Comment: Today's lesson: guinea pigs can show us the way

We are sorry. We know this will upend a few world views, distress some handwringing pessimists and affront those social conservatives who just know that the world is going to the dogs. But we cannot avoid reporting this truth - there is some good news for schools, and it has nothing to do with rote learning or bringing back the birch.

It comes in two sets of social studies cutting through the fashionable fatalism which says there is nothing government can do about social malfunction or educational failure. Our columnist Polly Toynbee pointed out how nearly 30 years' monitoring of the progress of American children educated in Head Start programmes showed how effective special pre-school teaching can be. And the other day, a team from King's College in London demonstrated how a structured programme for teaching 13- and 14-year-olds how to think raised their performance.

Behind these studies lies intellectual curiosity, yes, but more importantly, that old Enlightenment wish to know what works - what kind of teaching produces measurable improvement. It once used to be said that social experiments were somehow immoral, that researchers had no right using people as guinea pigs. On the contrary - without control groups, we are never going to be able to say with any certainty which teaching methods produce which results and so how teachers can be trained to better effect. And let us hear no snide references to Mr Gradgrind when we say examination performance is the least-bad measure we have got for educational success. However generously one acknowledges the improvements and the effort teachers put into their work in difficult circumstances, British schools still fail many children. Too many of them are not stretched, challenged and forced to explore their own potential as they prepare for examinations. These cannot tell us the whole story. But they rule the expectations of parents and employers and, if truth be told, children themselves.

Long lists of school examination passes are useful - up to a point. The Conservatives deserve much praise for pushing through the publication of league tables for schools against the opposition of teachers and the Labour Party. The latter has changed its official tune, because it belatedly realised that parents are not stupid and are able, inside their local educational ecologies, to assess the formal data that gets published and to square it with their own informal knowledge of schools' qualities. But that was only a start. Today, league tables, like questions of school organisation and finance, deserve far less attention than what happens in the classroom.

We desperately need to know how the attainment of average children can be raised. This week, the Schools Curriculum and Assessment Authority said that, generally, there has been improvement in primary school performance, that more children are now better prepared for transfer to secondary schools at the age of 11 - though the rate of improvement seems to be tailing off. Now, concern is focusing on those critical years between 11 and 14. Too many children, it seems, take too long to find their feet in the secondary schools and start preparing themselves for the GCSE at levels far below their potential - especially in mathematics. (Anyone who thinks this country can prepare for the 21st century with its current levels of mathematical competence is dangerously complacent.) This is why the King's College work - under the mind-dazing title Cognitive Acceleration Through Science Education - is so exciting. Here is a programme, available to secondary teachers, which develops the capacity to think - about logic, probability, proportion, correlation - and then to achieve far more in science. This is a real breakthrough.

That is, of course, only one programme. Even if its methods can be used elsewhere, it is no magic formula for problems in teaching English, foreign languages or history, let alone mathematics itself. But it shows two things. One is that educational experimentation isn't outdated, but is alive and well. The second is the importance of persuasion by results.

There are good reasons why teachers so often feel battered and bruised. There have been the changes in curriculum and in school management, and explosions of public concern at such issues as school discipline and exclusions. And there in the middle are many thousands of decent, hardworking and often underpaid people, getting on with the job of shaping and filling young minds. Little wonder, then, that teachers often hunker down in the hope the storm will pass, dismissing public anxiety as ill-informed or reactionary. Those concerned with educational improvement should recognise these facts, with sympathy. It is no good, as Chris Woodhead, chief inspector of schools, sometimes does, berating teachers as if they were dim and pimpled teenage anarchists at the back of the class.

Instead, where there is evidence that new approaches work and produce certifiable results, these need to be advertised and promoted, but in a spirit of aggressive optimism. The diversity of English schooling remains one of its greatest strengths, and teachers are right to resist universal, all-in-one formulae. But when the evidence points the way, as it has done this week, teachers' rush to try the new methods ought to be unstoppable.