But when classmates at the National Academy for Gifted and Talented Youth summer school ask the 13-year-old for help, they want to discuss the finer points of the day’s lessons.

“At school, I’m the only one listening to the teacher,” she said. “It does get annoying. But here we’re all interested, we’re all paying attention.”

Helen is spending three weeks studying ecology and the environment at Warwick university, as part of the government-backed scheme. The summer school was piloted last year, when free courses were attended by 100 children.

This year, 530 pupils are paying up to pound;600 to attend courses at five universities - Canterbury Christchurch, Durham, Exeter, Warwick and York.

Pupils spend three weeks examining topics that complement those covered at school. The 15 pupils on the Warwick ecology course, for example, have studied water chemistry and hunted for fossils in a nearby quarry.

Annabel Yeomans, 12, said: “You always have some days at school when you have all the rubbish subjects. But here you get to focus on stuff you enjoy.”

Sue Barker, ecology course director, believes that pupils benefit from the hothouse environment. She said: “The children ask searching questions, that in any other class would stigmatise them. They put what they are learning in school into a real context.”

But the launch of the summer school has not gone smoothly. Fewer than a third of the available places had been filled by the original application deadline in late May. The deadline was extended, but current numbers still fall significantly short.

Feedback has indicated that families find the three-week courses interfere with their summer holiday plans. And pupils are deterred from applying by the stigma attached by their schoolmates to academic achievement.

Deborah Eyre, director of the academy, said: “Often, achievement is not valued in school. It’s not cool to be bright.

“But the academy gives them insulation from that. They can see there are other people like them. It’s a supportive community.”