That set him thinking. And after he moved to a new job as head of music at Northallerton community school, North Yorkshire, to be near his daughter - who by then was at the Steiner school in Botton - he became more involved in the school as a parent, "as one does".
He had been "very happy" teaching in the state sector but became increasingly disillusioned with the rest of his job, which was "becoming more of a management function". Then an opportunity came up to teach science, maths and music - his specialist subjects - at Botton. He took it and has never looked back. There are another three state-trained teachers at Botton, who, like Mr Dyer, have had to unlearn many of their pedagogical habits.
"It's a wonderful feeling to be away from the pressure of exams that runs right through the system now, and which seems more to do with the need to feed league tables than the children's education," he says.
The curriculum in Steiner schools is prescribed, but offers the teacher a high degree of freedom. "By the time children leave this school, they will more or less have covered the same things as in a state school, but in a different order," he says. "And you are not bound by ticking boxes."
Andrea Dowle (above), in her second year as a teacher in the Greenwich kindergarten, was Steiner-educated herself, along with her four siblings.
She trained as an opera singer but now says: "I couldn't think of doing anything else. It has been a wonderful experience. From my own education and upbringing, so much of it is in me, it has just become so much of my life. I spend my evenings sewing, preparing, learning stories and songs, thinking about the children. I spend a lot of time on the phone to parents.
There's less time for friends." Luckily, she says, "I grew up with the idea that materialism isn't everything."
The training of teachers - mostly conducted on the job and on short courses at Steiner's headquarters in London or Emerson college in East Sussex - is one area of concern. "We know we don't train enough teachers," says Sylvie Sklan, founder of the Hereford Steiner school and a national lobbyist.
"Whether or not state funding comes we have to sort that one out." She is hopeful that other colleges will follow Plymouth University in offering a BA in Steiner education, the only course of its kind in the UK.
Each Steiner school is visited by inspectors from the Steiner Fellowship every year. But the schools are autonomous and run collectively; there is no headteacher, and individual members of staff serve 12-month terms as chairs of the teachers' meeting, where all major decisions are made.
Roxanna Bibi is chair of teachers at the St Paul's school in Islington, but the route by which she arrived there is even more remarkable than Andy Dyer's.
"It starts with me being a child in a state school in Derby. I went to a mixed comprehensive in a run-down area. There was a lot of unemployment, a lot of scraps in the playground, that kind of thing."
Her parents were immigrants from rural Pakistan. "The only thing my father could write was his signature. It was important to them that their children did well at school. That had a strong effect on me." She studied hard and won a place at the London School of Economics to read economics, but began to question the subject's absolute assumptions about human behaviour.
After working in publishing, she studied Montessori education but "something didn't fit". Then she heard of Steiner, and went on a teacher training course every weekend for two years. "It was the most exciting thing I had ever done. I could feel my brain starting to stretch and grow."
Teaching practice was a revelation. "The happiness and interest of the children was a surprise to me, not something I had experienced in my education."
Now in her early thirties, as the de facto head she is learning the practical details of running a school, including finances, recruitment and health and safety. But it's the teaching that excites her. "It's an immense responsibility. It's like you can pick and choose your ingredients but you don't have a recipe book. Every day you think, 'How am I going to put it together and create something?'"