Frances Goldman, of Glasgow University maths department, condemned the use of calculators, especially in primary schools. Speaking after the west of Scotland Maths Challenge, which had involved more than 3,000 pupils from P6 to S6 in 225 schools, she said: “There are good things which come out of school maths in Scotland. But anyone in the profession would say that manipulative skills have diminished.”

Dr Goldman went on: “I think the ability to do fractions and proportions has diminished, partly because of the calculator. People think it’s not necessary but in fact for a lot of things you use in maths, you need to understand how proportions work. If you have done this with numbers first, it’s easier when you come to do it in the abstract.”

Cliff Percival, a financial controller for Marks Spencer which sponsored the challenge, told the pupils that numerical ability was important in business. “We really couldn’t have a conversation in Marks Spencer without some reference to figures - how we are doing against the year, against targets and which departments are doing best. All that requires some mental and numerical ability.”

The Third International Maths and Science Study (TESS, June 13), revealed that about 70 per cent of teachers in Scotland allow access to calculators in maths lessons, a higher percentage than in any of the other 26 participating countries.

* Edward Patterson, chairman of the north of Scotland Mathematical Challenge, in which numbers increased from 758 last year to 1,009, said that “young people are going in for the competition in a big way as problem-solving is more and more seen as an integral part of life”.

Professor Patterson, who formerly held the maths chair at Aberdeen University, told The TES Scotland that he would not ban calculators outright, but pupils had to learn to assess whether their answers were feasible. “I also think teachers should devise exercises in which calculators are not allowed.”