Mike Finlayson, chief executive of Teacher Support Scotland (TSS), which is leading the initiative, said it was not just about relieving stress or providing counselling. "A sea change in attitudes and a revolution in understanding are needed," Mr Finlayson says.
There are wider educational imperatives, he believes. "This is not just about being nice to teachers, although they must be valued and supported.
It is more to do with improving the effectiveness of teaching which depends on the effectiveness of teachers and this in turn depends on their health and well-being, particularly their mental well-being. It is really about good management practice."
The Executive, no doubt sensing the potential for raising standards as well as a goodwill factor, has agreed to support a two-year pilot in at least three authorities.
There are also likely to be financial savings. A study by Stephen Goss of Strathclyde University suggests that counselling services for teachers could save up to pound;1.5 million a year in Scotland. Dr Goss also calculates that the costs of salaries paid to teachers in Scotland while they are absent is nearly pound;43 million a year.
Mr Finlayson says there are recruitment implications as well. If the Executive hopes to achieve its target of 17,500 "first appointment" teachers by the end of the decade, well-being matters. "How the profession is perceived must have an effect on the willingness of people to embark on a teaching career," he says.
Teacher Support Scotland is conducting research, with the help of 300 teachers, to establish the support that is available and what their needs are. It is being funded by pound;74,000 from NHS Health Scotland (formerly the Health Education Board for Scotland) and the Esmee Fairbairn Foundation, one of the UK's leading independent grant-making bodies.
In turn, teachers are being asked for their support. An appeal will be popping through the letter-boxes of all members of the Educational Institute of Scotland in the next few days from Ivor Sutherland, chair of Teacher Support Scotland, asking for pound;3 a month to help extend its work. Other union members can expect the same call.
The appeal is being reinforced by a heart-tugging message from "Margaret", a primary teacher suffering from stress who is being forced back to work because she is the family breadwinner. "I can't speak to the head," Margaret writes. "She has enough problems of her own."
She continues: "The people I work with are always too busy and most of them are stressed-out as well. I love my job and I don't want to do anything else. I have been teaching for 19 years and feel trapped. What do I do?"
The "Margaret needs help" campaign hopes a long-term national strategy can be developed. In a paper to the Executive proposing the pilot, Teacher Support Scotland says there must be a mixture of early intervention, ongoing support and initiatives within schools.
It also points to the need to recognise that management styles, educational policies and innovation processes all have an impact on well-being.
Teaching is said to have unique pressures and greater levels of stress than comparable professions. Teacher Support Scotland points to a 1996 TUC survey of safety representatives which found that stress was the main health and safety concern in four out of five schools.
Mr Finlayson cites a paper from Matt Jarvis of the International Stress Management Foundation which suggests that excessive stress among teachers is caused by factors intrinsic to teaching such as pupil behaviour, and by the way they work and are managed. The kind of people teachers are also makes them demanding of themselves.
Ewan Aitken, education spokesperson for the Convention of Scottish Local Authorities, said council bosses are generally supportive but other employees also have unique pressure points. "It's not a case of teachers and then everybody else is different," Mr Aitken said.
In a message calling on members to support the initiative, Dougie Mackie, EIS president, and Ronnie Smith, the union's general secretary, state:
"Workload, challenging behaviour and the way in which education is managed conflict with the dedication and commitment of teachers and so create a uniquely stressful environment."
A spokeswoman for the Scottish Executive commented: "In these modern-times, few professions are stress free and teaching is no exception. While it is undoubtedly a rewarding occupation, teachers find themselves facing a range of challenges on a daily basis.
"Help is available from a variety of sources and we welcome new initiatives in this field."
But David Cameron of East Lothian Council's education department, which has been co-operating with Teacher Support Scotland on a well-being pilot involving school staff in Prestonpans, reports mixed success. "In schools where there was already a good ethos, the situation has remained much the same. But there has been some positive impact in schools where there were problems to be resolved."
Mr Cameron none the less supported the need for a Scottish strategy which, he suggested, has to be linked to the wider health-promoting schools initiative. But he said that many of the current materials and training schemes were English-based and his authority would not be renewing its contract with Teacher Support Scotland to extend the pilot, although he agreed it had been "a useful vehicle".
He added, however: "If teacher well-being is an issue affecting both teachers and schools, it has to be addressed and time has to be made available.
"There is no doubt that if teachers are not able to give of their best, the effectiveness of the school is not going to be as it should be, and that is a powerful message which is emerging."
John Blackburn of the Health and Safety Executive said violence, aggression and stress are matters to which the law applies, and the promotion of occupational health and well-being is central to the work of the HSE.