# Prop or tool?;Mathematics

No one appears to have noticed the irony of a situation in which a government, professing itself to be committed to the effective use of information and communication technologies, then proceeds to argue for a restriction on calculators.

There has been a lot of fuss about "banning the use of calculators in primary schools", but what does the research evidence actually say? The School Curriculum and Assessment Authority's The Use of Calculators at Key Stages 1-3 (1997) and the Office for Standards in Education's publications suggest that pupil performance benefits from proper use of calculators. Moreover, reports show that calculators are used only in about 10 per cent of primary schools. The 1993 HMI report, Mathematics at Key Stages 1, 2 and 3 is critical of many schools for not paying sufficient attention to calculator skills. How then can calculators possibly be having such deleterious effects on standards?

Is the Government interested in research evidence? Consider the Numeracy Task Force's final report, The Implementation of the National Numeracy Strategy (July 1998). It argued, rightly, that calculators should not be used "as a prop for simple arithmetic," but also acknowledged that "used well, calculators can be an effective tool for learning about numbers".

And how was this balanced account reported? Given that the July 8 press release mentioned "a ban on the use of calculators by children up to the age of eight and restricted use throughout the remainder of the primary school" it is not difficult to imagine the headlines. This led to David Blunkett having to put the record straight in The TES (July 10) with the blunt statement "We're not banning calculators", and to members of the Numeracy Task Force "denouncing the Government's press machine" (TES, July 24).

There are two illogical arguments used for banning or seriously restricting calculators in primary schools: our international performance; and the relationship between mental calculation and calculator use. Unfortunately, England does appear to fare much worse at number in international surveys than do many other countries. However, it is also unfortunate that this situation is accounted for by the argument that, since we in this country use calculators and do badly, and our more successful rivals do not, then banning their use will help us do better.

It is important to note that in the recent Third International Mathematics and Science Survey (TIMSS), Singapore, with the highest teacher-reported frequency of calculator use, did better than every other country in the world.

The second argument seems to be based upon a vision of primary-school children working through pages of sums all day using their calculators to find the answers. No one believes that calculators should be used in this way: children would learn nothing and their mental calculation skills would no doubt deteriorate.

But, importantly, there is contrary evidence that calculators can be used effectively to develop mental calculation.

Studies of children's idiosyncratic use of flexible mental calculation strategies suggest that the more sophisticated an understanding a child has of the structure of numbers, then the wider the range of strategies the child has to call upon to deal with a given calculation. Calculators can be successfully used to develop that necessary "number sense".

For instance, the Numeracy Framework expects children in Year 4 to multiply mentally by 20 by first multiplying by 10 and then doubling. I would introduce this strategy by having children use their calculators to work out, say, 36 x 20. I would then challenge them to find pairs of numbers which, when 36 was multiplied successively by them, gave the same answer. Other large numbers would be multiplied by 20 and investigated in a similar way. In a whole group session we would compare and attempt to explain our findings. I would focus specifically on the x 10 then x 2 method (comparing it with the x 2 then x 10 method), and discuss how we might use this technique to help us multiply numbers mentally by 20. We would then put the calculators away and practise mental multiplication of small two-digit numbers by 20 using this method.

This approach involves the children in activity, reflection and discussion, as well as practice of the mental calculation technique. It can be modified for use with children from Years 1-6.

Ian Thompson is senior lecturer in the Department of Education at the University of Newcastle upon Tyne

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