2004 January 11
John
In reply to 28228 you ask why not teach fractions.
I answer with these two e-mails to USMA.
I also say that it has been said that even teachers have
trouble dividing 16 5/8 inches by 3.
Robert H. Bushnell
Subj: [USMA:5269] Kitchen counter top replacment
Date: Wednesday, May 17, 2000 16:19:25
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Monday and Tuesday we had our counter tops replaced.
The young man, David, doing the work looked out the
kitchen window and saw
my round outdoor Celsius thermometer and commented
on it. He used the term centigrade and I simply
replied that they modern version of metric useage
called it Celsius after the developer of the scale.
The ensuing conversation made it clear that he, aged 35,
would be pleased to see the US change. His made points
about the process of training young apprentices in
which it is very, very difficult to find anyone who is
really capable of using fractions and their industry
tolerances are down to 1/32nds inch. Hardly anyone can
compute fractions, and to ask someone how to find the
lowest common denominator is like rocket science. I
count him as another of the large silent group who would
welcome metrication, but he can't do it alone. He does
not own the company. When I asked David how would you
get workers to use metric, he said they would probably
have to throw away their inch tapes.
Subj: [USMA:12139] Re: Distance signage, in metric
Date: Tuesday, April 6, 1999 22:33:51
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED], [EMAIL PROTECTED]
1999-04-07
There seems to be some correlation: wombat and fractions
vs. metric and decimal. Never do the two mix.
(never do we see "3 1/2 km").
Anyone have any idea why?
cm
There is a very simple explanation. The SI is set up to work
with decimals, and does not lend itself to work in the
fractional format that non-SI units do. So, people in metric
countries are not taught about fractions in the same manner
as Americans are. They know how to divide fractions to get
decimal numbers. They don't have a feel for numbers left in
fractional form. So, it isn't done. So, 3 1/2 km is never
seen; it is always seen as 3.5 km. 3.5 takes up less space
than 3 1/2. There are many reasons why fractions are bad.
1.) You don't have the infinite range you have with a decimal
number.
2.) Decimal numbers, by the number significant digits shown,
have self implied accuracy. Fractions do not.
3.) Fractions are hard to add and subtract if the bases are
not the same.
4.) People have difficulty visualizing fractions smaller than 1/8
increments.
5.) Fractional bases other than divisors of two, are even more
difficult to work with.
In order for non-SI units to work and be effective, the user has
to have an very good working knowledge of fractions. The over
emphasis on teaching fractions at the expense of decimals, makes
it difficult for Americans visualize a decimal number, so
fractions are seen more often. Even if an American didn't have
a clue as to what 1/8-th inch was, they would be more comfortable
seeing 1/8 than 0.125.
I also find it strange that road distances are given in fractional
miles and feet, when odometers are gradiated in 0.1 mile increments.
I guess it goes to show, that the driver, is more satisfied seeing
something he can't measure, that something he can. He feels more
comfortable seeing fractions, even if he has no means of gauging
the distance. The driver might not be smart enough to realize that
a quarter mile would mean 2.5 tenths on his odometer. If the
distance sign said, 0.25 or 0.3 mile ahead, the driver might not be
able to relate the 0.25/0.3 to 2.5/3 tenths on his odometer. He
either recognizes that 1/4 figure and attaches no meaning to it, or
sees the sign and knows his exit is upcoming and just moves over.
If the distance figure was removed, the result would be the same.
This over emphasis on fractions, shows up when decimal numbers
have to be written in fractional format. Why must 0.3 be shown
as 3/10? Obviously, it is because Americans feel more comfortable
with seeing a number in fractional format. I've even seen gas
priced as 1.29-9/10 instead of 1.299. The extra 9/10 had to be
added on. Because of the emphasis in teaching fractions vs.
decimals, what seems simple to the rest of the world is seen as a
great difficulty to Americans. To end this, fractions have to be
de-emphasized and decimals emphasized. You can even buy
calculators, that display results in fractional format. This is
done to accommodate the American hunger to be communicated with
in fractions. As long as fractions are given a high ranking in
the American means of counting, metric has a slim to none chance
of ever gaining more than a foot hold.
John
Subj: [USMA:12140] Re: Fractions
Date: Wednesday, April 7, 1999 9:49:14
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
John is absolutely right. American schools waste an astonishing
amount of time on fractions. Even the SAT test students take
to get into college is full of unrealistic fraction problems.
Fractions are drilled into students so much they try to use
them everywhere.
