The papers which complained so vociferously about the “N for Nonsense” grade, as the Sun put it, had misunderstood the tests’ purpose. They are not designed to divide children and package them off to different institutions like the old 11-plus and the modern A-level but to give some idea of what they can and cannot do.

But the general train of thought was familiar enough. The notion that failing exams is good for people - like the idea that bullying makes a man of you - is a favourite among education’s traditionalist brigade. Oliver Letwin, now the shadow home secretary, defended the tests as a youthful Thatcherite by arguing thatseven-year-olds were not too young to learn about failure.

But my teacher meant something different. Her argument was not that her less able pupils should be labelled unequivocally as failures but that schools were not doing enough to help them through an inescapable experience. Every child, from the brightest to the slowest, needs help with failure and it is not enough to write “F” at the end of an exam script.

Even in grammar schools, some people feel that they are failing. Recent research backs up her belief that the problem is not confined to the least able. Studies of the practice of setting pupils by ability have consistently shown that those in the bottom sets suffer because they become demotivated and give up.

Recently, research from King’s College, London into 2,000 teenage pupils suggested that setting had the same effect on girls in the top set. The researchers found that most would have preferred to have been in a lower set where the pressure to succeed was less and the pace slower.

But the demotivating effect of failure on those at the bottom of the heap is often more serious. English schools have had difficulty in dealing with it because of their narrow academic focus. Grammars and the 11-plus which relegated “failures” to secondary moderns were replaced by comprehensives, which often aped the grammars’ values.

Tests, targets and league tables, backed by Conservative and Labour governments, have reinforced the importance of success in exams. Children who do badly in tests now do badly again and again.

There are some hopeful signs. One way to boost the confidence of the less academic is to show that we value a wider range of skills. Government plans to encourage more pupils to take vocational courses and to make more vocational options count in the league tables will help. So will the primary strategy, which urges schools to widen their horizons beyond English and maths.

New types of assessment emphasising constructive feedback rather than marks are being pioneered by the Assessment Reform Group.

Last year, the Government published a White Paper, Success for All, which outlines reforms in FE and training. A paper entitled Failure for All would have less political appeal. But for teachers who have to grapple every school day with educating pupils for failure, the subject is just as important.