The echoes from the UK’s rather modest performance in the PISA tests, and in Mathematics in particular, continue to reverberate.
The often excellent Simon Jenkins recently produced one of the wildest articles I have read for some years; the piece is so weak in reasoning terms that I would be embarrassed to show it, even as an exercise in logical criticism, to a group of A level Critical Thinking students.
(Notice the obligatory and misplaced reference to Gradgrind, the supposed architect of education by rote learning – see my December 2012 blog entry for a detailed discussion of the misuse of this particular insult from the Dickensian masterpiece ‘Hard Times’).
Mr Jenkins’ response to the UK’s poorer performance in Mathematics compared to Asian countries goes well beyond the usual PISA excuses (again see my recent blog for a handy list of these) and argues that the study of Mathematics is of no value, or even that it is malign, and the subject should be removed from the curriculum. This is sour grapes taken to the extreme – akin to a defeated athlete arguing that not only was the race unfair but running is actually bad for you. In a final flourish, marked by flawed reasoning and more than a touch of arrogance, he asserts that the UK has nothing to learn from Asia because education in China makes the students miserable and because it places insufficient emphasis on the nurturing of creativity and on social and emotional development.
The PISA tests show fairly conclusively that, by the age of 16, students in Shanghai are several years ahead of their UK counterparts in their ability to use Mathematics to solve problems; it would seem surprising if we could not learn something from the teaching and learning in Asian schools. Elisabeth Truss is currently investigating just this, probably a useful thing for a Schools’ Minister to be doing. http://www.bbc.co.uk/news/education-26228234. I suspect that she will discover that Mathematical education is valued, that the education system is very competitive and that there is an embedded notion that diligence and collective support and effort can overcome any perceived weakness in an individual’s mathematical ability. It seems likely that the last insight could be useful in the UK; there is no logical or practical reason why this would require students to become miserable or why this should result in the sacrifice of opportunities for students to develop creativity.
I take real issue with the contention that Mathematics should have no part in the curriculum. At Birkdale, Mathematics is a successful and flourishing subject with almost three-quarters of GCSE students gaining an A or an A* grade and well over half of our students choosing to continue with Mathematics in the Sixth Form. One might attempt to explain the latter statistic through the utilitarian argument of saying that many university courses require the study of Mathematics at A level but this simply leads to the obvious truism that these courses need this level of Mathematics as a foundation. For those who choose not to pursue Mathematics at A level one would assume that they have gained some grasp of Mathematics which will genuinely be useful in everyday life; whilst memories of quadratic equations may quickly be lost, life is both easier and more interesting with a rudimentary grasp of statistics, percentages, areas and volumes. It would be hard to find a job which does not require at least this level of numeracy. It is easy to scoff at the idea that we should study Mathematics as some sort of esoteric ‘training for the mind’ but, of course, battling to understand abstract concepts and honing logical thinking are crucial skills for learning other, more vocational subjects in the future – presumably exactly the subjects that Mr Jenkins would include in the curriculum. The traditional subjects have remained in the curriculum not through inertia or nostalgia but through the recognition that their characteristic modes of enquiry provide the perfect training ground for developing supple and resilient minds which can tackle problems of all types.
I enjoyed Mathematics at school and a degree in Theoretical Physics allowed me to relish not only the elegance of Mathematics but also to savour its remarkable ability to model and explain the behaviour of the material world. My interests have broadened considerably since my university studies to encompass history, literature and philosophy, subjects that seem to me much more accessible to an adult than Mathematics. I feel luckier than my humanities focused friends and colleagues; it is perhaps much easier for me to explore the French Revolution than for a history graduate to try to appreciate the beauty of a differential equation and to gain a passing familiarity with quantum mechanics. This asymmetry perhaps lies behind the oft-repeated, though ill-supported, notion that the UK has an ‘anti-maths culture’.
Mr Jenkins appeals to the famous quote from the eccentric mathematician G H Hardy that study of his subject “must be justified as art if it can be justified at all” to show that Mathematics should not be studied for its utility, but this strange piece of reasoning proves too much as Hardy advocates teaching Mathematics for its beauty. I think that exposing students to the strange beauty of mathematical proof is as valuable an exercise as exposing them to the different types of beauty to be found in a poem or a picture or a piece of prose.
The article asserts that Mathematics keeps its place in the curriculum only because the nature of the subject allows students’ performance to be measured easily. Perhaps Mr Jenkins has conveniently forgotten that PISA also tests use of language and science or that the government’s new league table measures will look at the best grades in 8 different GCSE subjects; there seems no intrinsic reason to doubt that performance can be measured across a range of intellectual endeavours.
Lastly, Mr Jenkins argues that the UK is doing fine without being very good at Mathematics or perhaps even because we are not good at Mathematics. I am not sure how one could develop any sort of argument for what is at best an unsupported correlation rather than a causal link; one might as well advance the view that the UK is doing well because we are bad at learning foreign languages or because it rains a lot here. (Again he apparently contradicts himself through the assertion that the financial crash was a result of UK mathematical prowess: human greed seems a more likely cause.)
I think that learning some Mathematics is part of a good education for all the reasons given above: utility, aesthetics and mental training. If we can find the humility to learn a little from Asia and boost our students’ performance in this area it seems likely to be a positive development both economically and in terms of happiness.