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TOPIC SECTION:
Improving minds; obeying rules
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The Maddux medal, a portable multiplication table.
Credit: Science Museum/Science & Society Picture Library |
In the eighteenth century only a tiny elite could enjoy the beauty of mathematics. No more than one in four of the population was taught maths in school. Instead people often taught themselves using primers, the most popular being Edward Cocker’s Arithmetic. Many of these books used verse to hammer home the multiplication tables. The idea was to make arithmetic as painless as possible.
Basic gadgets helped toavoid the strain of multiplication. In 1753 John Maddux sold brass medals with the times tables engraved on them, and many sets of ‘Napier’s bones’, which allow the user to add instead of multiplying, also survive from this period. The complexity of the systems of weights, measures and money made ‘Ready Reckoners’ indispensable for traders. Where numbers needed to be recorded, tally sticks were still used – for example, to record loans and deposits to the exchequer.
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Napier's bones allowed the user to avoid multiplication.
Credit: Science Museum/Science & Society Picture Library |
Britain lagged behind other cultures in the provisi on of elementary mathematical education. In Japan a moreegalitarian attitude was leading to a wider dissemination of mathematical skills. By the end of the eighteenth century, India had a fairly widespread village-based system of child edu
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For the wealthy, ‘the mathematicals’ were regarded as a pleasant occupation to fill ‘vacant hours’
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cation which provided tuition in basic numeracy. Prussia was the first European state to introduce universal elementary education, in the mid eighteenth century.
As an expanding colonial power Britain needed some of its workforce to have skills in navigation, surveying, and in assessing taxation. But at this level the emphasis remained on rote learning and following procedures. Even astronomical tables were designed to avoid the application of trigonometry wherever possible. One author boasted that ‘all the rules made for solving the astronomical problems are as short and easy as the Paternoster [The Lord’s Prayer]’. In all these disciplines slide rules and other mathematical rules were used to reduce calculation.
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Carpenters' rules often had engraved tables for the price of wood.
Credit: Science Museum/Science & Society Picture Library |
In 1779, Alexander Ewing in A Synopsis of Practical Mathematics contrasted this utilitarian attitude with that of the upper classes: ‘Mathematics are studied either by gentlemen of birth and fortune…or by those in the middle rank of life…the views of these classes are as different as their stations.’ For the wealthy, ‘the mathematicals’ were regarded as a pleasant occupation to fill ‘vacant hours’. For these gentlemen a culture of quantification had brought numbers into many spheres of life, such as weather records and efficiency of machines. They believed numbers provided certainty in a rational world.
Few benefited from enlightened teaching in the eighteenth century, but the small voice of reform was starting to be heard. In 1741, Isaac Watts, in Improvement of the Mind, argued for a good start in mathematics to enrich the whole of life.
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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 |
The debate over the use of calculators in schools still rages today. Should we simply learn how to use the tools or try to understand how the problem was solved? The abacus can serve both these functions. > more | |
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Beautiful mind-games; mind-numbing calculations
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