I recently ran into the World Class Arena, which was an attempt started around 2000 by the QCA to focus on the needs of the more gifted children. It was a modest beginning. A few academics in the School of Education at Leicester University devised some problems targeted at children aged 8-14 to pick out the more able in maths and problem-solving. Yesterday’s article looked at the sample problems on the site. I found it hard to see what distinction, if any, was being made between “maths” and “problem solving”.
But it was certainly clear that this was not aimed at finding maths geniuses or even at those capable of getting a first in maths as an undergraduate. It was aimed at maybe the top quartile. I doubt those involved saw it that way, but then the consequence of 50 years of decline in UK education for ages 4-18 is that we have become hopelessly unambitious by international standards. It has suited everyone to pretend that schools are getting better, and children brighter and harder-working. To be fair, there are some signs of improvement over the last five years or so, but overall the last fifty years have seen a substantial decline.
It is worth starting with a quick look at geniuses. Such people are a vital resource for any country. They can have a huge impact for good or ill on many people’s lives. To take an example which has bobbed in and out of the news over the last decade, the bizarre collection of misfits and others at Bletchley Park during World War II. It is greatly to our credit as a country that we were willing to entrust such critical work to such a crew. They performed spectacularly well.
The first question is: are geniuses born or made? There is perhaps one confusion which has foxed many. The application of genius is mainly about hard, intense and prolonged work, often dealing with apparently minor details, whereas the popular image is often of effortless superiority. Indeed many geniuses and near-geniuses seek to cultivate that image. They pretend to be meeting a question for the first time and tentatively giving a few first thoughts on it, when actually they have been up all night or a week preparing those thoughts. On the one hand, sayings such as
genius is 1% inspiration, 99% perspiration
and
… the fruit of “genius” (which means transcendent capacity of taking trouble, first of all)
[Thomas Carlyle, History of Friedrich II of Prussia, volume IV, chapter III]
have seriously misled people into thinking that only hard work is needed. It isn’t.
Of course, the old Confucian saying that some people acquire a skill almost immediately, others take “10,000 hours”, but it is the same in the end, has a good deal of truth. Less talented people can indeed achieve a great deal, and certainly a great deal more than either they or others expect. But some achievements require a hard-working genius.
On the other hand, the pretence of effortless achievement has misled many talented people into thinking they can get away with being lazy, and many untalented people into thinking that geniuses do not need help in acquiring good habits to channel their talent effectively.
When I was young the conventional wisdom was heavily on the side of born. Even the idea that a genius might fail to reach his or her potential was occasionally thought relatively unimportant because a genius was perceived to be driven and almost incapable of not pursuing their talent. Obviously if you placed them in a sufficiently unfavourable environment, they might be unable to do much with their talent, and the world might derive little benefit from it, but on the whole the genius needed relatively little nurturing to develop it. On the other hand, there were certainly individuals and institutions which tried hard to nurture and develop genius, or at least truly exceptional talent. Perhaps a fair summary would be that the genetic element was thought to be necessary, but nurture was thought to be essential for full flowering.
[Harold Wilson in March 1964 (7 months before he became prime minister for the first time) in a photo by Harold Wise for the US Dept of Defense]
But soon after Harold Wilson got into power in 1964, the UK started to move towards comprehensive schools, abolishing the old two-tier system for state education, with “grammar schools” for the more able and “secondary moderns” for the rest. This seemed to me to be driven, at least initially, by socialist ideals more than by a desire to give everyone the best possible education. Indeed, some seemed content if the outcome was to deny the able and privileged a good education thus making it more difficult for them to surpass in later life the less able and under-privileged.
After a while, the battle for a single tier versus two tiers was won, and the argument became focussed on streaming. The extreme view was that there should be no streaming. All 12 year olds should be taught maths together irrespective of ability of progress.
That meant the best kids would grasp the lesson’s topic in the first 5 minutes. What were they supposed to do whilst the slowest kids struggled to grasp it over the next 40? The extreme view was that they should help to teach the slowest kids. This fitted well with bizarre educational ideas along the lines of a teacher’s job being not to teach but to supervise discussion or activity groups in which the children somehow discovered things for themselves.
[Manchester Grammar School (MGS), one of the most famous of the direct grant schools in the 1960s. It became an independent school in 1976. Two members of the UK's IMO team (see below) in 1968 were from MGS. Both went on to join GCHQ after doing maths at Trinity College, Cambridge and discovered public key encryption, by far the most important development in cryptography in the history of the subject.]
The impact of all this on the education of the most able was mitigated by the survival of the “public schools” and, for a shorter time, of the “direct grant schools”. Public schools (the confusing UK term for private schools) have always varied enormously, but some have made a major effort to foster talent. In the 1960s Winchester College was the leading example, although I am unclear how it has fared since. Admission to “College” on a scholarship was, and still is, by the school’s own competitive examination. In the 1960s a poor child with limited education could, in principle, sit the examination with almost no prior notice and win a scholarship that paid almost all his fees.
At best, this excluded half the population, since girls were not eligible. Almost as important – or more important if you take the now unfashionable view that the best academic education requires single-sex institutions – there were clear limits on how limited your prior education could be. I went to a fairly poor “preparatory school” that never, as far as I know, got anyone else a Winchester scholarship before or since. I just scraped in (at the bottom of the list). By comparison with schools like the Dragon School at Oxford, which won scholarships to Winchester every year, my prep school was hopeless. But its fees would have ruled it out for a substantial proportion of families, and it was certainly much better than many state schools.
Equally, too many families never realised that their child was a genius, or at least failed even to think about how to get him or her a suitable education. Today, the problem is rather the reverse. Far too many parents think that a relatively mediocre child is a genius. There is an ever proliferating focus on the “gifted and talented”. Of course, if your child is a large fish in a small pool, you may quite reasonably fail to grasp what a small fish he would be in a larger pool.
Anyway, at age 8 it may not matter too much. If he is in the upper quartile he probably needs encouraging and developing, even if it later becomes only too clear that he is right at the bottom of it. The problem is more that the new low standards for “gifted and talented” seem to be preventing a focus on the much smaller number of geniuses.
For example, when I last checked a few years ago, our training courses for the International Mathematical Olympiads (IMO) ignored the most difficult questions on the grounds that our team were unlikely to be able to do them. The IMO exams have two papers each with three questions, graded easy, medium and difficult. Contestants are marked out of 42 (7 marks per question) and graded gold, silver, bronze and other. Any country is allowed to send a team of up to 6.
From small beginnings with only a few countries, it now attracts teams from about a hundred countries. These days the winning team usually has close to the maximum possible marks (6 x 42). So the UK with a strong tradition in maths, including many of the world’s all-time great mathematicians and with relatively few countries having a significantly higher population, does not even try to do well! We are usually beaten by Bulgaria with a population less than an eighth of ours.
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