Mastering mathematics for everyday life remained as demanding as ever in the twentieth century, but the advocates of enjoying it as a life-en

Coloured abacus from the mid 20th century. Credit: Science Museum/Science & Society Picture Library

hancing subject also became more vociferous. In the early years of the century pioneers such as Maria Montessori advocated enlightened teaching with real objects. Unlike the nineteenth century, however, these methods were increasingly introduced into education for the masses. Nursery and infant classes were brightened with bricks, counters and rods. Unfortunately, when secondary education was introduced for all after the Second World War, mathematics for those deemed less able – especially girls – was still very mechanical and utilitarian.

Change was to come with a vengeance with the introduction of the School Mathematics Project (SMP) or ‘new maths’ in 1962. Advocates of SMP hoped it would ‘reflect modern trends and usages’. It included pure abstract maths: sets, mappings, binary numbers and bases, topology, transformations, groups, fields and matrices. Ten years later it was criticised for ‘trying to get children to run mathematically before they could walk’. The enlightened SMP did not suit everyone and was not producing useful mathematicians.

Number balance, c.1985. Credit: Science Museum/Science & Society Picture Library

Some instruments, such as mechanical calculators, were principally avoiding mechanisms, but had a secondary role in aiding under

‘Trying to get children to run mathematically before they could walk’

standing. As maths teacher David Fielker commented in 1973: ‘The mechanical calculator has been particularly successful with the less able, who benefit from the tactile, dynamic features of the machine. Turn the handle to add, turn it back to subtract, turn it many times to multiply, etc. It is a physical model of the four rules. A lever set machine lets you feel the numbers.’ Likewise, the abacus continued to be used in Japanese education, and was advocated here.

The Sinclair Cambridge calculator, one of the first electronic models. Credit: Science Museum/Science & Society Picture Library

The electronic pocket calculator – first produced by Canon and Texas Instruments as the Pocketronic in 1971 – was the ultimate avoider of effort and, potentially, understanding.

Its use in education has been controversial ever since. In the USA in 1989 the National Council for Teachers of Mathematics endorsed calculators, but large majorities of both teachers and parents were opposed. In England calculators now feature in the National Curriculum, but even ‘Maths Year 2000’, a government initiative, shied away from promoting them. Do we simply need the answers or should we be looking for something more? Can the many instruments developed as avoiders of thinking come back and help us think?

Even today we argue about the purpose of learning maths. Is maths an elitist intellectual pursuit to fill the vacant hours or simply a matter of learning a few basic rules from a book? In the eighteenth century, businesses and the state alike, needed people who could do basic calculations. > more

Should we examine models to understand maths better or just use calculators to get the job done? In the nineteenth century, the introduction of new methods of teaching maths foreshadowed today’s modern maths. The development of the calculating machine removed the need to do huge sums using pen and paper. > more