There was a Protestant teaching in our school in 1964. More amazing still, she was a woman. The only people who had any difficulty with this, as I recall, were some of the boys in the class who rattled their rosary beads in an effort to discombobulate her when she was up at the blackboard demonstrating the impossibility of drawing a perfect circle freehand.
This was in a Christian Brothers secondary school in Belfast in the fundamentalist age before Vatican II, when the standard teaching of the Church, conveyed eagerly by the brothers themselves, was that Protestants lived in error, while we belonged to the One True Church.
I liked this teacher, but I looked on her as a strange visitor from another world, the world of damned sinners. I would love to catch up with her and ask her about her own memories of that experience.
Nowadays, there are many Protestants teaching in Catholic schools. There is now a core religious education curriculum which determines that the same elements of faith are taught in schools of all denominations.
So there is no bar to Protestants on the understanding that they would be disqualified from teaching the doctrinal preserve of a people closer to God than themselves.
Many Catholic-trained teachers themselves now are relaxed about the principles of Catholicism.
Some are atheists; some don't have a label for themselves at all. They can get jobs in Catholic schools because they are no longer judged by the quality of their religious lives.
The days are gone when the parish priest could expect to see all the teachers in a local school at Mass on a Sunday.
The test question at a job interview is no longer about faith. It is: are you comfortable teaching within a Catholic ethos?
And a Catholic ethos is not a collection of recondite teachings. Ask any teacher these days and they say it is about community and justice and good neighbourliness.
The only thing offensive about it is the implied suggestion that there is something specifically Catholic about it.
You would have to be a cannibal to say you weren't comfortable with it. Even Richard Dawkins could teach comfortably within a Catholic ethos in Ireland these days.
Here's another story. A friend of mine who is Catholic sends his children to a state school. One day recently, the children arrived home with a form to fill in, to help the school assess the type of chaplaincy services which it would make available to pupils.
The form asked the parents to identify their religious denomination. The options listed on the form were: Presbyterian, Church of Ireland, Methodist, Baptist, Pentecostalist and Other.
This school does not even recognise the existence of Catholicism. Perhaps it regards it as an anathema. It is invisible to them in spite of the fact that some of the pupils are baptised Catholics.
So there is no broad, radical front in education advancing towards integration by the back door and without a fuss. Some schools and communities are liberalising; others would insist on defending their right always to be more right than others.
But education in Northern Ireland is proving to be a porous front in the old inter-communal war.
This became clear to many schools during the quarrel over academic selection. What they found was that many parents on both sides were prepared to cross the divide for the type of education they wanted.
That means that academic selection was more important than religion to them and that the old horror of having your children sit in a school in which the religious culture was other than your own was no longer compulsive; there were other considerations more important.
It may be difficult for some Protestant teachers in Catholic schools to find that they are expected to go to Mass, for instance at end-of-term services.
They can be conspicuous, like the non-practising Catholics among them, during the eucharist, when they are expected to distinguish themselves from those going up for communion, either by sitting still, or crossing their arms in front of their chests to receive a blessing.
But those who go to Catholic weddings and funerals will be familiar with this crude custom and even its theological underpinning. They at least know that it is not an expression of the school's will.
We are seeing the creeping integration of education and there will be other developments forcing this along. As pupil numbers fall and resources tighten, it will make greater sense for schools to pool resources. Why should neighbouring schools of different denominations both lose, say, their French A-level class for want of demand when between them they can provide a single, full class?
Education was one of the historic dividing walls between two mutually-suspicious communities in Northern Ireland. The changes we are seeing are potentially as important as the changes in policing in signalling a relaxation of inter-communal tensions and the potential for resumed conflict.
It may seem a small thing when children and teachers of different communities learn and pray together. Actually, it changes everything.