Fractions DO have a role - in algebra when one is manipulating symbols, but I agree with Pat, they do not have a role when one is manipulating numbers.
_____ From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Pat Naughtin Sent: 26 July 2008 05:30 To: U.S. Metric Association Cc: USMA Metric Association Subject: [USMA:41501] Your sixty second lecture -- Down with fractions! 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.
