Problems have been exacerbated by a dispute between the Prison Officers Association and the Government over implementing extra measures to ensure personal security and safety. Last year it was discovered that this had been compromised by the IRA, which had gathered details on more than 1,400 prison staff.
Maghaberry, in Lisburn, holds around 620 inmates, of whom 350 are on remand and 270 are serving sentences. There are 100 lifers. The paramilitary population is estimated at just over 60, loyalist factions outnumbering republicans by two to one.
Jim Turley, the senior teacher, has worked in prison education for 23 years. He is dismayed by the current situation - hardline republican and Protestant prisoners have mixed at Maghaberry since 2000, when the Maze prison closed down. "Prisoners want education to work but we can't do anything," he said.
Education at Maghaberry has yet to recover from disturbances at the prison, which attracted support from outside organisations. Inmates had been receiving tuition from basic skills to post-graduate level.
"Until the trouble I would have had four IT classes but, since the end of May, I've not had one," said Mr Turley. "If we can get education up and running again, it will ease some tensions here."
Paramilitaries were prepared to regard educational spaces as a neutral venue. But disputes over deploying prison officers - where they should be allocated and in what numbers - has made this impossible.
One day last month when, as part of their dispute, one in five officers at Maghaberry failed to return after lunch to complete their shift. Everything from IT classes to a pioneering magazine project has been stalled.
Currently, the prison can offer only a limited service with tutors giving lessons in cells.
The mood contrasts sharply with the optimism of last spring when, as part of an EU adult education project, Maghaberry was co-ordinating the first edition of Open Doors, a collection of creative writing pooled from prisons in England, the Republic of Ireland, Poland, Bulgaria and Norway. Each country, with its own editorial team including prisoners, produced material in-house before e-mailing it to Maghaberry, whose students acquired additional IT skills through the editing of the magazine.
Open Doors was produced under the Grundtvig scheme, named after Danish clergyman Nikolai Grundtvig, widely regarded as founding the Nordic tradition of lifelong learning.
Grundtvig promotes educational opportunities for school leavers without basic qualifications and encourages innovation through "alternative learning pathways".
"The project was starting to show social as well as educational benefits," said Mr Turley. "The increase of our disadvantaged students' self-esteem was immeasurable. The uptake in education significantly increased.
"In May we had a visiting party from Bulgaria and one of the guys who welcomed them had previously spent seven years in solitary confinement.
Meeting people from outside gave it impetus. In all, we had more than 80 people involved. But a week later, some of them were on the rooftops."
However, he is determined that further editions of the magazine will appear. "Some students are still working on the material and that will continue," he said.