On Aug 13 , at 7:04 PM, James R. Frysinger wrote:
However, if we do away with teaching the math skills needed to deal
with fractions of one form or another, students lose a whole sector
of understanding.
In short, we must teach students to deal with both decimals and
fractions. Each representation has advantages and disadvantages.
While I wholeheartedly agree with the above, I would add one other
thing. As was pointed out a the start of this thread, the primary
reason to use common fractions (as opposed to decimal fractions) is
the ease with which they make certain kinds of ALGEBRAIC manipulations
(and solutions) easier. Thus, while agreeing that common fractions
should be taught, I would suggest that they should not be taught until
algebra class (usually high school), not in elementary school*. In
elementary school, teach ONLY decimal fractions, along with teaching
ONLY metric measures.
Bill Hooper
1810 mm tall
Fernandina Beach, Florida, USA
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*I do realize that younger students will encounter a few common
fractions in daily life, esp. 1/2, 1/4, 3/4 and maybe 1/3 and 2/3.
These students can learn that these things (using 3/4 as an example)
stand for "three of the pieces when something is cut into four equal
pieces". That may also be expressed as a decimal fraction by simply
treating "3/4" as "3 divided by 4", or 0.75. There would certainly not
be any pressing reason for them to start learning common fraction
arithmetic like adding and subtracting common fractions.
In the unlikely case where that need should arise, teach them to
convert the common fractions to decimal form and then do the
arithmetic. If a student needs to know how much pie he or she has when
given 1/3 of one pie and 1/4 of another pie, they don't need to go
through the complicated process of converting 1/3 and 1/4 into
fractions with a common denominator (4/12 + 3/12). (This also requires
learning the additional skill of how to find the least common
denominator). They would then have to do the additional step of adding
4/12 + 3/12 which is equal to 7/12. (One also has to teach how to do
this additional step - it's easy but not obvious. Many students want
to add 1/3 + 1/4 to get 2/7, or 4/12+ 3/12 to get 7/24.)
Instead, just change the problem from "1/3 + 1/4" to "0.33 + 0.25" and
get the answer 0.58. I think that a 0.58 fraction of
a whole pie is easier to comprehend than 7/12 of a pie. (Who ever cuts
a pie into 12ths anyway? And even if they did, would getting 1/3 of
one pie and 1/4 of another pie somehow magically turn the two given
pieces into 7 pieces of pie divided into 12 equal sized pieces?)
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SImplification Begins With SI.
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