There has been a chronic crisis situation in school mathematics since the 1980s when an alternative (i.e. a remedy) to ‘New Maths for Schools’ was urgently needed. The broad outlines of a replacement were suggested by the much hyped  Cockcroft Report Mathematics Counts (HMSO 1982).  It threw attention onto the need to relate maths to the real world and its role in so-called ‘practical applications’.  The SMP 11-16 scheme reflected this emphasis in a lively way. It got off to a promising start, but by the mid 1980s it had run out of steam.   

So a new paradigm operating under the banner of ‘Practical Maths’ began to emerge. It sounded very sensible after the fiasco of trying to interest ordinary children in set-theoretical aesthetics, and it made much of the catchy mantra <<Using maths to make things happen!>>. Some dramatic examples of this kind were found for introducing new methods and concepts in schools. They caught the attention of many learners at the beginning. But there were not enough of them to sustain the approach. The early dramatic challenges tended to lose their freshness as a result of over-use. And by clinging to the supposedly sure-fire motivational notion of ‘practicality’, this approach became increasingly distant, technical, grey and tiresome. The senior ‘applied mathematicians’ who claimed the right to call the shots, tended not to be very sensitive to the characteristic interests and thoughts of children. These experienced ‘experts’ idea of ‘practical maths’ was finding a formula which saved 2.5% of the cost of some tedious industrial process. As a result, the original challenges were over-used, and the new teaching approach ran out of fresh, exciting, interesting questions very quickly.

[The Cockcroft Report was a kind of mainstream response from the corridors of power to Mathematics Applicable. Its backers took the first key point that students could be re-energised by using interesting applications, but they missed the second point that the supply of such problems could only be secured if you adopted the Peircean Interpretation on mathematics. The “professional support” group on which they relied was —applied mathematicians in industry and universities. They were not free to switch over to a Peircean Interpretation, because they were under pressure from (1) corporate business and (2) the pure maths hierarchy.] 

There is a general message here. The very notion that maths can be a ‘practical activity’ is dodgy. There are some bits of useful maths which tend to be treated —by slightly mathsphobic users— as ‘practical know-how’, but they are on the margin, and not typical of the essence of the usefulness of maths. They simply involve using formulas in practical contexts and go nowhere near the heartland of using maths to explore interesting possibilities. Talking about this use of formulas as ‘maths’ is already an over-statement, and, in effect, a consequence of mathsphobic attitudes. Slightly mathsphobic people who “get over” their mathsphobia sufficiently to use effective practical formulas do, no doubt, feel some pride in their achievement. But they are not appropriate general role models for young students.  Treating them, as “the voice of commonsense” amounts to treating Mathsphobia as part of commonsense… an absurd emphasis to recommend for teachers who need to be transmitting the immense positivity and interest of maths regarded as the chief ‘pathfinder for progress’.  

So what has gone wrong? Well, there is a wide spectrum of human constructive activities, from the Very Practical to the Very Theoretical. Mathematics is, of course, at the extreme (‘Very Theoretical’) end of this spectrum. It might be described as ‘pure theory’.  So the notion that school maths could be properly and fulsomely conveyed to learners as a ‘practical’ activity, is about as silly a howler as it is possible to conceive. Modern applicable maths deals with real, interesting, up-coming, potential situations, but it throws light onto the consequences of a host of different variations. Surveying this range of results can be used to find the optimum way to turn the proposed development into reality. It is not about describing a single, already given material status quo. This ‘light’ involves much thinking and envisaging: so its exploration can only be properly described as ‘theory’.

So when ordinary people say that they ‘want maths teaching to be more practical’ they usually mean that they want it to throw light onto serious, real-life, physical problems, not artificial, concocted ‘busywork’, ‘pointless puzzles’, ‘airless fantasies’ or ’theory-for-the-sake-of-theory’. 

The new Campaign for Narrative Maths in Schools which the P E R Group launched at Conway Hall in October 2022 is based on the self-evident premiss that mathematics —the most potent, forward-looking discipline which homo sapiens has been able to develop since the dawn of history, and which now underlies every kind of human activity—  needs to be introduced to children in as meaningful a way as possible. This is a much under-registered priority and one on which our future well-being actually rests. Getting every child to understand and really appreciate what maths does, must be our main objective. This is too important to allow the continuation of old-fashioned simplistic approaches, i.e. ones which pitch maths as if it were a ’performance subject’ all about learning to manipulate obscure, elegant, meaningless rigid symbols. 

Unfortunately maths has been led and organised by gurus since the time of Classical Greece.  They have managed to operate a self-serving monopoly of control over maths for more than two millennia. They have been fixated on mathematics as a self-elevated, performance-minded, quasi-religious cult. Throughout history they have been drawn from a tiny circle of exceptionally gifted, mentally energetic, privileged individuals who realised the huge social standing of maths from an early age.  But they also badly misconstrued this ‘standing’, which they tended to credit to the subject’s supposed eternal, Godlike associations. They also tended to assume that their special interpretation of the huge importance of maths was unchallengeable and hence infallibly correct.  But such unchallengeability was itself a long-term consequence of their own narrow “throw them in at the deep end” style school teaching approach. This threadbare pedagogy has succeeded in putting most children off mathematics for hundreds of years. Today the gurus of maths have lost the argument and this gives us the chance —at last— to bring out the interest and fascination involved when young people realise that they can use maths seriously to explore realistic, exciting possibilities.

CHRISTOPHER ORMELL 1^st March 2023

If you would like an online copy of the P E R Narrative Maths Manifesto, send an email to per4group@gmail.com asking for this.