Children's Methods of Calculation

CCh Note: Activities like counting backwards in Predict A Count (see Sarah's example in this link), Smarties and Take A Score lead children to 'discover' negative numbers. It is not so much their existence which is a discovery, especially for students who have experienced a very cold winter; it is investigating how to operate with them that leads to an 'aha' about the broader structure of the number system.

From Page 18 Calculators, Children and Mathematics
Children began to make use of negative numbers in their mental calculations. The method of subtraction shown in Figure 3.8 was discovered independently in several classrooms, by children who liked to work from the left-hand end of a calculation. The child whose work is shown writes the result of the calculation on the first line, and then records an explanation of the steps used.

Figure 3.8, p.18. Calculators, Children and Mathematics.

Thus children who use calculators quickly become able to interpret negative displays on the calculator, and to make sense of negative numbers in which their use is appropriate. The teachers have been ingenious in devising situations such as the 'Smarties' game, which were within the children's comprehension and where it was necessary to extend the number-line below zero. Children have also found their own uses for negative numbers, such as the subtraction method shown in Figure 3.8.

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