Innumerate teachers, parents, children and others as Ward mentions/implies
is a primary cause in math illiteracy.
The refusal of the education establishment in the United States to adopt
interactive student-centered learning and assessment using technology such as
One Laptop Per Child (an OLPC costs less than $150) which can be used Any time
in Any Place on Any Path at Any Pace.
More than a million OLPCs have been sold for less developed countries; it
was developed by MIT for that purpose. However, OLPCs also should be used here
in the US to learn math, English, physics and science, geography and other
subjects.
Stan Doore
.
----- Original Message -----
From: J. Ward
To: U.S. Metric Association
Cc: U.S. Metric Association
Sent: Sunday, July 27, 2008 10:57 PM
Subject: [USMA:41510] I'll keep fractions, thank you
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/ for more metrication information, contact
Pat at [EMAIL PROTECTED] or to get the free 'Metrication matters' newsletter go
to: http://www.metricationmatters.com/newsletter/ to subscribe.
