Maria Alhambra hands the first girl a plastic cup. The cup is full of Smarties; the girl smiles broadly. Then Ms Alhambra hands the second girl a cup. This has only a handful of Smarties in it. "Thank you," this girl says, although her face falls.
Ms Alhambra then hands out cups containing varying quantities of Smarties to the rest of the girls. When one receives a cup with nothing in it at all, she laughs out loud. By now, it is obvious that something is going on.
This lesson - described as a "tutorial" - is being offered by the Brilliant Club, a charity that trains PhD students and postdoctoral academics to deliver lessons to schoolchildren. It targets both primary and secondary pupils from the most deprived communities, encouraging them to apply to top universities.
The idea for the charity came when co-founder and chief executive Jonathan Sobczyk, pictured below, was working as a teacher in East London. In charge of gifted and talented provision, he realised that he was happy arranging activities in the arts and humanities but had no idea what to offer young scientists.
His sister, however, was studying towards a doctorate in neuroscience at the University of Oxford. And so she came to his school and delivered the kind of lecture she might offer first-year undergraduates.
At the same time, Mr Sobczyk also noticed that only one in 20 children from the lowest-income backgrounds progressed to top universities. So he persuaded his sister's two flatmates to go into a school in a disadvantaged area of North London and deliver university modules in philosophy and economics. At the end of the course, the pupil "graduates" were rewarded with a day trip to Oxford.
And so the Brilliant Club was born. The charity now works with about 300 primary and secondary schools, and 450 PhD students. A third of the places on the programme are reserved for pupils on free school meals.
"Five-sixths of children eligible for free school meals live within 40 minutes of a Russell Group university," Mr Sobczyk says. "And there's a whole army of PhD students out there. They have a wealth of knowledge, information, vocabulary, skills."
Mr Sobczyk is sitting in a cafe in Cambridge. Around the corner, in the wood-panelled rooms of St John's College, pupils from a selection of primary schools are being taught philosophy by Smarties-wielding PhD students.
While the postgraduates delivering tutorials in secondaries give students simplified introductions to their own thesis topics, there is a different approach for primary pupils. Here, the PhD students are given a preselected subject - in this case, philosophy - as well as suggested activities and lesson goals.
So, having handed out the sweets, Ms Alhambra asks the pupils to summarise how they feel about their allotted portions. "I feel lucky for getting nine Smarties," says one girl. "But then I feel sorry for the people who didn't get any."
Ms Alhambra considers this. "Would it be better if we said that Freya had the most because she'd done the best?" she asks.
"Unfair," says one girl. "We all tried our best."
Freya, however, disagrees: "I think it's fair, because other people might have tried their best but some people might not."
The girls ponder this, as the afternoon sun filters through the enormous, draped windows. "So we think people shouldn't be rewarded if they work hard?" Ms Alhambra says.
The pupils are from Norfolk, a county with some of the lowest GCSE results in the country. Rosie Welch, deputy headteacher at Acle St Edmund CofE Primary School in Norwich, says that most of the students come from a farming background.
"There are a lot of fantastic things about being a rural community," she says. "But lots of our children have quite a narrow experience of the world. We just want to give them the absolute best opportunities they can have, by broadening their horizons and working beyond what's obvious to them and their parents.
"The younger you catch them, the more open they are to suggestions and ideas and new things - especially in a community that says `You can't' or `You shouldn't' or `That's not what we do'. The longer you expose them to that attitude, the more it becomes ingrained."
Road to brilliance
The first Brilliant Club tutorial is always delivered at a university, which allows pupils to tour the campus or college. At St John's, the guide points out the Bridge of Sighs, the library and the great hall. "We don't have floating candles, but that's as close to Harry Potter as you'll ever get," he says.
After this initial session, the PhD students deliver tutorials in school. At the end of the course, pupils are given a university-style grade, ranging from a third ("good level for Years 5-6") to a first ("excellent level for Years 7-8"). And they take part in a full graduation ceremony, complete with certificates.
"Obviously we're not so naive that we think we can work with primary schools and that's enough eight years later," Mr Sobczyk says. "We work with them at secondary school as well."
Younger secondary pupils are offered advice about what university is and why they might want to go there. By sixth form, this guidance becomes much more focused: how do they choose which universities to apply to? What should they write in their personal statements? The aim is to provide the information and experience that their immediate family might lack.
Back in the tutorial, pupils are still debating the fairness of the Smarties situation. One of the girls puts up her hand. "It's like the same with black and white people," she says. "It doesn't matter how you look - we should all be treated fairly."
The conversation continues until Ms Alhambra tells her tutees that it is time for them to attend a lecture on study skills. Before leaving, the girls pool their Smarties and divide them up equally.
"Does that seem fair?" Ms Alhambra asks. But there is no time to answer this, so the girls just wolf down the Smarties and leave the philosophical implications until next time.
`We know there are people out there who get the results but don't apply'
State school teachers are not doing enough to encourage their brightest pupils to apply to top universities, according to the head of a University of Oxford college.
Sir Drummond Bone, pictured, master of Balliol College, says that many teachers do not want to "expose their students to failure" by giving them the impression that they will win a place at Oxbridge when they might be let down.
But schools should be less concerned about this, he tells TES. "What we hear is that teachers are disappointingly conservative about their view of the likelihood of their students getting into Oxford or Cambridge. We know there are people out there who get the results but don't apply.
"You only have to look at the ratio between the number of applicants and the number of places offered. For us, it hovers between four-to-one and five-to-one, but for other universities it is much higher. Some have seven or even 10 applicants per place."
Sir Drummond says he often speaks to Balliol students from the state sector who say their schools did not give them enough support or encouragement, or were "risk-averse" in their approach to Oxbridge applications.
He says outreach work is "very much on the radar" of Oxford colleges and has become an increasingly important part of their work.
But Richard Tyson, assistant headteacher at Bennett Memorial Diocesan School in Kent, says he does not recognise Sir Drummond's criticism.
According to Mr Tyson, his school identifies early on which pupils are in the "potential pool of highest achieving students" and encourages them to apply to Oxbridge.
Its strategies include inviting former pupils now studying at Oxbridge to speak to students, holding information evenings and getting potential applicants to talk to senior staff.
"Probably the biggest barrier to overcome for students is thinking that they are not good enough or won't `fit in'," Mr Tyson says.
"We have to point out to them that with their track record they will be good enough and they will `fit in' because they'll be working with others who have achieved at a similar level."