Published in the official EU European Schools journal Panorama in May 2002, this is an explanation for teachers and parents of why it is that teaching children to learn from teachers simply makes them dependent on the ability of their teachers to communicate ideas. Whilst this is nearly always successful at first, as children grow older and the concepts they have to understand become more important, more and more children find that they are failing - and that they do not know why. This is when we tend to explain that they 'lack aptitude'. This attitude is particularly ruinous in maths and other sciences. The truth is that letting them become dependent on their teachers' abilities rather than improving their own means that they are literally programmed to fail.

Programmed to Fail or Taught to Succeed?
A Modern Teaching Strategy for European Schools

     In 1998 the President of the 1997 European Baccalaureate reported that in 80 percent of the classes of the nine European Schools he had visited the lessons were too stereotyped, and exchanges between teachers and pupils were too shallow and predictable.
     The same report showed that for the previous five years the European School at Culham had been the most successful of all the nine European Schools. Whilst no-one can distrust statistics quite as much as mathematicians do, and knowing that this particular statistic must conceal at least as much as it reveals, nevertheless, in a spirit of sharing our knowledge and experience, as well as our hopes for the future, this paper describes the particular aim of teaching mathematics in the English section at Culham as being not only to produce good exam results in school, but to train pupils to continue their learning after school.
     Paradoxically, some may think, if they are to be able to do this successfully, young people need to be taught how to learn without a teacher!
     Throughout Europe this expectation is imposing an increasingly urgent and difficult demand on teaching. School inspectors are asking for more varied discussions in class-work; for more unexpected questions in testing the pupils' comprehension; and - with increasing insistence - for more encouragement of the pupils to use text books. The reasons are obvious. To remain in continuous employment young people will need to learn new skills at every level of their careers. It is surely not too much to claim that the future prosperity in Europe - and the survival of its democracy - will depend on the rational, economic and moral independence of multi-talented citizens.
     To prepare for these demands, all European Union countries are investing very large sums in facilities for life-long learning. But the value of these facilities will be realised only if young people are taught to use them. This means that they need to know how to assess their own learning needs; how to decide their own learning strategies; and especially how to use textbooks and other media, entirely independent of teachers. If they are not taught these skills at school, they will have been programmed to fail rather than taught to succeed - and all over Europe the great investment in these facilities will be mainly wasted.
     Programming for life-long failure is an unpleasant concept. The reality of it, however, is all too common: and it can begin at an early age.
     To understand how, press together your two fists in front of you. This is a good model of your own brain, containing all that you will ever learn, know, or dream. The knowledge it contains, however, is never managed equally. Generally speaking, the right side of the brain manages knowledge in the form of patterns. Only one region of the left side of the brain has the ability to describe these patterns logically - and in words.
     Learning to recognise and manage patterns is a much easier process than learning words and logic. As children enter secondary school, almost all their knowledge is in the form of patterns which they know and manipulate. Of course they may attach some private meaning to them to make them easier to recall, but these are not logical. They are more like book-marks. Most children learn naturally and well in this way. But they are still only using about half the capacity of the brain, and in mathematics classes this will not be enough for very long.
     In the first few years of secondary school, most children next learn, quite naturally, how to describe with words the patterns which they know, and then how to articulate both the words and the patterns logically. They thus begin to use more of their innate intelligence, and are usually saved from disaster ever knowing how close they have been to it. But can also happen at this age it that a child does not learn that there is nearly always a logical explanation to go with the patterns they recognise. There are no visible signs of this catastrophe, but for this child the natural progression in learning has stopped.
     Certainly these children do not know this has happened. All they know is that learning for them, especially in mathematics, is becoming very much more difficult than for others. Their teachers' judgements also become increasingly arbitrary and bizarre. Attempting to remedy their situation themselves, they try to remember all the patterns they must learn. But there are more and more patterns - soon there are far too many, and there is no connection between them They are connected, but by verbal explanations that these children do not know. They cannot remember enough patterns, and they do not know their logic. They begin to realise that they cannot understand anything. They begin to fail. Schools tend to say that this degree of failure is natural. In fact it is produced only by the way such children are trying to learn.
     One invariably successful way to overcome this very common problem is to ask our pupils, one at a time, to read aloud the text in their text-book, a few lines at a time - and then to ask the reader or others to describe what the text means in their own words. An equally successful method in senior classes is to ask pupils to write their solution to a problem on the blackboard: again explaining in their own words why certain steps are taken and what result is expected. This practice of course is common elsewhere. Its real value, however, is perhaps underestimated. This habit and practice of discussion is the key of life-long learning.
     Mathematics texts are usually not easy to understand. The writers of mathematics text-books clearly rarely expect their books to be used in this way - and frequently do not write all that well anyway. After their first reading aloud, your pupils will often need to make repeated attempts to explain what is meant. Soon, however, it becomes a habit in which pupils will participate enthusiastically.
     This habit is essential for learning, because it engages both the ability of the brain to recognise patterns and the verbal and logical abilities to explain them. Pupils soon begin to see - and experience - that the two sides of the brain operate more powerfully together. More of their intelligence is being engaged. Then with their new verbal skills they begin to understand better - and sometimes for the first time - what it is they are doing! Finally they begin to understand that they can do this alone!! By this time they are then on their way to becoming fully emancipated and independent adults.
     It is frequently very shocking to discover highly intelligent children with most serious deficiencies in verbal understanding. The simplest sentences - that is, the most apparently simple sentences - may be completely misunderstood. You will often need to conceal your surprise. To overcome these weaknesses requires hard, patient work from both teacher and pupil. But, with perseverance, the fruits of this labour also appear. One finds oneself working with increasingly interested, cheerful, confident pupils. They are more and more able to work independently. They can more often correct their own failure themselves, and therefore are less nervous of failure. They have learnt how to use far more of their intelligence. They know it - and it shows. They are more eager to learn. Best of all, the habit can be continued by parents at home: from whom first response on being told, "I don't understand what to do!", should now be, "Well, find your text-book, and let's read it together!"
     Most people understand one essential fact of life the wrong way round.
     Clever children are not able to read and explain well because they are clever. Usually they are usually clever, because they can read and explain well!
     And this habit can be taught.
     It can be taught almost as well by teachers who are themselves not very conversant with mathematics. It is therefore perfectly suited to help novice or replacement teachers (or classroom assistants!) to work with pupils safely and effectively, without anxiety, and without continuous supervision. "Does everyone want an personal, individual, highly experienced, and qualified tutor to help them?" Every pupil does. "Well, the personal tutor with all those wonderful qualities is right there: under your hand: in your text-book. All that you have to do is learn to listen to what your individual tutor has to say!"
     Teaching children to read their textbooks is fun for the class, is less stressful for the teacher, and provides important and fascinating insights into the way that children understand and think. It is communicable and productive in all other branches of learning. It makes learning mathematics as well as other subjects both easier and more enjoyable at every academic level, and as pupils become increasing able to work independently and alone, they are helped to a greater social maturity and individual confidence.
     So, what more do you want: a magic wand?

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(with Ian Christie)
March 2002