# Mathematics

As Socrates discovered to his cost, nobody should take up philosophy for a quiet life. The editors and contributors to this slim, scholarly-but-readable volume have recently found themselves caught - not unwillingly - in the media spotlight.

Why all the attention? Because these philosophers (as most of them are) have written a book that dares to question the necessity of all pupils studying mathematics to 16.

"Why learn maths?", John White argues, is a question not just for mathematicians, but for all citizens. I share the authors' delight that their perceived heresy has brought these philosophical deliberations to the attention of an audience outside maths and education.

Their suggestion that things need not be as they are provokes outrage because the position of mathematics in the school curriculum, along with that of English, is supposedly unassailable. This is the essence of an entertaining endpiece by John MacBeath, whose high school teacher once insisted he did not have to justify his subject to a 14-year-old.

The 10 contributors are by no means unanimous in their views about the privileged place of mathematics in school, and some argue for its compulsory status. But none seeks to justify the kind of mathematics programme to age 16 specified in the national curriculum.

Paul Ernest analyses the significantly varied perspectives on the aims of mathematics in school held by a range of interest groups from the "New Right", which prioritises basic skills and social training, to the democratic socialists, who value the empowerment of learners as critical citizens. He argues that the curriculum is biased towards capability rather than appreciation, where the latter might involve an understanding of some of the "big ideas" of mathematics - such as infinity, symmetry, recursion, randomness - and a sense of the subject as a central element of human culture.

John White engages in some user-friendly polemic, setting up utilitarian and non-utilitarian arguments for learning mathematics, and testing each in turn. He concludes, as many have before him, that the "basic skills" argument justifies mathematics no further than key stage 2. A more persuasive train of apologetics related to culture and intrinsic interest points to a compulsory post-primary "taster course" to test the power of such motivations for individual students.

Peter Huckstep pushes the usefulness argument a little further, to see if mathematics can be justified (as is commonly supposed) in promoting logical thinking or mental trainig with application to fields beyond the subject itself. His tightly reasoned argument, drawing on Thomas Tate, comes to the perhaps surprising conclusion that such arguments are strongest in the primary years, when the practical utility argument is already incontrovertible.

I smiled at Eric Blaire's suggestion that mathematical training might combine with emotional detachment to the benefit of personal relationships, having seen little evidence to support this thesis.

A delightful chapter by non-mathematician Richard Smith is the most overtly mathematical contribution. It unfolds four vignettes, chosen to exemplify what might be a new kind of post-compulsory syllabus in "mathematical studies" of topics that convey the cultural value of mathematics. Freed from the necessity to train students in techniques, such a syllabus might reveal to students "the extraordinary power and beauty of mathematics, its distinctiveness as a form of thought, its place as an astonishing achievement of the human mind".

Tony Parsons, head of mathematics at Streatham Hill and Clapham high school, south London, gives a defence of his subject in a spirited and, at times, romantic call to arms. While regretting the effects of compulsion, he believes a world without mathematics would be too impoverished for the individual. But even the apologist for school mathematics makes no attempt to defend the status quo. Although much school mathematics is about turning the handle to grind out results, Parsons says: "It does not have to be like that."

Elsewhere, the claims of mathematics relative to other subjects are examined. Steve Bramall argues that mathematics is the science of means, whereas the social, political and moral sciences help us make responsible choices concerning ends. To prioritise mathematics is to put the cart before the horse.

Similarly, mathematics communicates a partial description of the world, whereas we can use English to communicate any kind of human experience. At this point I was prompted to ask myself what I treasured more in the legacy of Omar Khayyam - his contributions to the solution of cubic equations or the verses of the Rubaiyat. Suffice to say I was not unduly taxed by my own question, and reflected later that one stanza might be read as an allegory for the debate conducted in the book, one which might gain the approval of Parsons and his co-authors: "Ah, Love! could thou and I with Fate conspire to grasp this sorry scheme of things entire, Would we not shatter it to bits - and then re-mould it nearer to the heart's desire!

Tim Rowland is a lecturer in mathematics education at Homerton College, University of Cambridge

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