Current beliefs about calculators are still confused and misleading. On the one hand it is maintained that pupils should not use a calculator for arithmetical problems before the age of 10 or 11, by which time they are likely to have grasped the mental and written strategies that should always be seen as the preferred way of working; on the other hand there is an acceptance that, from the age of eight, it is appropriate to use a calculator as a resource for learning about maths ideas.
Yet the Calculator Aware Number project (CAN), set up in 1986, demonstrated that when calculators were used right from the start of schooling, both to learn about mathematical ideas and to develop mental methods they enhanced number competence rather than inhibiting it. CAN argued that pupils should be allowed free access to calculators in line with what was happening in the general community and in workplaces. Within weeks of starting the project, development in pupils' mental calculating skills was noticed, along with the development of mathematical ideas. Project activities required pupils to be able to calculate mentally rather than use the calculator to do the work for them.
One activity consisted of a drawing of a snake marked out into sections, in each of which there was a number. The task was to key inthe first number and then to work out what operation was required to get to the next one before keying the operation into the calculator and checking that the number produced was the one predicted by the pupil. For example: from 12 to 24 you might key in either +12 or x2; for 12 to 41 you would need to key in +29.
Pupils proved to be very good at devising their own calculating methods and, since teachers were interested in fostering this, they were able to support its development and discourage inappropriate calculator use.
The CAN approach is an integrated one: give everybody a calculator and help them to use it properly from the start of schooling, rather than the fragmented one that isolates calculator use from the development of mental and written methods and yet expects efficient calculator use to be achieved in just two years instead of being a complete experience from the age of five.
It is my firm belief, based on many years of teaching at all levels, that if people could be encouraged to develop and value their own mental calculating methods we would not have a community full of people who think they cannot do maths and, in particular, cannot do arithmetic.
Janet Duffin is a lecturer in mathematics at the University of Hull. E-mail: firstname.lastname@example.org