, and other factors.)
Isn't amazing how such a brief note results in some of us becoming
long-winded??
Jack
--
<<<<<<<<<<<<<<<<<<<< from >>>>>>>>>>>>>>>>>>>>
Jack Rotman phone (517)483-1079
Math Professor ROTMAN@ALPHA.LANSING.CC.MI.US
Lansing Community College Lansing, MI
"Like all art & science, mathematics surrounds us."
<<<<<<<<<<<<<<<< Math Success ! >>>>>>>>>>>>>>>>>
dept web page http://www.lansing.cc.mi.us/sas/mathsci
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