Every week, the 24-year-old information systems student from Newcastle university, meets a group of eight to 12-year-olds to help them with maths.
They are all of average ability and might feel undermined in lessons by brighter classmates.
The classes, held at Sunderland football club's Stadium of Light, are partly funded by the Government's Aimhigher initiative and organised by the university's Students into Schools project.
A study of the scheme, published last week by the Department for Education and Skills, found little evidence that it was succeeding.
Mr O'Keeffe, who is involved in the project as part of his degree, hopes to prove the experts wrong. He said holding the classes in the stadium rather than a classroom was more exciting for pupils.
"They find it easier to ask questions because the whole class isn't going to listen to them," he said.
Most of the pupils come from families in which neither parent went to higher education. According to Mr O'Keeffe: "They want to know what you have to study to be something - like a nurse - and they want to know what university is generally like."
Researchers said Aimhigher's lack of success nationally was not surprising as the project was still in its early stages. Marian Morris, co-author of the research findings, said there were signs that contact with undergraduates was helping to raise aspirations.
But Penny Jane Burke, a lecturer at London's institute of education, said wider structural and cultural issues about academic exclusion needed to be addressed.
Ms Burke said: "One Aimhigher co-ordinator said they took a group of young boys to Oxford.
"It was a wonderful day - they got really excited and inspired.
"But the reality is that the likelihood of them ever getting into Oxford is quite low."