Figures at work
They do more than sum up the profit and loss - discover the wide role played by numbers in business.
Centuries-old homework
About our expert
Sue Johnston-Wilder is Associate Professor of Mathematics Education at the University of Warwick. Previously she was a Senior Lecturer in the Centre for Mathematics Education at the Open University. She researches in several areas including motivating mathematics, mathematics anxiety, and the use of ICT and history of mathematics in supporting mathematics learning.
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Much of what has been known about number development came from studying young babies, animals and people who can no longer deal with numbers. Brian Butterworth, a leader in the study of extreme difficulties with number (dyscalculia), describes an example of an Italian hotelier who, after sustaining a stroke, could not do anything with numbers above 4, where previously he had been without difficulty.
It is possible to use brain imaging to identify what areas of the brain are damaged in such cases, or alternatively what areas are used by those successfully manipulating number. Educators have known for many years what brain science is beginning to confirm, that human ideas are grown from early sensory-motor experience. Learners begin with physical manipulation of apparatus, developing their use of mental images and memories of actions. Later, they learn to manipulate symbols which represent those images.
While in the womb, a baby has experiences which lay the foundation for comparing, for example, loudness of noises. The baby further develops its ability to compare as it develops its sight, for example, nearer or further. This ability to compare seems to be inherent in animals as well as babies. However it tends to be presented as ‘lions can count’ when they may be comparing.
When numbers are small, comparing involves ‘knowing how many’. This ability is known as ‘subitizing’ and is demonstrated by both babies and animals. Dr Karen Wynn, a child psychologist at the University of Arizona, showed that babies of six months expect that adding one object to another object will produce a set of two objects, not one or three, and that they are surprised when this does not happen. Some scientists think that the human genome includes a code for building a specific neural mechanism for subitizing.
As a baby explores its body, it develops sensitivity to the ends of its fingers. The part of the brain that seems to be responsible for representing numbers lies adjacent to the part that is responsible for touch sensation in the fingers. Many children who have difficulties with number have impaired sensation in their fingers, so the two may be connected.
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