Tim Brighouse, Birmingham's chief education officer and a leading adviser to the Labour Party, called for pupils to take exams when they were ready rather than at a set age.
Four pupils from an inner-city primary school in Birmingham had passed GCSE maths last year and another 650 in the city were capable of doing the same, Professor Brighouse said.
No child should be held back, but, on the other hand, none should be made to take exams they were bound to fail, he said in a lecture to the Royal Society of Arts.
Birmingham is planning to set up a "children's university" to stretch particularly gifted students. Schools will be able to refer such pupils to the university so that they can receive more advanced tuition.
However, Professor Brighouse said slower pupils should not be made to sit GCSE exams before they were ready. "Passing exams is important: it boosts anyone's self-confidence. Failing has the reverse effect."Reuse content