17 March 2016
Teaching Maths
UK at 26th
by John Watson
“A mile wide and an inch deep” might be an achievement if one was talking about some new way of manufacturing plate-glass. It certainly isn’t, however, when the subject is the nation’s maths curriculum. And yet that is the expression used by Andreas Schleicher, the director of education at the OECD, when he was explaining to the Global Education Skills Forum in Dubai why Britain is ranked twenty-sixth out of sixty-five countries, coming in behind Poland, Estonia and Vietnam.
Of course Mr Schleicher is not alone in deploring Britain’s performance. Business leaders and other employers say the same. Even graduates can come through the system innumerate and some companies run remedial maths programs for new employees. More important is Mr Schleicher’s analysis of the cause. He compares China and Singapore, where children are given a deep understanding and taught to think like scientists or mathematicians, with the UK where the emphasis is on relatively shallow knowledge acquired by rote; a system where relatively simple mathematics is made to appear more difficult by being used in complex contexts. The result of this? Children in Shanghai whose course does not deal with finance come out as more financially literate than those in the UK who are taught finance, because they have a deeper understanding of numbers and can apply it to finance or to anything else.
No doubt all this comes as a great surprise to the trendier educationalists, who have always been seduced by the idea of making education more relevant and getting away from difficult things like teaching children how to think. Actually, however, they should have known because, if they had spent their time reading rather than parroting patronising assumptions about children being unable to deal with difficult concepts, they would have come across a paper entitled “The Lost Tools of Learning” which was published by Dorothy L Sayers in 1947; that’s right, the Dorothy L Sayers who also wrote the detective stories featuring Lord Peter Wimsey.
Sayers’ essay is available at http://www.gbt.org/text/sayers.html but her essential point is that education should teach children how to think, analyse and learn and then, as a secondary matter, allow them to apply those techniques to the various subjects. That is different from the alternative system, apparently as prevalent in 1947 as it is now, of teaching a number of subjects and hoping that the pupil will pick up some idea as to how to analyse and learn as it goes along. Understanding logic and reasoning should be the fundamentals, as should be the ability to explain ideas. Rather than learning how to order a meal in a foreign language the student should begin by understanding the structure of languages – one of the great values of a classical education – and then later apply that understanding to those languages he or she wishes to master.
All this is still as true as it was in 1947 but if anything it is now more important. We are constantly told that rapid change and advances in longevity mean that, during a career, an individual will typically have to do a number of quite different things. It’s not much use, then, if his or her education only serves as a preparation for the first of them rather than giving the tools to unlock the subsequent disciplines as and when it becomes necessary to do so.
Many years ago I asked a distinguished maths teacher about the qualities he looked for in the children he taught. “Well there’s intelligence, of course, and perception and then of course there’s laziness”.
I was a little taken aback. “Laziness?” I asked, slightly surprised. Actually he didn’t mean laziness in the teenage sense with coffee cups piled in the sink and an inability to get up before midday. What he meant was that the best maths students, when faced with a problem, will not mindlessly cover sheets of paper with formulae they have learned but will rather ask themselves the question “isn’t there some simpler and easier way of doing this?”.
The same spirit of analysis and enquiry lies behind success in other disciplines as well. The good historian, having read his sources, sits back and thinks through the analysis. The linguist applies his knowledge of grammatical structures. The artist tries out a series of sketches. To teach pupils to think laterally, a teacher has to have a very good grasp of the subject.
That is why it is worrying to hear of subjects being taught by those who, although they may hold teaching qualifications, are not themselves expert in the subject being taught. Yes, with determination and effort they can teach those parts of the syllabus which can be learned by rote but they cannot begin to communicate a deeper understanding if they do not have it themselves.
The Department of Education reacted to Mr Schleicher’s comments by saying that they are already improving the quality of teaching. Nicky Morgan, the Education Secretary, has brought in teachers from Shanghai to help raise standards. In the end, though, real improvement in maths and in other subjects too will be dependent on the teaching profession becoming more attractive so that the best people are recruited. The recession has helped a bit here and so will other changes in demand which move teaching up the social and economic pecking order. There is a lot of concern at the disappearance of office jobs as computerisation makes people redundant. Perhaps an improvement in the standard of education will prove to be a silver lining.
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