At first sight the school week is what mathematicians call a zero sum game: when one subject gains, another loses. So if the Education Minister insists, as he did this summer, that all schoolchildren must have two hours of PE a week, the first reaction of most teachers is: “Where is that coming from, Mr Peacock?”

In some Scottish schools, however, the entitlement already exists and, in a few of those, other departments not only do not complain but may even welcome the increased allocation for PE.

North Lanarkshire has taken a broad view of physical education to support three secondary schools - sports comprehensives - in developing the self-esteem, health and motivation of their pupils and the wider community through physical activities.

Elite athletes may emerge but that is not the objective. It is firmly tied to North Lanarkshire’s educational mission of raising achievement for all.

The sport is important but the “comprehensive” is fundamental.

In this respect the model differs from specialist schools and sports colleges in England, while borrowing and adapting their best features, says North Lanarkshire’s physical education adviser.

“These schools are using their funding to develop a range of projects that benefit other schools as well as their own pupils,” says, John French.

Typically, these include in-service sessions for secondary staff, enhanced provision for associated primaries and support and funding for sports clubs based in other schools. There are also more specific instances, such as a sports comprehensive specialist visiting another school to provide Higher PE expertise.

Provided they can share in the educational benefits, other schools in an authority, it seems, accept the existence of the sports comprehensives. But how do other departments in the schools respond to the increased allocation of time for PE?

“Getting the other departments on board was a key issue for the authority,” says Mr French. “The initiative is people driven rather than structure driven and the whole-school aspect is vital in selling the idea to teachers.

“Each of the heads in the sports comprehensives has expressed a desire to be part of the programme. Without their commitment to the idea, it would not work.”

Every North Lanarkshire secondary was given the chance to bid to become a sports comprehensive. The eventual aim is to extend the model to other subjects, just as St Ambrose High in Coatbridge is a music comprehensive.

Loughborough University is currently evaluating the sports comprehensives - St Margaret’s High in Airdrie, St Maurice’s High in Cumbernauld and Braidhurst High in Motherwell - but early indications are that the idea is working.

The philosophy and core activities around the sports comprehensive are similar, says Mr French, but each school has moulded these, played to its strengths and constructed its own identity as a sports comprehensive.

There seems to have been significant improvement in exam results at St Maurice’s High, he says, but the most obvious change in all the schools is in that unquantifiable but crucial quality, ethos.

“At Braidhurst High, there are posters all over the walls, the staff are buzzing, the kids are walking around with their heads up.

“At St Margaret’s, they have really focused on diversity and the alternative curriculum.”

St Margaret’s High, which dates from the mid-19th century, is currently in a 1970s five-storey building that wins few awards for architecture, but there is a pleasant, welcoming air about the school and - unusually these days - all its pupils seem to wear smart uniforms.

Headteacher Frank Berry is convinced that extra PE can deliver great benefits to an entire school, provided it is organised well and implemented innovatively. “You have to overcome the problem of colleagues who are naturally concerned that they have limited time to deliver their own curriculum.”

Schools have a huge responsibility for the health and well-being of their pupils, however, and arresting the marked decline in physical activity as teenagers approach adulthood is a challenge.

“Radical steps have to be taken,” says Mr Berry. “In the sports comprehensives we have been saying - as the Scottish Executive is now saying - that, as a minimum core, PE should be provided from first to sixth years for all pupils. So we have to challenge ourselves about what we have on offer. Is it just going to be more of what we had in the past or are we going to really look for ways to engage our pupils?”

Some of the ways being tried at St Margaret’s High might raise a few eyebrows. “Football, rugby, cricket and swimming are still there, of course, but we have also introduced dancing, golf, girls’ football, outward-bound activities, fun runs, even Frisbees.

“There is a high level of skill and physical agility involved in skateboarding, for instance, and for some youngsters it’s their main physical outlet. So, last year, our PE teachers bought in material to work with them, which has proved very popular.

“In fact, I had to have a word with a young skateboarder who was going down that wall outside my window.” He smiles. “Being innovative is fine but there are limits.”

Besides appealing to a wider range of pupils, many of these activities also draw in individual teachers from other departments. However, to ensure progress in embedding more PE in the timetable in a way that prevents it being eroded in the future, cross-curricular projects are essential and the support of the senior management is seen as crucial.

Collaborative projects are being developed by PE staff at St Margaret’s High, says Jim Mullen, the energetic head of the department. “We would have found that much more difficult before we became a sports comprehensive. The extra PE teacher that gave us has made a huge difference.”

However, without senior management conviction of the value of PE, there would not only be greater resistance to the novel ideas emanating from teachers such as Mr Mullen, but also fewer suggestions for collaborative projects from other departments.

At St Margaret’s High and the other sports comprehensives, such projects have included sports statistics with the maths department, newsletters and debates about sport and competition with the English staff, sports photography and logo and calendar design with art, nutrition and healthy eating with home economics, music for sporting events with the music department, and enterprise activities and career opportunities with business studies staff.

“The challenge is to make physical activity a whole school responsibility,” says Mr Berry. “We encourage staff from other departments to come forward with ideas to enhance the learning of their subjects through physical activity.

“There have always been teachers outside the PE department taking football or rugby, but what we are starting to see in our schools - and what we need for our health as a nation - is a widening of the consciousness of the value of physical education.”