Dear Pat,
I vehemently disagree with this recurring theme of "down with
fractions." Had you only sought to remove fractions from physical
measurements such as expressing lengths in fractions of inches or volume
in fractions of liters, then I would happily agree. In these cases
fractions are difficult to manipulate, obscure comparisons, etc.
However, fractions are a fundamental concept common to nearly all
mathematics. It is extremely common in daily life to need to divide a
whole into equal parts, from dividing up a pizza or a bag of candies to
leaving one third of my estate to each of my three children. Forcing
the use of decimals to replace fractions isn't practical. For example,
the fraction 1/7 is extremely simple and easy to grasp. The decimal
number 0.142857... is difficult and clumsy, and it obscures the meaning
of the number.
The real problem is that American schools are failing at teaching math.
Too many elementary school teachers are innumerate themselves, and too
many textbooks are written from the ivory tower. Removing fractions
from elementary education would be yet another nail in the coffin,
watering down an already weak curriculum.
J.
Pat Naughtin wrote:
Dear Professor Dennis DeTurck,
Congratulations on your rethink of the place of fractions in primary
school education. I found out about your idea from the sixty second
lecture you made for iTunesU — Down with fractions!
I really liked your presentation and I thought that you might be
interested in the fact that I have come across a very similar concept
in three other areas that may be of interest to you. These areas are
historical, practical, and economical.
1 Historical
In 1585 Simon Stevin, from Brugge in Flanders (now in Belgium)
published two books with the same content. De Thiende (Of Tenths) was
written in Flemish and La Disme (The Tenths) was written in French.
These were decimal arithmetic books in which Simon Stevin described,
and vigourously promoted, the use of decimal numbers instead of common
or vulgar fractions. For an English translation of Stevin's work I
suggest Robert Norton's translation of 1608 (DISME, The Art of
Tenths, OR, Decimall Arithmetike).
For a full treatment on this subject, and to place it into an
historical perspective, you might like to refer to the article
'Metrication timeline' that you will find
at http://www.MetricationMatters.com/articles.html or you can go there
directly
at http://www.metricationmatters.com/docs/MetricationTimeline.pdf
where you might find the dates from 1584 through to 1608 particularly
interesting. While you're there, you might like to review the part
that Benjamin Franklin, Thomas Jefferson, and George Washington played
in promoting decimal fractions (and inadvertently, perhaps,
de-promoting fractions?) by searching for their names.
2 Practical
This takes your suggestion of ridding the world of fractions one step
further.
In the 1970s, I had had the opportunity to work on the metrication
programs of several building trades where the metrication program was
quick, smooth, and relatively cheap (mostly completed in less than a
year). This was before I moved to the textile and clothing industries
where the metric transition is still muddled, bitter, and enormously
expensive (nowhere near completion after more than 38 years — and
counting). In comparing these metric transitions, I was immediately
struck by one significant difference: the building industries had all
chosen the millimetre as their small length unit, and the textile
industries had all chosen the centimetre as their small length unit.
I was simply curious to see whether these same conditions applied in
other industries so I investigated further and found that it is
generally true that industries that choose millimetres make their
metric transition much faster than those that choose centimetres.
Despite this clear observation it took me years — I must be a slow
learner — to reach any conclusions as to the reasons for this profound
difference. Here are some of my thoughts.
If you choose millimetres as your small length unit you have these
immediate advantages:
All measurements are whole numbers, so there are no fractions at all.
You remove all references to vulgar fractions (such as halves, and
1/16ths).
You remove all references to mixed numbers (such as 4 2/3 and 6 7/8).
You remove all references to decimal fractions (such as 2.34 and 3.456).
In short, there are no common, or vulgar, fractions, and there are no
decimal fractions.
All measurements can be entered into a calculator without any conversion.
