This system of measurements – now known as the Imperial system – worked quite well up until about two hundred and fifty years ago, or until the advent of the Industrial Revolution.

The science of mechanical engineering developed at a heady pace in the eighteenth century (in much the same way as computer technology has developed over the past thirty or forty years) and engineers who had, in their youth, been happy to work by eye, found themselves making more and more intricate machinery that had to be built to very precise specifications. They soon found that the old systems of measurement did not lend themselves to this sort of work – for example, while it is possible to divide an inch quite easily into halves, quarters, eighths, sixteenths, and thirty-seconds, it would obviously be easier if there was a unit much smaller than an inch when one had to work with very small measurements; another problem was that there was no logical correlation between the system for measuring weights, and that for measuring volumes, and that for measuring distances, a fact that resulted in scientific calculations becoming very complicated.

At around the time that people were becoming aware of these difficulties, a cataclysmic political change took place in Europe’s largest and most populous country – France. For a brief period of time, there was no aspect of life that was regarded as being too sacred to be changed by France’s new revolutionary government, and amongst all the other changes – which included introducing a new calendar and abolishing the church – the country’s system of weights and measures was designated as being in need of reform. A commission of revolutionary scientists and mathematicians was set up and given the task of devising a system of measurements that would be based on pure reason.

The system that they devised was essentially the Metric system that we use today.

Its starting point is a unit of measurement – the metre – which was originally defined as being one ten millionth of the distance between the North Pole and the equator, on the line of longitude that passes through Paris. Standard prefixes were used to denote multiples and fractions of the basic unit: kilo is a thousand, so a kilometre is a thousand metres, a kilogram is a thousand grams, etc.; centi- designates a 1/100th so a centimetre is one hundredth of a metre; milli- is a thousandth, so a millimetre is 1/1000th of a gram, and there are therefore ten millimetres in a centimetre.

Other units were developed in relation to the metre: a gram, for example is the weight of 1 cubic centimetre of water at a standard temperature and pressure, and a litre is a thousand cubic centimetres of water.

From the outset, the metric system made use exclusively of decimals, and left no room for ordinary fractions – there is no place within it, therefore, for one third of a metre, or one seventh of a gram.

This supremely logical system won great acclaim amongst intellectual people in France, and was soon imposed upon the rest of Europe by Napoleon Bonaparte, as part of the reforms that he inaugurated in the wake of his conquests.

The subsequent history of the two systems of measurement raises some interesting questions. It is not surprising that Great Britain did not immediately embrace the new system of units – because it was at war with Napoleon – but it could be considered as surprising that it was Britain, with its old-fashioned system of Imperial units, that continued to lead the way in industrial and technological innovation over the next one hundred years, while its continental neighbours, with their super-logical units, lagged far behind.

Similarly, the United States did not adopt the metric system, but here too the Industrial Revolution progressed at a breakneck pace – once again without any standardised or rational system of measurements.

In the field of pure science, however, the new system had been almost universally accepted, and as new branches of science were developed that required new units for things such as power, work, force, current, capacity, heat, etc. it was units compatible with the metric system that were always used. Also, the fact that the metric system exclusively uses decimals has made it perfectly compatible with computers and electronic calculators.

The dominance of the metric system in the field of science is the reason why governments want schools to teach the metric system rather than the Imperial system, but there is another side to the story. Even in countries in which the metric system has been used consistently for two hundred years, it is still not universally understood or accepted: in France, for example, if one buys vegetables on the market, one still asks for a ‘livre’ (one is given half a kilogram, but a livre, or pound, is a measure that pre-dates the metric system), and farmers still pace out their fields in the time-honoured fashion if they want to work out who owns what. Also, perhaps because of the economic dominance of the United States, which has remained remarkably attached to its old system of measurements, even some of the most high-tech products on the market are still rooted in the Imperial system – for example, television screens and computer monitors are made and sold in inches, the world over, and nearly all taps are sold as ½˝ or ¾˝ fittings.

