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Topic section: Beautiful mind-games; mind-numbing calculations
Beautiful mind-games; mind-numbing calculations
During the nineteenth century there was a reform in attitudes towards mathematical education, but these changes had yet to filter through to the majority of the population.
He opposed the prevailing system of memorised learning and strict discipline
 An important pioneer of new methods in education was the Swiss educational reformer Johann Heinrich Pestalozzi, who wrote his principal work, How Gertrude Teaches Her Children, in 1801. He opposed the prevailing system of memorised learning and strict discipline and sought to replace it with a child-centred focus. He believed that girls’ education was as important as boys. As he thought that education should be based on concrete experience he advocated the use of tactile objects in teaching.
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A 19th century French mathematical surface in string.
Credit: Science Museum/Science & Society Picture Library

In France, the revolution of 1789 swept aside the old mathematical schools in favour of the École Polytechnique, a national centre of excellence where leading mathematicians taught students. One of these teachers, Gaspard Monge, introduced the use of geometrical models as teaching aids. An 1819 biography of Monge praised his ‘hands-on’ teaching methods. By the late nineteenth cen
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An early arithmetical teaching aid by Adolf Sonnenschein.
Credit: Science Museum/Science & Society Picture Library
tury models were standard items in higher mathematical education. Although the underlying aim of the École Polytechnique was utilitarian, it introduced progressive teaching methods.

In Britain the Enlightenment eventually reached elementary mathematics. John Leslie’s The Philosophy of Arithmetic, exhibiting a progressive view of the theory and practice of calculation appeared in 1820 and treated arithmetic as a branch of liberal education. Leslie had studied arithmetic in ancient and other cultures and was impressed with the Chinese abacus. His followers used the abacus in the classroom. Augustus De Morgan, professor at the newly-created University of London, argued that mathematics was extremely useful ‘…but were this all, it must descend from the rank it holds in education’. By the end of the century elementary texts such as Adolf Sonnenschein and Henry Nesbitt’s ABC of Arithmetic were bringing a more enlightened arithmetic into some people’s lives.
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Coggeshall rule.
Credit: Science Museum/Science & Society Picture Library

However, much mind-numbing calculation was still required, especially in astronomical calculations for navigation, and increasingly for insurance, savings banks and census surveys. At Greenwich Observatory, human computers were used throughout the nineteenth century and into the twentieth century to make mathematical tables. Not until the 1860s were mechanical calculators made in sufficient numbers to play a part in office life. Thomas Arithmometers, the first commercially successful machines, were used by the vast Prudential Assurance Company and also supplied around the world. Shops and smaller businesses began to use adding machines and cash registers. By the end of the century the office machinery industry was taking off, particularly in the USA.

While these machines helped to avoid the need for much pen and paper work they did nothing to help promote the life-enhancing qualities of mathematics.

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Topic section: Improving minds; obeying rules
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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

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Topic section: Engaging brains; pressing buttons
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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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