On 2005 Oct 14 , at 8:19 AM, Paul Trusten, R.Ph. wrote:
With regard to the positive aspects of studying "fractions," I think
what is
being described here are ratios. Equations, functions, relations,
often involve
a ratio, which is an indispensible concept. Trigonometric functions
are ratios,
plain and simple. At the same time, it should remain the goal of
educators to
curtail those rote fraction drills that are more related to supporting
WOMBAT
than they are to advancing the study of mathematics.
Thank you, Paul, for clarifying what I have been trying to say. I can
agree that learning ratios is important (and I guess you can call them
"common fractions" if you wish). Ratios like 1/2 which we can call "one
half" and 1/4 which we can call "one quarter" are useful. Even ratios
like (15 982 378 )/(295 734 134) are useful. (This is the ratio of the
population of Jacksonville, Florida to the population of the entire
United States.)
What is NOT useful, at least in the lower grades in school, is the kind
of mind-wracking arithmetic that is taught regarding such ratios. While
we can easily memorize (and visualize) such relations as "two quarter
make a half" and "one half and one quarter equals three quarter", we do
not need such foolishness as "how much smaller is a 17/64 inch hole
than a 9/32 inch hole" and "what is the area of a rectangle that is 7/8
inches long and 9/16 in wide". Similar absurdities are subtracting (3
and 5/16) from (5 and 15/24) and adding a string a values like
7/12 + 8/3 + 9/14 + 5/8 + ... etc.
Even my example of the ratio of Jacksonville's population to that of
the entire US would never be used in a situation where this ratio would
have to be added, subtracted, multiplied or divided by another such
ratio. It would be most likely dealt with by dividing it out (and
probably expressing it as a percent), giving the result that
Jacksonville's population is 5.404 % of the US population, rounded to
four significant figures.
Learning the rules for multiplying, dividing, adding, subtracting and
comparison of numbers written in common fraction form is mainly useless
to the general public and certainly to elementary school children.
There are indeed situations in mathematics where it is useful to know
how to do such things. When students have learned some algebra, these
processes become almost trivial. These operations can be taught in high
school or college when the student's take more advanced math courses
and/or when they need it in situations such as science or other
specialized fields.
Eliminate Ye Olde English units and you eliminate in the lower grades
the need for the arithmetic of common fractions.
Regards,
Bill Hooper
Fernandina Beach, Florida, USA
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Go Metric America! Or get left behind!
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