St Andrew High, one of the schools which rank high in the quality score for both mathematics and English language, says its achievements are not just based on the quality of students entering at grade seven.
Sharon Reid, the school's principal, said she has a team of trained professionals who take the business of education very seriously.
The school's success, she said, does not happen by chance, but is achieved through a deliberate strategic plan.
"Planning is very high on the school's agenda, with each department head being held accountable for their department's performance."
She said the school has crafted a five-year plan, culminating in 2010, where each department sets specific targets.
"We don't analyse student performance on its own, we also analyse teacher performance."
President of the National Parent-Teacher Association of Jamaica, Sylvester Anderson, said parents with students attending the non-traditional and upgraded high schools should make a special effort to ensure that their children are provided with the necessary tools to attain good passes in external exams.
"It stands to reason that (these) children require much more support in terms of making sure that they have all the requisite material, if needs be, additional classes," he said.
"Because I am still not convinced that the children are given the appropriate number of contact hours for certain subjects (particularly) English and math."
He said, more important, parents should ensure that their children do additional work when they get home.