The reason why the metric system has not been able to gain universal acceptance outside the world of science is probably because of the false premise that was in vogue at the time of its origin, i.e. that man is purely a being of reason. Experience has shown that man is not only rational but also has feelings; the Imperial system of measurement is much easier to relate to in an intuitive sense than anything in the metric system, and this explains its enduring popularity with ordinary people: everyone understands the concept of a foot long, an inch wide, a stone weight, etc. Also, because they evolved over a period of time, the Imperial measures fit the requirements of everyday life – a pint of liquid is a useful amount; a pound of flour, is enough to make one good loaf, etc. The metric system, because it was invented more or less overnight, and because it is constrained by being linked to 1/10 000 000 of the distance from the North Pole to the Equator, often generates units that are not particularly suited to everyday life: for example, no one ever really wants a gram of something; a litre is too much to drink, but not as convenient as gallons when filling the car; and kilometres aren’t quite long enough when it comes to measuring distances from one place to another.

This leads to the question of how measurements should be taught. Ideally, you ought to be able to make use of the the complexity of the current situation to help a child to gain a better understanding of the concept of measuring than would be possible if they only had to deal with one system.

The aim should obviously be to help children to become fully conversant with both systems: this will not only prove to be useful in later life, but it will also help them to understand that all attempts to measure are arbitrary, and do not have any fundamental or absolute truth associated with them.

The obvious starting point is the Imperial system - because it makes more sense intuitively, and young children are very finely attuned with their feelings. However, even with young children it makes sense to have rulers, measuring jugs, and scales, marked with both sets of units, so that they can subconsciously pick up the idea that there are two systems of measurement in use.

A big advantage of the Imperial system for young children is that it uses fractions rather than decimals. Most children readily understand the concept of halves, quarters, thirds, etc., but often have great difficulty in understanding the concept of putting numbers after a decimal point (1.5 cm, for example, does not make sense to most children).

The easiest way for children to become familiar with decimal points is in relation to money, and if metric measurements are put to one side until a child is familiar with working out sums involving money, a lot of potential problems can be avoided.

Fun can be had by making comparisons between the two systems – guess how many centimetres there are in a foot, etc. – and you can practise measuring things out first with one system of units and then with the other, to discover for yourselves the relative strengths of each system. If children become interested in science, then, obviously, they will encounter the metric system in text books and articles, and, in a sense, it will explain itself automatically. If they do not become particularly interested in science, then they may never become fully conversant with the intricacies of metric measurement – but in this they will be no different from the vast majority of people, many of whom have been subjected to years of schooling on the subject which has left them deeply confused.

As with other areas of maths teaching, when telling children about measuring it is important to remember that learning has to be enjoyable. If you feel that a child is starting to become distressed or confused by trying to understand what you are telling them, it is best to tactfully move on to something else - read a story or go for a walk, for example. Experience shows that when allowed to work at their own pace, children learn everything that they need to learn, and this is sure to include being able to use any conceivable unit of measurement that they may come across.

Gareth Lewis

Shan Jayran explains the origins and the philosophy behind new internet-based courses designed with home educating families in mind: www.firstcollege.co.uk 

Home Education school? – a lively contradiction.

We home educated autonomously for 7 years - and loved it. But from 12 upwards we found more was definitely needed. First College UK is what we tried to find, but it didn’t exist. It’s been great seeing our boy come sharply alive and stimulated intellectually, and making new friends.

Basically we’re a halfway house between home education and school.  We’re veteran home educators, plus experienced teachers.  With other teachers we provide 10-12 hours of classes a week for small groups of 5–15 students.  Classes are interactive, lively and fun.

The internet is our blackboard for English, French, History & Geography, Maths, Sciences, and Philosophy&Society.  Art&Webdesign starts in the summer term.  We do prepare for IGCSE exams (but exams are optional). We rely on classic well tried learning skills, not the National Curriculum.

