Today the case for embarking on a radical reform programme for mainstream school mathematics teaching is overwhelming.  The existing status quo is palpably in trouble, and in a significant subset of secondary schools the subject has sunk to the point where it is regarded, both by teachers and students, as a ‘cycle of despair’. There are many schools where the subject is being taught by people with no track-record of identification with mathematics, its values, or its objectives.  

     So we need to start thinking about a necessary radical reform, and a master plan to bring mainstream maths teaching in schools into line with today’s knowledge, today’s technological capability, the mindset of today’s mainstream (i.e. not-maths-inclined) students, and their needs.

The arrangement that the gurus of higher maths determine the mainstream maths curriculum in schools has been questioned more and more forcefully since the late 1960s, and it has gradually become apparent that this long-standing convention has done untold harm to the academic subject’s presence, wider credibility and influence.  It was alright when the higher subject’s reputation with the lay majority was based on deference and awe.  But that has gone. In the 20^th century the leadership of the subject made some dreadful mistakes, which have had the effect of alienating public opinion. 

The only plausible explanation for these “howlers” is that the leadership of higher maths had a seriously mistaken view of their own subject.  A large part of the misconception was that higher maths was regarded by the subject’s influential gurus as akin to religion.  But, especially since the arrival of the four whammies (atomic energy, the computer, space travel and DNA), religion has been upstaged by the awe of science. Forging associations between maths and religion —e.g. Cantor’s transfinite exotic sets— no longer counts as a “plus”, it is much more like a liability.

Anyway, whatever the explanation, a succession of ill-conceived attitudes were adopted by the leading gurus. Russell’s Contradiction was not properly solved, Ulam’s dangerous Dilemma was allowed to grow and grow, the attempted revolution in School Maths launched in the US in the 1960s turned out to be a disaster, and Silicon Valley was allowed to steal mathematics’ applicable thunder. The subject’s leading gurus, one can only presume, regarded their subject as being on an altogether higher, quasi-religious plane. They were not aware that pragmatism had come to dominate in public and cultural affairs. The lapses have resulted in a complete disappearance of mainstream public deference and awe towards mathematics. 

    This is an extremely dangerous existential threat to maths. It could easily have led to the extinction of mathematics as a once proud academic subject.      

     But we are fortunate, in the sense that, that during this long period of confusing, difficult-to-read modernity —when the morale and grip of the gurus leading the higher subject was becoming increasingly shaky— advanced maths itself was achieving amazing modelling triumphs, and its useful applicability was increasing spectacularly.  It is galling that Silicon Valley was allowed to steal 99% of the glory that resulted from this early automation of mathematics. Not only did this “steal” appear to make old-fashioned maths irrelevant and obsolete, but it has also given the leaders of IT a dangerously false sense of the inherent power (magic) of their own discipline.  The very notion of ‘computer modelling’ is fallacious.  The computer is in the end merely a sophisticated electronic device which automates mathematics. Computers don’t “think” or “understand” or “model” anything: they simply implement modelling strategies devised by highly perceptive flesh-and-blood mathematicians… some of whom may have fallen into the habit of calling themselves ‘computer programmers’ or ‘analysts’.

So we have the extraordinary situation that mathematical modelling has enjoyed an all-but invisible golden age since the arrival of the reliable solid-state computer around 1960. Today it is virtually all implemented on computers, but the secret of its success does not reside in the mechanical operations which these electronic devices put it through.  The “magic” of the modelling results from the skilful selection, and inter-weaving of, the manipulative processes involved.

Serious students of mathematics have long since come to see that it is not a quasi-religion but a quasi-science.  Charles Peirce declared that <<Mathematics is the science of hypothesis>> more than a hundred years ago.  Of course it is. It provides us with the capacity to assemble reliable working models of every kind of proposed innovation —new schemes, arrangements, gadgets, innovations, inventions.  This is our prime “Pathfinder for Progress” …as I have called it in my six articles in the New English Review (2021-22). 

We need first to “get clear about” what mathematics is —which means dumping the hoary academic so-called ‘philosophies of mathematics’ which were based 99% on mathematics and the logic needed across the subject, but only 1% on what mathematics actually does for the human race… that is, the root source of its meaning.

Children need to be acquainted with maths as the premier discipline we have for foreseeing the future. Their whole maths experience in schools needs to be based on this perspective.  I did a talk in London in October 2022 which launched a Narrative Maths Manifesto to this effect.

 CHRISTOPHER ORMELL 1^st January 2023

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