It is impossible to over-state the seriousness of the fiasco surrounding ‘New Maths for Schools’ which imploded disastrously in the 1970s. It was, from the beginning,  a fantasy based on an ideological single-mindedness, a specialised (‘modern mathematics’) mindset  which turned its back on a panorama of ordinary human pursuits and satisfactions. It was also a product of myopia, because it tried to drag the learner’s concentration onto airy, nominal classifications, otherwise known as ‘sets’. If it was to work, it needed an extraordinary degree of deviation from common norms —i.e. ordinary human valuations and judgments. Would any intelligent person even consider that sets might be a possible lively focus of interest for the average child?

And the fact that this ‘extraordinary degree of divergence’ from ordinary human concerns had become —was the supposedly ‘modern’ in-house point of view in higher mathematics— was also, in its own way, a damning verdict on the state of the guardians of the subject at that time.

     Fifty years ago it was still considered reasonable to think that a subject might be ‘genuinely important’ in its own ‘intrinsic’ way, in spite of a lack of links with other things. But today there is a much greater sense abroad that everything is inter-connected, and that the authentic meaning of mathematics must (can only) rest on what mathematics does for the human race. The new tentative consensus, which seems to be firming-up, is that mathematics offers the best way to model promising new ideas, innovations, inventions, reforms… etc. It is becoming, in a word, our main ‘Pathfinder for Progress’. 

It should be said at this point, though, that this is not the whole of the story.

     There are some exceptionably neat, easily understood mathematical proofs which also offer us the best paradigms of truth, because they Imply a limitless out-reach of unobvious formal applications and they are absolutely reliable, because they can be checked as many times as you like. (Here the ordinary, commonplace meaning of being ‘absolutely reliable’ is intended… and the notion that such things also have a superior, transcendental form of timeless (‘sub specie aeternitas’) meaning can be forgotten.)

     This development is visible in the research agendas of mathematics departments of universities, which have mostly switched over to modelling explorations. 

     Even so, some bits of pure mathematics survive, mainly represented by number theory, especially prime number theory, which has acquired new significance since immense prime numbers began to be extensively used in cryptography.

     But the method of teaching maths in schools is still stuck in a time warp, because it still tacitly operates with the fantasy notion that the main meaning of the subject is based on timelessness… which can be treated as verbal code for a total lack of connection with all normal human here-and-now vivid concerns.

     From this point of view, to teach maths in schools as a bald, uninterpreted, raw symbolic language, is about as daft a pedagogical mistake as it is possible to imagine. It is equivalent to the method of teaching swimming by throwing children in at the deep end. 

     If the meaning of the subject hails essentially from the use of maths to predict the future (an insight which had already occurred to the high priests of ancient Babylon who used it to awe their citizenry), then we must, of course, begin teaching it by airing situations where the future is clouded and obscure… and yet which manifestly need to be predicted.  This is the new <<narrative maths approach>> of a campaign which we launched at a P E R meeting in Conway Hall in October 2022.

    It can’t happen overnight, because many thousands of narrative intros are needed —longish, tailor-made initial paragraphs which make palpable sense to students, which refer to visibly occluded, obscure, states… of a kind which are crying-out to be illuminated. Writing these scenarios is not easy.  They only work when they capture the imagination of students… which means that these narratives must reasonably reflect the sensibility of the students’ points of view. There is no time to lose, because we urgently need a renewal of the spirit of education, and this is probably the only innovation which could have that effect —and which could in principle attract support from the corridors of power.

    The source of the wall of obscurity which such narratives initially present is that there are many ordinary, intelligible situations in which what is going to happen is known to be predictable (falling under well-attested regularities), but where the precise details involved become lost in a fog of multiplicity.

     It should also be said that the motivating effect of such narrative maths is the experience of sudden, delightful mental clarity, not any actual material benefit the students might, or could, acquire. Education in the true sense of the word is the acclimatisation of youth to the joy and appreciation of sudden mental clarity, sometimes called ‘intellectual eros’.

     This was where the policy-makers of the 1980s went badly wrong with their ‘Practical Maths’. They thought (and worked on the basis that) it was the actual material benefits of applications which would motivate children. But his was a mistake, arising from lack of experience of school environments. How could material benefits of any kind be delivered in a dusty classroom? Such motivational effects, if they existed at all, were no more appealing in dusty classrooms than those aroused by promising a youngster an ice-cream in two months’ time!

CHRISTOPHER ORMELL 1^st April 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.