Students log on at 9.30 finishing 2pm Monday–Thursday. There are homework projects, and students can socialise as much as they want outside classes, in groups or one-to-one online, or by phone. Family meet-ups and a summer camp are coming. Interested parents are getting involved in the running of the project.

Students are very varied, many in the UK but some international.  Most are home educated but we’re also rescuing some from school tragedies. It’s wonderful seeing deschooling happening very fast in a daily home education style community, though this takes a lot of personal attention of course.

“I really like schoool now lol ! the 1st time in my life!” (Day 2, one student to another.)

Parents have said:

“The steepest learning curve seems to be for us parents in getting to grips with this new way of learning - the students all seem to be taking to it really quickly.”

“We are really impressed with the sites and [X] is hopping with excitement to get back on. It is far more interactive and interesting than I was expecting.”

“Her ability to converse and contribute intelligently was  something we had underestimated.”

“I particularly like the way the children are helping one another and are being encouraged to work as a group.”

www.firstcollege.co.uk 

Letters

Feedback on last Month's History Article:

Dear Gareth,
I remember a documentary on Television last year which was about the oldest art work to be found in prehistoric remains 'proving ' that people of that time had finally learned how to think!! and discussing as if it were fact, the point that poor old cave-men were virtually without thought or imagination.

I often wonder if these experts ever had an original thought themselves. So often today, children are expected to accept what they are told in school or by 'experts' without question.  My daughter had an interesting conversation with a US girl on the internet about why the US were THE world's leaders??? (could fictional films have anything to do with that?)

Up until about 30 years ago, little was said about aboriginal peoples and what became of them. 'Natives' were just quaint , slightly rude (naked sometimes) people who lived without modern conveniences. Children were not told why these peoples were disappearing from the world or shown evidence that these people had wisdom superior to 'civilised people' eg. medicines from plants, vetinary knowledge and superb levels of fitness. Nor that these people were sociable far beyond anything in modern man's experience.

Captain Cook and Christopher Columbus were heroes. The Crusades (and later missionaries) were to teach poor heathens how to have religion , so that they could go to heaven.

My 2 children are coming to the end of Home schooling (but not self education) ,one is in 6th form college and the other will be in September. The one already there is doing very well (he has been mistaken for a teacher a few times ;) ).

I believe they have learned to question everything around them (this was not seen as a good thing when they were little, hence home schooling) and surely that is what we humans have been doing ever since we began.

Excellent article re. history. I think I can tell you when the idea of progress began. I've been researching Darwinism and contained within evolutionism is the idea of progress - onward and upward towards the perfect human being (eugenics, or Hitler's racial hygiene). This goes together with the promotion of euthanasia (involuntary killing), abortion and infanticide, promoted today by the bioethicist, Peter Singer (Princeton University). I've been quite surprised by how much the modern world is influenced by Darwinism, also called naturalism/materialism/humanism/modernism. It leads also to moral relativity as opposed to absolute morality, since the morals evolve along with the man.

Interestingly, there is no actual mechanism for the transmutation of one genus/kind into another. Natural selection can lead to the formation (by isolation) of new species which cannot breed with each other, but this doesn't provide the mechanism for molecules to man evolution. Darwin's finches were still birds. Prof. Dawkins insists that one kind evolves into another by the accumulation of mutations. But mutations are a loss of information and although many diseases and disabilities are caused by mutations, few beneficial mutations are known, eg. sickle cell anaemia ameliorates malaria and wingless beetles which are not blown away off their island.

The word "evolution" is used interchangeably (and dishonestly) for microevolution which is happening all the time, and macroevolution which is supposed to have happened in the past but no-one saw it. It's therefore an untestable hypothesis.

Your letters and comments are welcome. You can send them to Gareth Lewis at the following address, or to me at the address beneath:
gareth.lewis@freedom-in-education.co.uk

wendy@freedom-in-education.co.uk

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