Begin forwarded message:
From: Pat Naughtin <[EMAIL PROTECTED]>
Date: 30 July 2008 8:56:47 AM
To: [EMAIL PROTECTED]
Subject: Re: [USMA:41510] I'll keep fractions, thank you
Dear John,
Thanks for your response. I will respond in turn by interspersing
some remarks in red.
On 2008/07/28, at 12:57 PM, J. Ward wrote:
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.
As you will have noted from my congratulations to Professor Dennis
DeTurck (below) they were for his proposal to rethink the teaching
of fractions which in many instances are now out of place in a
modern world and therefore out of place in a modern curriculum.
Consider the case of the fraction 3 1/7 that I had to spend
countless hours manipulating so that I could become autonomously
familiar with its operations. I knew it as the mixed number 3 1/7 as
well as the improper fraction 22/7. This has now all passed. I now
own a calculator and 3 1/7 is no longer needed in my life (although
its still there) and I tend to just push the π (pi) button on my
calculator.
However, that said, I thank you for your support of my campaign to
remove fractions (both decimal and common or vulgar fractions) and
to replace almost all of them with whole numbers and whole number
calculations as the wise use of the SI metric prefixes allows us to
do. For example millimetres in the building trades work extremely
well and micrometres could work just as well in all of the
engineering trades and the printing trades.
By the way, your letter prompted me to think about the way that we
were taught to use 3 1/7. One of the short-cuts I was taught
involved the approximate formula:
Area of a circle = diameter squared by 11/14
I now use this as:
Area of a circle = diameter squared by 0.8
This is as useful, as approximate, and quicker that the old way of
doing x 11/14 in my head.
However, fractions are a fundamental concept common to nearly all
mathematics.
I agree completely. And this is absolutely true if your sole aim is
to produce mathematically able engineers, mathematicians, and
scientists. However, other goals in schools are surely to produce
people who are competent measurers of paper, cloth, timber, metal
for machining, and metal for welding. These require well grounded
measuring skills using practical measurements. There needs to be a
balance between measuring skills and arithmetical manipulation
skills such as fractions. I suppose that I am arguing for such a
(new) balance.
As you know I firmly believe that a thorough and practical grounding
using millimetres is core to this development in the minds of
students.
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.
I don't think that I have ever argued against knowing basic
practical skills using as you outline here. However, the amount of
this has to be developed within the context of the modern reality of
our current physical and intellectual environments. The world has
calculators for example. We don't need to use the algorithms based
on the manipulations of fractions that we needed in a world without
fractions. For example, when was the last time you calculated a
square root from the basic algorithm you were taught at school or
college (instead of pushing the sq.rt. button on your calculator.
The real problem is that American schools are failing at teaching
math.
Agreed.
Too many elementary school teachers are innumerate themselves,
Agreed. And it follows that American schools are failing at teaching
math for a long time.
and too many textbooks are written from the ivory tower.
Agreed. And don't forget the power of the textbook lobby to
influence curriculum decisions.
Removing fractions from elementary education would be yet another
nail in the coffin, watering down an already weak curriculum.
No, I don't agree with this. I think that mathematics curricula need
to be constantly upgraded — and strengthened — to suit the
environment in which children currently live (with due consideration
given to their perception of this environment). I think that this is
the best course for the individual children, the best course for
their mathematics education, and the best course for the nation of
the USA as a whole.
I also think that mature adult thought must be considered to
project the expected environment into which these children will
become adults in a working adult world. For example if, as the
President of the USMA stated to the recent USA Math Review, the USA
is already about 60 % metric in its manufacturing industry, then
practical measuring using the metric system needs a much higher
priority in USA schools. If time spent on fractions must be reduced
for this to happen then so be it.
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.
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.
