It doesn't add up. Live in Singapore and your child can sit a rigorous mathematics exam set by a British examination board. Send your child to a state school in this country and the same rigour will elude you. This is one small sign, one little fact among many, which shows that mathematics standards in this country are slipping.

The Reform think-tank has conducted an analysis of O-level and GCSE exams over time. They tell a story of a gradual decline in standards. In 1990 the percentage mark for a grade C was just over 50 per cent. Now scores of less than 20 per cent regularly suffice to gain the same grade, despite a much reduced level of difficulty. The paradox is that making maths easier at GCSE has coincided with a fall in the numbers going on to study it at A level. The drop has been of about 15 per cent in a decade.

Over the past 30 years maths exams have drifted from insisting upon rigour to being obsessed with relevance. In other words the curriculum has become broader, but shallower. From being required to know arithmetic, algebra and geometry in depth, candidates are now asked to show familiarity with, for instance, handling data and applying mathematics. Abstract and conceptual questions, testing the logical thinking of the candidate, have been replaced with ones in which the problems are embedded in artificial contexts. The students are led through the problems, often with the required formulae provided.

As standards decline so does Britain's ability to produce elite mathematicians and scientists. This country has in the past nurtured a remarkable number of Nobel prizewinners and Fields medallists. The future looks less promising.

Why should anyone worry about this? There are two reasons. The first is global competitiveness. The Government's estimate is that 15 million adults struggle with basic mathematics. A CBI survey suggests that 50 per cent of employers are dissatisfied with the basic numeracy of school-leavers. Businesses are finding it difficult to recruit appropriately qualified graduates. The ability of this country to succeed as a service economy is threatened by the decline in maths. That holders of an A level in maths earn, on average, 10 per cent more, or £136,000 over a lifetime (see page 9) demonstrates the difference that competence in maths makes to earning power and gives an idea of how much is at stake.

The second problem is one that should concern even those who care little for commerce. Mathematics can be a powerful engine for social mobility. Answers cannot be fudged. Raw intelligence wins out over the gift of the gab, however acquired. Robbing state school pupils of the chance to succeed in maths robs them of an important opportunity to succeed in life.

For this reason the growing inequality between pupils in state and private schools is tragic. Private schools are free to set more challenging exams and can attract to their teaching staffs the dwindling number of maths graduates who can resist the lure of City salaries.

The Government has established OfQual to examine the examiners. There is a tendency, however, both in Whitehall and in Westminster to dismiss talk of slipping standards as just more carping from the “Britain's going to the dogs” brigade. In the case of numeracy this is wrong. There are the numbers to prove it.