The way to a massive, much needed, renewal of morale in teaching maths can be via a new approach —‘Narrative Maths’ based on the methods of Mathematics Applicable, an idea-before-its-time (a ten-year project) which the present author led from 1969 to 1978 at Reading University.

Narrative Maths is a radical departure from the traditional platonic approach to teaching maths because it rests on the illumination maths can throw onto exciting practical future projects. The good feelings released by this illumination can take over the role of the ‘pure structure aesthetic satisfaction’ which used to be the driving idea behind most school maths. (Unfortunately the sense of ‘aesthetic satisfaction’ on which this relies is a rareified acquired taste. It motivated a thin vein of research in maths for two millennia, but it is not easily conveyed to average disaffected students at the secondary level: they see it as a weird minority in-house culture which is, in effect, rejective of ordinary, commonsense values.)

Today maths, taught in the traditional way, has also (sadly) become a victim of a profound culture-change in society away from ‘spiritual values’ towards a qualified form of ‘material values’. But it is a mistake to think that maths can become just a deliverer of material goods. Maths, being an advanced intellectual activity, cannot begin to thrive on a crudely ‘practical’ basis. (This was called <<Maths to make things happen>> in the 1980s, a teaching aberration which soon ran out of steam.). Small bits of maths can be used to “make things happen”, but they are few and far between, and cannot be harnessed effectively for long in crowded, under-motivated classrooms. 

The main role of maths in today’s relatively materialist culture is to preview all kinds of exciting potential developments. It offers an authoritative, rational way to think-about-the-future. It can illuminate new, unexpected projects. This is just what we need in an age when IT can put a gloss on every possible permutation of old news and past information, but which wholly fails to prepare young people to cope with the future. ((That this happens in a world irreversibly engulfed in a tsunami of technical change is an anomaly of the nth degree.) 

When we switch to teaching via Narrative Maths we are initiating students into forward-thinking, or if you prefer, the role of maths as the main ‘Pathfinder for Progress’. It does not pander to the pathology of <<instant satisfaction>> but rather instils the habit of ‘being prepared’. 

The Reading Project (1969-78) showed the way.  Every topic on the Maths Applicable course was presented from the beginning as a modelling kit needed to explore some aspect of the future. The project was generously funded by the Schools Council and lasted for ten years.

The team included Prof. Wilf Flemming, John Morgan, (former President of the Mathematical Association), Frank Knowles and David Malvern (later Prof. at Reading University).

A course was devised which was offered to sixth-formers who needed some mathematics in their intended careers, but who were not willing or able to take-on a full A-level in the subject.  It was examined by means of modelling coursework, and an examination paper which was built round a sustained modelling scenario.  These scenarios included a proposed system of inflatable rubber bumps to slow down traffic on foggy motorways, a fire-escape system which offered a rolled-up ‘sleeve’ into which people trapped near the top of a burning building could climb and slide down to safety, a rapidly moving station name system which would enable passengers on an express train to read the name of each station they were speeding through…

Most of the students who embarked on this scheme were initially somewhat jaded and demotivated by their earlier experience of maths up to GCSE. It was striking that most of them soon became enthusiastic about the illuminative effect of mathematical modelling. The schools which entered their students for this AO qualification were all volunteers, and their numbers grew almost linearly for eight years. By the time that the project finished, roughly 500 secondary schools had contacted the project.  The AO course was initially planned to continue after the end of the research project. Unfortunately, however, after 1979 Mrs Thatcher decreed that “all experimental maths schemes were OUT”.

The course textbook series incidentally also sold well in Australia.

Although this scheme produced Narrative Maths problems suitable for teaching at sixth-form level, it tackled the hardest part of the problem of devising such material.  To sustain a mainstream maths course for students up to the age of 16 would require about five times as much problem-creative work as was undertaken by the project team during 1969-78.  

CHRISTOPHER ORMELL 1^st September 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.