Twenty-eight neat and orderly nine-year-olds sit on the floor in an expectant circle in the basement of the French Institute in London. They are junior pupils from the nearby French Lycee and they sit straight and cross-legged, as French children do.

But what is this? “I’m going to do something that may shock you,” says Brigitte Labbe, who is taking the class. “I’m going to take off my shoes.

You think better with bare feet. Perhaps you feel freer, as if you were on the beach.”

So off come the shoes and the straight backs relax. “How do you know that time is passing?” asks Ms Labbe conversationally. “Because you get wrinkles,” comes the cruel reply.

But Brigitte Labbe, a slim blonde with few wrinkles, is unfazed. She welcomes the mention of wrinkles because she knows it leads naturally to the idea of transformation.

In three minutes, with some skilful prompting, the children have moved from the notions of time and transformation to death. From there, the discussion moves on via laughter (“why do people laugh?”) to the ideas of pride and shame.

This is no ordinary class but an hour-long session to introduce children to the delights of philosophy - to “the pleasure of thinking together”.

And Ms Labbe is no ordinary teacher. In fact, she is not a teacher at all but a former marketing executive who decided in her late thirties to study philosophy. She became so seized with the desire to spread the ideas to children that she started writing books for them.

The presence of her little daughter, asking profound questions while her mother was peeling the carrots, was a spur to action.

Her books have titles like fat Russian novels - Life and Death, Laughter and Tears, Good and Evil - but they are slim, pocket-sized books full of pictures and anecdotes.

There are now 20 of them and they are selling like hot cakes, more than 800,000 at the last count. Ms Labbe writes them after long conversations with her former teacher at the Sorbonne, Michel Puech, who appears as co-author.

You will find the theories. but not the names, of philosophers like Heidegger and Wittgenstein in them, translated into conversational prose.

Aimed at eight to 15-year-olds, they have been bought by many parents and teachers wanting help with those awkward questions. And they have been translated into 15 foreign languages (including German and Greek) but not yet into English.

The books have turned Ms Labbe into something of a star in France and she could spend all her time visiting schools and libraries to promote them.

But she does not want to take too much time out from her writing nor become involved in what she calls the “science of education”, either in the classroom or in teacher training.

She limits herself to two visits a month, usually responding to requests from individual teachers. She normally restricts the number of children in the group to 12 or 13 and places drinks and snacks in the centre of the circle to keep things informal.

She spreads her books out on the floor and lets the children choose a topic. She discourages not only the wearing of shoes but also the putting up of hands when children want to speak (“I’ve noticed they stop listening while their hand is up,” she says) and changes position if they start to fidget.

While the conversation is wide-ranging, she says that it must be professionally conducted. She does not wade into psychology, for instance, and questions about personal problems are gently deflected. She looks for a “thread” she can pull out, a word (like “wrinkles”) on which she can pounce to steer the debate.

How much philosophy is already taught in French primary and middle schools? “Not enough,” she replies instantly, although she acknowledges that some primary teachers were doing sterling work of this sort long before her books came along.

She points out that it is difficult for teachers, used to being the voice of authority, to become one of the group, guiding and listening rather than answering questions. And it is hard for those who spend their lives struggling to meet objectives to take part in an exercise where there are none. The answer, she suggests, may lie in training philosophy students rather than teachers to take philosophy sessions.

But she is convinced that all children would benefit from at least an hour a week of informal discussion about serious, non-practical issues. It gives the less academic a chance to shine, she says.

“Whatever the social context, the depth of thought is always striking.

Sometimes they struggle to find the right words. It’s our role to help.

Children hear themselves saying interesting things on interesting subjects and it boosts their self-esteem.”

Good conversations can lead to a transformation in pupils’ behaviour, she says, and could be more effective than the programmes initiated by the French government to tackle poor discipline. At a troubled school in a deprived part of Lyon, a discussion she held on “beauty” led to further informal debates between pupils and the head and to a much calmer atmosphere, as well as the introduction of mixed-sex basketball.

At the end of her session in the French Institute, the children’s class teacher thanks her and says; “Today, I discovered my class.”

That, says Ms Labbe, is the saddest aspect of her work. Nine out of 10 teachers of the classes she talks to say the same thing.