Some readers will have registered that we are passing through a period of great strain, difficulty and hardship arising from factors like the Pandemic, the Crisis in Education, Turbulence in the Financial System, Scarce Energy, Climate Change and the War in Ukraine. The gloomiest congenital pessimists may read all this as a ‘breakdown of Western Civilisation’, but thanks to the omnipresent computer, we now have an information-sphere and economic-sphere with immense distributed stability.

What we don’t have is an education system commensurate with the needs of this highly sophisticated 21^st century world. 

This means that the mental calibre of democratically elected representatives is going downhill, as shown by the current crisis in Westminster.  AI has been hyped as the agency which will save us from the worst consequences of this decline of mental calibre.  But the bad news is that AI is nowhere near the level of intelligence needed to solve our problems.  Anyone who watches TV programmes with sub-titling generated by AI knows that it issues howling mistakes every few seconds. The very notion of AI is a hype devised by publicists. It hugely overblows the pattern-seeking capacities of neural netwaorks.

Today the education system in most countries around the world is being operated by so-called ‘Cognitive Scientists’ who have thrown away virtually all the accumulated educational wisdom of the past.  Their “Know How” arose originally from Dr Pavlov’s experiments training dogs. They should never have been allowed anywhere near the education system, because the central task of education is to build up the power, energy, sharpness and range of the human mind. These ‘Cognitive Scientists’ used to call themselves ‘Behaviourists’. At the time when they took over the school system (1980s)  they went round denying that there was such a thing as ‘the human mind’!  Whyever did well-educated government advisers agree to put such people in charge of schools? Education is the growing and energising of human minds. It was naïve to put people in control of education who didn’t even believe in the existence of the ‘human mind’. (The mental calibre of democratic leaders at the time must have already fallen lower than we realised.)  Nowadays ‘Cognitive Scientists’ think that the phrase ‘human mind’ refers to a neural register somewhere in the brain, which they suppose is a kind of computer.  But it is only guesswork, because no one knows how the human brain works, and no one has the slightest clue where it stores its prodigious memories.  These ‘Cognitive Science Managers’ originally rolled out what they called ‘The Skills Revolution’ with a promise to put all the emphasis of the school system onto teaching skills.

What has been the result?

A skills famine of extremely serious proportions has emerged. A chorus of bitter complaints from employers and universities    —about school levers not possessing the most basic skills— has been getting louder and louder for forty years.

Q: What can be done to re-establish commonsense? 

A: A radical change in maths education, which has been left to wither in the wind by today’s maths hierarchy… which seems to be bewildered and has stultified itself into a state of overall incomprehension.

The change needed is one which recognises that since the arrival of reliable computers (around 1960) the old way of teaching maths is no longer relevant. It should have been reformed more than sixty years ago.

The ‘old way of teaching maths’ has one huge misapprehension at its centre, namely that <<maths is learnt best if you first strip it of all its common meaning>>.

‘Common meaning’ is the kind of meaning to which ordinary people and ordinary children respond.  It implants new insights about what you can do, what you can’t do, what is possible, where the most interesting, which things are valuable… etc.

The simplest kind of arithmetic (=counting) has probably been around for more than 20,000 years.  We know that artworks have been found in caves which are surprisingly realistic dating from more than 20,000 years ago.  But if homo sapiens at that time was capable of such artworks, they were certainly capable of using tally bundles like \\\\, \\\\\\\\, \\\\\\\\\\\\\\\ to count things like a stack of bricks, a cache of spears, a basket of fish, flocks of sheep, rows of amphorae…

This was the beginning of maths used instrumentally. It possessed common meaning in spades.  It must have developed very slowly over thousands of years before the emergence, first of Ancient Egypt, and then Classical Greece in the 6^th century BCE. The Greeks invented a ‘pure’ version of maths, treated as a superb nounless language, which just focused onto raw adjectival symbols and ignored the common meaning.

These Ancient Greeks realised that maths was a marvellous, perfect symbolic language, which could be studied by an able minority for its own sake. (Also, it must have been used by God to create the universe. Though they went on to claim arrogantly that God “made a mistake” when he created the universe because he did not allow the squareroot of 2 to be a rational number!) Anyone who has this feeling about maths and the required ability, can, of course, treat it as an end-in-itself.  This is ‘pure maths’ = maths sans common meaning. 

The trouble today is that the public has completely lost the feeling that maths is a ‘marvellous symbolic language’.  Computers have grabbed all the glory which used to be associated with maths. Children in schools are confronted with orders to learn (memorise) what is (to them) a meaningless, broken, noun-free dialect.  It is a form of low-key child abuse to force children to learn what they see as meaningless. This is bad enough when done in good faith by well-trained teachers. But today most maths teaching in schools is being done by mathsphobic non-specialist teachers who have had no training to do it.

The author has produced a Manifesto which puts the case for Narrative Maths in schools… maths approached via common language, the purpose of which is to preview plans, initiatives, projects, innovations, etc.  Maths seen in this (Peircean) predictive context makes very good sense.  The Manifesto is a plea to movers and shakers in the corridors of power to get school mathematics switched over to this urgently needed meaningful mode as soon as possible.

CHRISTOPHER ORMELL 1^st November 2022
If you would like an online copy of the Manifesto, send an email to per4group@gmail.com asking for this.