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A Miscalculation about Maths

The Prime Minister announced to the Conservative Party Conference his plan to abolish A levels and replace them with ‘Advanced British Standard’,  requiring pupils to study more subjects until 18, including Maths and English. But, says David Abulafia*, while there is much to be said for offering classes in a wide range of subjects, pupils’ interests and aptitudes must not be neglected, and in any case the International Baccalaureate already caters already for this. More importantly, compulsory examination in maths for all until 18 are neither needed, nor wise.
Is the idea of making pupils study maths until the age of 18 a miscalculation? There are some obvious difficulties at a practical level, notably the availability of teachers. And ‘maths’ means many things, from statistics to the arcane world of number theory and those brilliant mathematicians who insist that all they need is a pen and a piece of paper to conjure up new theorems and proofs. It is not even clear that maths means what it meant twenty or thirty years ago, not just because of the need to understand the related science of computing, but because the level at which it is studied has not been consistent. Several years ago I attended a Politeia lunch at which the star guest was the then Secretary of State for Education, Michael Gove. It is no disparagement of what he said to admit that what I carried away most clearly was a comment by a Cambridge professor of physics, now alas deceased, named Mark Warner. I asked him how the O Level exams of half a century ago, particularly the Additional Maths exam taken by high fliers, and full of calculus, compare with GCSE. He said that Additional Maths certainly matched the standard of A Levels, and possibly first-year mathematics at university. He was particularly worried that some very good universities were admitting students to read physics who did not even have a maths A Level.
      It goes without saying that the debate about maths teaching is not simply concerned with those who are heading for university. Basic numeracy and literacy are an absolute requirement in a modern labour force. Numeracy has been eroded by the ease with which we can all add up numbers using calculators. Knowing 7×9 by heart seems less important, though it is hard to understand how a builder or plumber can work effectively without a feel for numbers. Quite simply, though, this is something that needs to be instilled well before one’s teenage years, followed by basic algebra and geometry. If the system does not offer that nowadays, it is broken.
     These comments may make it seem that it is all the more necessary to keep maths going longer. But there is another argument that pulls in a different direction and particularly concerns high-flying students. The English education system has often been criticised for early over-specialisation, but the simple fact is that this suits a large number of pupils. It has meant that they arrive at university able to move straight into the mainstream of the subject they have chosen to study, without the need for a general preparatory year of the sort that is required in the United States and has also been the custom in Scottish universities. It make a three-year degree feasible, certainly in arts and humanities (there has been a drift to a fourth year in plenty of science subjects). The best students emerge with formidable expertise and a rich experience at a significantly higher level than most of their American peers.
    To all this the answer is that there are plenty of all-rounders who are happy to combine humanities and sciences at school, and that is surely a good thing. Yet not every student is an all-rounder. Just as some of those studying history and languages are not enthused by maths and physics, many, maybe most, of those studying maths and physics have no enthusiasm for the humanities, at least at an academic level. The education system needs to accommodate different types of brain – there are natural mathematicians whose grammar is weak and cannot retain French vocabulary; and there are natural historians who never wanted to think about measuring the amount of water in a bathtub coming through a pipe 5cm thick at a speed of 5 mph for fifteen minutes. This was my own dilemma at school: arriving at the age of 13, I found myself in the top maths set where almost everyone else intended to go on to maths and physics A Levels, and I wanted to study history and classics. We were presented with all sorts of sophisticated proofs of theorems when all I needed was the most basic version.
     The International Baccalaureate does a fine job in providing a broad education encompassing maths, science and the humanities. It suits some of the most able pupils. But it does not suit all of them. In assessing the merits of a candidate for entry into a top university, is his or her maths grade important when the candidate wants to read English literature? Leaving aside the strong possibility that a middling score in maths will be used to discriminate against the candidate if he or she comes from an independent school, it is simply not proof of competence in the future area of study.
     One neat answer is to provide limited teaching in both maths and English up to 18, but not to examine the subjects unless a pupil is taking an A Level in those subjects. General education in unexamined subjects can be a precious opportunity to broaden minds outside the formal syllabus. There are areas of mathematics that do need to be somewhere on everyone’s syllabus: at O Level I benefited from the study of statistics, which became enormously helpful when writing economic history. That and elementary computing would make a suitable core for an unexamined course at ages 16-18. Winchester College is famous for its tradition of classes called ‘Div’ in which the  ‘don’ opens up the widest range of topics. In my days at St Paul’s we were sent off to a science master once a week to hear about the planets or to fill balloons with hydrogen, but I never took any science exams (‘Do you want to do Greek, or do you want to do science?’ I was asked, and that was it). Things have moved on since then, no doubt rightly; but the underlying principle that education is not all about the curriculum is of vital importance.
     Recognising that point is a way to accommodate both the idea that pupils should continue to do a bit of maths, and that they should not be compelled to take a public, graded exam in the subject once they have completed their GCSE. This is a solution that would suit both the best and brightest students and those of lesser ability. For once it is possible to have the best of both worlds.


Professor David Abulafia FBA

David Abulafia is Professor of Mediterranean History at the University of Cambridge and Papthomas Professorial Fellow at Gonville and Caius College, having previously chaired the university's History Faculty. His publications include The Great Sea: A Human History of the Mediterranean (updated, 2014) and The Boundless Sea: A Human History of the Oceans (2019), which won the 2020 Wolfson Prize, while his Politeia publications include Triggering Article 50, Courts, Government and Parliament (2017) and History in the Making: The New Curriculum: Right or Wrong? (2013).

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