On the other hand, the choice of centimetres in the textile industry
gave no such clear advantage to textile and clothing workers. The
halves and quarters formerly applied to inches were simply transferred
to half centimetres, quarter centimetres, half metres and quarter
metres. And, even worse, textile and clothing workers had the added
disadvantages of decimal fractions of centimetres — that they had
rarely met in the textile trade before — and all the problems of
converting between fractional or decimal metres or centimetres into
fractions of yards or inches.
In 1974, as part of the metrication process in Australia, the building
industry adopted a policy of using millimetres (only) on building
sites, and as I wrote above, this had the effect of removing fractions
from almost all practical arts and crafts in Australia because most
other trades followed their example, and subsequently followed their
successful metrication program.
In Australia where the recommended small unit for buildings is the
millimetre. In Australia, the building trades were very clear about
this. The Australian Building and Construction Advisory Committee
policy was:
The metric units for linear measurement in building and construction
will be the metre (m) and the millimetre (mm), with the kilometre (km)
being used where required. This will apply to all sectors of the
industry, and the centimetre (cm) shall not be used. *
With these words the Australian Building and Construction Advisory
Committee effectively banished centimetres from the building trades in
Australia, with the result that metric conversion in these trades was
smooth, rapid, and complete. They made it clear that the centimetre
should generally not be used, and in particular:
… the centimetre should not be used in any calculation and it should
never be written down. *
*Standards Association of Australia 'Metric Handbook, Metric
Conversion in Building and Construction 1972
Typically, a metrication upgrade was completed in about a year (and
definitely in under two years) if millimetres were chosen. As the
choice of centimetres retains all of the old pre-metric common or
vulgar fractions it dramatically slows down the metrication process. I
know that this sounds ridiculous, but based on my observations you
should expect a metric transition to take more than 100 years if you
choose to use centimetres.
Where metrication has been successful, rapid, and economical, the
millimetre has been the chosen unit not only in Australia but also in
many other places in the world such as India, New Zealand, and South
Africa.
The Australian Building and Construction Advisory Committee seemed to
be well aware that centimetres (together with their fractions, mixed
numbers, proper and improper fractions etc.) were not only unnecessary
but also a major impediment to learning and using the metric system.
Their position has been proved by subsequent practice over almost two
generations. It's just as easy to estimate distances in millimetres or
metres as it is using centimetres; in fact, if you already have a
mindset that includes centimetres in your measuring vocabulary then
you have already (perhaps inadvertently) chosen the most difficult
measuring path, and that path will be strewn with fractions (both
common and decimal) and many conversion errors.
For a full treatment and discussion of the issues pertaining to
centimetres and millimetres, see centimetres or millimetres — which
will you choose? from http://www.MetricationMatters.com/articles.html
or you can go there directly
at http://www.metricationmatters.com/docs/centimetresORmillimetres.pdf
3 Economical
Please watch this short funny YouTube clip
(at http://youtube.com/watch?v=Omh8Ito-05M ).
As you watch, keep these thoughts in mind:
a This motor bike was built in metric — the exhaust is 180 millimetres
at the front and 140 millimetres at the back — the problem the
mechanics seek to solve is 'What is 180 minus 140?'
b How much are these fraction calculation costing this motorbike company?
c How much does preserving fractions cost the economy of the USA? My
attempt at an answer is
at: http://www.metricationmatters.com/docs/CostOfNonMetrication.pdf
Cheers,
Pat Naughtin
PO Box 305 Belmont 3216,
Geelong, Australia
Phone: 61 3 5241 2008
Metric system consultant, writer, and speaker, Pat Naughtin, has
helped thousands of people and hundreds of companies upgrade to the
modern metric system smoothly, quickly, and so economically that they
now save thousands each year when buying, processing, or selling for
their businesses. Pat provides services and resources for many
different trades, crafts, and professions for commercial, industrial
and government metrication leaders in Asia, Europe, and in the USA.
Pat's clients include the Australian Government, Google, NASA, NIST,
and the metric associations of Canada, the UK, and the USA.
See http://www.metricationmatters.com/
<http://www.metricationmatters.com/>for more metrication information,
contact Pat at [EMAIL PROTECTED]
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