From next year calculators will be barred from one of two maths papers in tests for 600,000 11-year-olds. Officials are also considering banning them from one of the maths papers taken by 14-year-olds.
In maths, say reports on this year's tests, 14-year-olds did well at simple mental arithmetic and using simple fractions and percentages. However, they had difficulty with two-digit divisions without calculators and with questions needing mathematical reasoning and problem-solving skills.
One in 10 could not multiply 840 by 63 and one in five could not divide 1.24 metres by 14 centimetres.
Dr Nick Tate, chief executive of the School Curriculum and Assessment Authority which published the reports, said: "There are vital parts of maths which can only be taught without ready access to calculators. The move to calculator-free papers will signal more strongly to schools the importance of thinking very carefully indeed about the way they use calculators. The overuse of calculators can be damaging."
At present pupils are allowed calculators in all maths papers and those questions in which calculators must not be used are indicated.
Dr Tate said pupils found that confusing. It was also difficult to police when calculators were being used.
The authority has commissioned an international survey to examine how calculators are used in other countries. A report from Her Majesty's Inspectors suggested recently that calculators are used much more widely in British primary schools than abroad.
The authority's reports on national curriculum testing for more than 2 million children say standards of reading and writing among seven-year- olds are rising while those in maths remain much the same. Standards in English, maths and science for 14-year-olds are about the same as last year. Full details will not be known until the new year.
Boys scored higher than girls on the non-fiction test and girls did better than boys on story-reading.
Dr Tate said that the tests had been a success. The reports acknowledge that there were problems with marking the 14-year-old English tests with hundreds of able pupils being given marks that were too low. The training and supervision of markers will be improved this year.
After allegations of cheating in the 11-year-olds' tests, schools will next year be forbidden from opening test papers in advance.
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