At the end of one particularly bruising session, Colin Callaghan found he had become an object of sympathy. While most of his colleagues have barely batted an eyelid, there has been the occasional dissenter and it seems the visiting speaker was one.
"I get the feeling some of them think it isn't the right environment for men," he says. "This particular talk was very anti-men and was trying to promote girls' education through stigmatising men. It was hard-hitting stuff and some women heads came up to apologise afterwards.
"You begin to feel what it must be like for women who go into male places and feel their contribution is not valued as much as it might be."
Thankfully, those occasions are rare. In the five-and-a-half years since he became one of the few male heads of an independent girls' school, he says the reaction from parents, colleagues and pupils has been positive.
While women make up 63 per cent of all heads in the maintained sector, in the independent sector women have only recently broken through the glass ceiling to lead boys' schools, with the appointment of Katherine Haynes as head of John Lyon School in Harrow last year and Felicity Lusk at Abingdon School near Oxford from September. In contrast, men have a long history of running independent girls' schools. Mr Callaghan's predecessor at Derby High School, for example, was also a man, and was in post for 21 years. But that is not to say that it is all plain sailing.
Mr Callaghan says he may have ruffled a few feathers in those early days, and he believes this could point up a difference between the sexes. Men can be more sarcastic, he says, and it took the girls a while to get used to his sense of humour.
"Things I could have said fairly easily in my previous school caused ripples here," he says. "It was throwaway comments, just teasing girls slightly, but I found I upset them because they took it more personally."
Before moving to Derby, Mr Callaghan's career had mainly been spent in co- educational schools. A girls' school - although it takes boys up to 11 - was an opportunity to try something new. "I was interested in a different environment," he says. And Derby High is a day school, whereas his previous schools have been boarding schools.
He did have some all-girls' experience, though. At a boarding school in Suffolk he was in charge of a girls' boarding house. "It was just me looking after 60 or 70 girls, so I wasn't entirely unused to the challenges of a girls' environment," he says.
It helped that he was following another male head, and he says both parents and other staff took his arrival in their stride. But he acknowledges that he has had to adjust his approach to management since arriving at Derby High. "You become more conscious of the need to persuade and to encourage, which perhaps is something that comes more instinctively to women in leadership," he says. "I have changed my management style since I have been here and I try to be more inclusive."
Unlike Mr Callaghan, Alun Jones has spent most of his career in girls' schools. A musician by training, he relished the opportunities to develop music and choirs in girls' schools and his experience over the past 20 years has made him an enthusiast.
For the past nine years he has been head at St Gabriel's near Newbury in Berkshire. The day school has about 500 pupils and, unlike Derby High, they are all girls, with no boys in the junior school.
While he believes particular qualities are needed to be the head of a girls' school, he says it is the head's emotional intelligence rather than their sex that makes the difference. "It is important to be able to nurture and support the girls, and help their confidence, but it doesn't make a ha'p'orth of difference whether you are a man or a woman," he says.
Perhaps because he has spent most of his career in girls' schools, Mr Jones has not had to make the same adjustment in style as Mr Callaghan. "Maybe it is because I have come through a female environment, but the relationship with my team is very collaborative," he says.
His predecessor was also a man, and this may have contributed towards the positive reception he received at St Gabriel's. Parents are more interested in whether a head will care for their daughter than in whether they are a man or a woman.
Colleagues in the girls' schools movement have been similarly welcoming, although there have been exceptions.
"Now and again we miss the point and start talking about the importance of women in leadership positions," he says. "I suppose that is important, but the point is that we are about promoting girls' schools.
"You do get the odd eyebrow raised and people ask if I'm feeling uncomfortable, but I feel settled with the Girls' Schools Association and included in what they do."
If Jonathan Forster ever felt left out when girls' school heads got together, he is reluctant to go into detail. But things are different now. "I have felt very welcome in recent years," he says. "It may not have been the case 15 years ago, but it has been the case for the past five or six years."
There is wider recognition now that it is more important for a head to be good than to be a certain sex. "You will always find someone who feels we shouldn't have male heads, but that isn't the prevailing view. People realise we are after the same thing, which is to run schools well," he says.
Mr Forster has been head at Moreton Hall, a boarding school in Shropshire, for 17 years. For most of that time it was an all-girls' school. Boys were admitted into the junior school for the first time two years ago, but the senior school is girls only.
It was his first experience of an all-girls school, although he had run a girls' boarding house with his wife at a co-educational school. But there was no conscious desire to work in a girls' school: it just happened to be the job that came up, he says. "The fact it is a girls' school doesn't make any difference," he says.
"My job is to ensure the pupils are properly educated and provide the right environment, and that is the same whether you are running a boys' or a girls' school."
But he does admit to having changed his management style since being in charge of a predominantly female environment. "I have learnt a lot about how to deal with colleagues, about listening and how to manage situations," he says.
"There are many different ways to approach problems and getting everybody on side and sitting around a table is maybe more of a female approach. I think I have improved my management style."
This change of style was more evolution than revolution for Steve Callaghan, head of Sutton High, a day school in Surrey. All his senior leadership experience has been in girls' schools. He arrived at Sutton High seven years ago after four years as head in another girls' school.
"I quickly grew to understand the value of a consultative approach and talking about things. However much you think you have the answer, it is always better to consult your colleagues," he says.
His arrival at Sutton High caused a stir. "There were some raised eyebrows. Not so much from the current population, but from the old girls, who had been here when it was an exclusively female environment," he says. "The school already had a number of male members of staff, but some of the former generations thought it surprising."
From attendance at conferences, he estimates as many as one in 10 heads of independent girls' schools is male, making them a sizeable minority. He does not believe the gender of the head makes any difference to the school. The only difference for him is there are some no-go areas, as there would be for heads of co-educational schools.
But there are some lingering concerns about having male heads of girls' schools. "One issue that is sometimes raised is whether it's better to have a female head as a role model," says Mr Forster at Moreton Hall. "That is a point I don't particularly argue against - all I would say is we have a lot of women in senior managerial posts and in life you need to have a balance."
Mr Jones acknowledges that there are valid reasons why some governing bodies may be keen to appoint a female head. "Sometimes girls' schools are looking for a female role model in a head," he says. "I can see why that would be attractive and I have to compensate for that with my unequivocal support of the girls."
Women in senior positions can help mitigate the effect of having a male head. "I wouldn't want girls to think this is a man's world," says Colin Callaghan at Derby High. "You can be a role model in behaviour without being a woman, and our girls do have very strong female role models among the rest of the staff."
Girls can also see strong role models in other senior managers, chairs of governors and heads of other girls' schools, says Steve Callaghan at Sutton High. "It is a valuable lesson that the girls see men can be in a minority in some areas," he adds.
Some parents, too, see it as a positive thing to have a strong male influence in the school, says Adrian Aylward, head of Leweston School in Sherborne, Dorset. He suggests the idea that girls need to have female role models is outdated. "The world has moved well beyond that," he says.
Mr Aylward arrived at Leweston three years ago after a decade as head of Stonyhurst, a co-educational school in Lancashire. Both are Catholic schools and he says it was that rather than a commitment to girls' schools that drew him to Leweston, which takes boys up to seven but is all-girls from seven to 18.
He acknowledges that being in a predominantly female environment has affected his approach to management. "I probably have had to learn to be more co-operative," he says.