Does the new exam index work?

But the school in Pollokshaws, where more than one-third of children are from disadvantaged homes, is revealed as the most successful in Scotland under a new formula calculated by Professor Keith Topping, an international schools researcher, of Dundee University.

Looking at exam results in the raw form released by the Scottish Executive - which do not take deprivation into account - the school has 23 per cent of S5 pupils passing three Highers or more. This is just above the national average.

Yet when the 37.3 per cent of pupils eligible for free school meals are taken into account, Hillpark scores the highest figure in Scotland for weighted exam results.

So does the new methodology not simply patronise pupils in poorer areas, implying that deprivation must automatically equal lower achievement? In decades past didn’t some of the best-performing schools draw many of their pupils from deprived areas?

The headteacher, Joan Donnelly, does not see it that way. She said she was delighted by the recognition for outstanding staff and a good old-fashioned school. She added: "There is no magic, fashionable formula. The staff build up a strong relationship with parents and the children, partly by running an absolutely wonderful range of extracurricular activities.

"School is fun but we put in good, solid hard work and focus on attendance, late-coming, quality in the classroom - and the pupils’ own teachers give up most of their Easter holidays to run a revision course for them before exams begin."

Mrs Donnelly also attributed success to good attendance at after-school homework sessions and to goals negotiated with the children in every year group, which are communicated in an "action plan" to parents. She said: "Even if things aren’t going well, we can say: ‘Here are six things you could do that would make things better.’ It works."

Prof Topping, a professor of educational and social research at Dundee University, who has worked in the United States and the UK on ways of evaluating the performance of schools and pupils, believes exam results do not always reflect huge successes by schools in deprived areas and may mask some underachievement by schools in leafier areas.

Glasgow, which traditionally comes out very badly in exam tables, has the top three schools in the so-called "weighted" list; Hillpark is followed by Notre Dame High and St Andrew’s Secondary.

Other education authorities performing well under Prof Topping’s formula are Inverclyde and Renfrewshire - making spectacular rises on the conventional table - as well as East Renfrewshire, which has topped the normal exam-based table in recent years. Edinburgh is next, rising from its middle placing in the conventional table, compiled from Executive data, to become fifth best in the country, with James Gillespie’s and Holyrood performing best.

The calculation was made with the help of the Executive’s new website, which allows access to key information on individual schools. In recent years, the Executive’s education department has worked out several ways of charting how effective individual schools are but many of these have proved to be of limited reliability and validity.

Prof Topping stresses the data on meals does not reflect low income perfectly, but is widely-accepted as the best single indicator of deprivation. He said poverty does not predetermine low results, as factors such as parental back-up and the calibre of teachers and departments have an impact.

Low numbers of claims for free school meals in the education authorities of Aberdeen and Aberdeenshire has resulted in a low placing in the new table of several of their schools. John Stodter, Aberdeen’s corporate director of learning, said: "There is greater social stigma being poor in a rich area, particularly at secondary level as families don’t want to come forward."

Since 1998, Aberdeen City Council has been monitoring all children through tests at regular intervals including when they first start at schools.

Prof Eric Wilkinson, of Glasgow University’s faculty of education, described free school meals as "the best and most easily accessible poverty index".

However, he said recent reforms to Scottish education such as Early Intervention, based on more focused, structured lessons and extra adult help in the classroom, have weakened the link between home background and results.

Ronnie O’Connor, Glasgow’s director of education, said: "When vital factors such as social and economic circumstances are taken into account, our evidence is that, on average, Glasgow schools do well compared to others."

Children from Glasgow who have fewer qualifications than others from neighbouring education authorities might disagree when it comes to securing places at university or employment. But the new index is certain to stimulate debate.

• To see the full results, go to swts.oldsite.jpimedia.uk/schooltables. Information providing a rounded profile of individual schools is available on the new Executive website: www.scottishschoolsonline.gov.uk