They argue that this would spread resources more evenly across the whole school, require fewer extra teachers and classrooms, and be easier to timetable and organise.

They also claim that in times of funding cuts, a limit of 20 pupils would reduce their flexibility to run larger classes and may lead to “part-time education” unless staffing was ring-fenced.

A policy paper written for the Association of Directors of Education in Scotland by Bill Coyle of East Renfrewshire EMIS (Educational Management Information Services) unit, and adopted as ADES policy, calculates that the Executive’s plan to cut English and maths classes in S1-S2 to a maximum of 20 would require an extra 834 classrooms and 940 teachers across Scotland, compared to an additional 717 rooms and 815 teachers for its model.

Colin Dalrymple, the association’s general secretary, accepted that the plan may leave some magnet schools with class sizes of 26 but argued that headteachers would have greater flexibility to vary class sizes and create much smaller groups for pupils with particular educational needs.

The ADES move comes in the wake of the announcement by Peter Peacock, Education Minister, that he had listened to arguments put forward by headteachers and local authorities in favour of greater flexibility to vary class size maxima and that he was prepared to consider giving schools greater discretion provided they met certain criteria such as educational benefit and winning parent support.

Ronnie Smith, general secretary of the Educational Institute of Scotland, criticised the ADES position, saying he did not accept the argument that setting a slightly higher class size limit would create greater flexibility.

Mr Smith said that the association’s case was based on a resource rather than an educational argument and that essentially the directors were asking to be allowed to “rob Peter to pay Paul”. They were saying that if a school wanted to create a class of 10 pupils, either because they were being fast-tracked or because they needed additional support, the price would be enlarged class sizes in the middle of the school.

He insisted that protections should be built into the system to stop extraneous financial pressures driving up class sizes.

However, the ADES paper argues that:

* It is common practice in the lower school to set for English and maths with a variable class size, ranging from 33 to 10, depending on the level of additional support needs. This flexibility largely disappears by reducing the maximum class size to the new proposal. Classification is determined by number and not by sound educational needs, and the headteacher is no longer in control of this important aspect.

* The present maximum class size of 33 provides a flexible approach which is useful if there is a funding shortfall where in practice the actual class size rises as staffing is cut. By reducing the maximum class size further, managing a deficit is no longer an option and would lead to part-time education unless staffing is ring-fenced.

* The running of the school largely becomes a “numbers game” where the teachers’ contract is the determining factor.

Mr Coyle also argues that using a proposed class size maximum of 20 pupils in S1-S2 English and maths equates to a class size in practice of 16.6 pupils. Nationally, a proposed class size maximum of 26 pupils across all subjects would equate to a class size in practice of 21 pupils. He calculates the “class size in practice” by subtracting the absentee pupils from the “timetabled class size”, using the average absence rate for the authority for S1 pupils or the actual absence numbers, if known.

Both Mr Dalrymple and Mr Smith agree that there needs to be more cohesion in relation to class sizes than the current policy of a maximum of 25 in P1; 30 in P2-P3; 33 in P4-P7; 20 in S1-S2 English, maths and practical subjects and 33 in other subjects; and 30 for non-practical subjects in S3-S6 and 20 for practical.

Mr Smith said: “We have now got the EIS asserting our claim for 20 across the board, the Executive committed to 20 for S1-S2 in English and maths, and ADES wanting a maximum of 26. We are all agreed that we are going in the right direction of travel on class size but we have different takes on how far, how fast and in what way. Maybe there is a case for everyone sitting around the table and trying to thrash this out and inject some coherence.”

Henry Maitles, head of curricular studies in Strathclyde University’s education faculty, said there was evidence from research in New York City and California that, where class size was reduced from 30 to 20 or fewer, there was a major impact on “almost every indice you care to measure - from pupil attendance to teacher stress levels and so on”.

Mr Maitles said: “Twenty seems to be something close to the area where you get the maximum return for your money. Twenty-six would be welcome - it is better to have 26 than 33, but it does not quite give you that impact of when you reduce to 20.”

Both New York and California had offered schools the funding necessary to cut class sizes to 20 and researchers then evaluated the impact. However, some schools were unable to “buy into” the project because of teacher shortages and accommodation problems.