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Freedom-in-Education Newsletter November 2005
The topic is Logic
and the Standards of Education. Anyway, there are a few new Jamboree updates too, a sonnet, a short account of Yongle, the Chinese Emperor, and a recipe - and the instructions for making an advent calendar are back on line - so check it out! Wishing you all the best for a
fun-filled November, If you would like to send a comment, link, favourite quote, or news about an upcoming event to be included in next month's newsletter, please contact me. Logic & Standards of Education
Have standards of education fallen over the last half century? Simple though this question may appear to be, there is no consensus on the answer. The reason for this is that the meaning of the word education is being constantly redefined. For a graduate of a pre-war, British public school, education means a knowledge of Latin and Greek, ancient history, Shakespeare, algebra, trigonometry, and geometry. After the War, people ceased to see this as a sensible curriculum for modern life, and introduced a range of new subjects such as modern languages, physics, chemistry, biology, modern history, geography, and new branches of mathematics. In more recent times, information technology and computers have been given a larger and larger place in the school curriculum to reflect their overwhelming importance in the world of employment. These innovations have always been introduced with the best intentions - but the innovators have rarely taken the trouble to ask themselves if they are truly competent to decide what other people should learn or whether they even know what they mean by the term education. Our ideas of education can be traced back to ancient Greece. The text books that have survived most intact from those times are Euclids Elements of Geometry, (which are serialised in the Freedom in Education Magazine). Euclid followed in the tradition of other Greek philosophers: students came to study with him before embarking upon a career or taking up the responsibilities of adult life. In a sense, one could say that he taught in a school or a university, but it was a school that had no intention of teaching anything that could be used directly in employment, or that was of a practical nature. The ancient world was clearly not short of skilled artisans, technicians, builders and craftsmen - if the modern world could build cities comparable to ancient Athens, then urban life today would be quite different! - but none of these people learnt their trade at school: they were not educated people. In all probability, many of them could not read or write.
The schools of the philosophers had another purpose - to educate; i.e. the people who invented the idea of education regarded it as being something very different from a set of practical skills. A serious study of Euclids Elements of Geometry is probably one of the best ways of gaining an understanding of what people meant by education two thousand years ago - and from that, gaining a clearer picture of whether or not, in the long term, standards of education are improving. The Art of Logic Firstly, it must be noted that the schools of the ancient world did not admit young children: teachers wanted students who were old enough to form independent judgements. Before one starts to study the propositions in the Elements of Geometry, one agrees to a range of definitions, postulates, and common notions. The first of these is the idea that everything in geometry - lines, squares, triangles, circles, etc. - is made up of very small points. There is a paradox in this idea because the mind cannot conceive of an entity that is so small that it cannot be further divided: people have been tempted to say that a point is something so small that it no longer exists, but it does not make sense to suggest that things can be built up from things that do not exist. Thus, the idea of things being made up of points makes sense from one point of view, but not from another, and it is important that the student of geometry should be able to appreciate this difficulty and to bear it in the back of his or her mind throughout their studies. Having agreed to accept the definitions, postulates, and common notions (but with reservations because of their inherent paradoxes), the student then goes on to investigate the degree to which they can be used to build up an understanding of the world around us. The Elements of Geometry is a work that relies upon the application of logic: nothing is accepted that has not been already established with the aid of the agreed rules; an understanding of geometrical figures is built up by using one proposition to prove another - proposition 1 describes the construction of an equilateral triangle; proposition 2 makes use of proposition 1 to draw a straight line equal in length to another straight line; proposition 3 makes use of proposition 2 to cut off from a larger straight line a line equal to a smaller one and so on and so forth. There may be some practical applications for this sort of study, but these schools did not train builders or engineers; geometry was studied to help students to understand the uses of, and the limitations of, logic: to see how one thing follows logically from another to build up a coherent whole, but also to understand that behind everything that appears to be certain there lies a paradox, which makes everything uncertain. When one looks around at the modern system of education, it is hard to see where this respect for logic has been preserved: and, in particular, who, if anyone, is applying any rules of logic to determining the value of what is going on in our school system. If one simply applies a modicum of logical analysis to the education system, one arrives at some disturbing conclusions: Social aspects: The first argument that many people give in favour of school is the social aspect, but, logically, there is no -reason to suppose that children derive any benefit from being with large numbers of children of their own age, and, logically, there is no reason to suppose that school-based friendships are of any help to people in later life. Learning to Read: There is no logical reason why a child of five, six, seven or eight years old should learn to read. They are not able to understand grown-up books and have better things to do with their time than reading books written for children which have no relevance to later life. Passing Exams: There is no logical justification for exams: they suppress originality, creativity and innovation; a student who surpasses his or her teachers in understanding will fail the exam; students who only know how to repeat what they have been told will do well; they do not mimic any situation that people meet in the real world; they cause intolerable stress; and they serve to divide people instead of teaching people how to work together. Specialist Subjects: People send their children to school so that they can do science lessons, information technology, and other specialist subjects. No one knows in what direction technology is going to go, but everyone knows that it will not stand still. There can be no logical reason for teaching children about technology that will no longer be in use when they leave school. Skills Training: Some people still advocate that schools should try to train people to do useful jobs, but schools have never managed to do this, and there is no logical reason to suppose that they ever could - people generally learn how to do a job by doing it, and by working with people who have been doing the job longer than they have. Everyone else is going to school: When everything else has been stripped away, the reason why most people tolerate the school system is because everyone else does so: this would ring alarm bells in anyone accustomed to making decisions on the basis of logical analysis. One of the reasons why people learnt logic through the medium of geometry was that it helped them to be fearless in its use: it is relatively easy to apply principles of logic to abstract ideas such as circles and triangles, but it is more difficult to be logical in real life. One proposition that is being put to us is that schools can provide our children with an education; another proposition that is being put to us is that teachers and government bodies are capable of taking charge of our childrens education. Neither of these propositions stand up to logical analysis. Unfortunately, we have neither been trained to be logical, nor to put our trust in the results of logical analysis. If we had been, neither would we send our children to the schools that exist today, nor would we make them sit the current examinations, nor would we expect the approval of education officials when we decide to home educate. The fact that schools exist in the form that they do is proof that educational standards have fallen - educated people would not tolerate their existence. Gareth Lewis
Your letters and comments are welcome. You can send them to Gareth
Lewis at the following address, or to me at the address beneath: wendy@freedom-in-education.co.uk
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