The appeal from Eastbank Academy underlines the demand from local authorities for less Scottish Executive intervention and more licence to innovate.
Ewan Aitken, education spokesman for the Convention of Scottish Local Authorities, said that where there are national problems, such as with literacy and numeracy at the P6-S2 stages, authorities should be allowed to find local solutions.
"There will undoubtedly be problems reducing class sizes in maths and English in S1 and S2, including pressures on accommodation and staffing.
But if the plan is to go ahead, it has to be resourced," Mr Aitken said.
George Gardner, depute director of education in Glasgow, said the city was keen that heads look at local solutions when dealing with pupils who are still at levels A and B when they enter secondary.
"One of the issues we want to look at is the kind of training primary teachers undertake and whether their teaching methodology is perhaps more appropriate for kids struggling with levels A and B," Mr Gardner said. "We want the Executive to look at solutions such as Eastbank's."
In its partnership agreement, the Executive is pledged to cut classes to no more than 20 in the first two years of secondary for English and maths and to bring in more specialists to work across the primary-secondary boundary.
But experienced headteachers such as Jim Dalziel at Eastbank Academy want more flexibility. The Headteachers' Association of Scotland points to pressures on classrooms and timetabling.
George Ross, the association's general secretary, said: "Clearly we welcome any reduction in class sizes but it raises the question of what happens to other subjects, such as modern languages, history or religious education."
Eastbank's pilot scheme, called Enable, is now entering its second year and showing that there are more ways than ministers think to lift the commitment and achievement of secondary pupils at levels A and B in the 5-14 curriculum.
Some 75 pupils who have been identified with difficulties - 45 in S1 and 30 in S2 - are working in groups of 15 with two primary teachers on core work in reading, writing and numeracy. They spend roughly two periods a day building basic skills.
Mr Dalziel said: "Last year, we could not see a downside. Most are quite vulnerable children and have problems with self-esteem but they have made gains that we would see as quite significant and have moved forward in national testing. They have achieved more than some children who are not in the Enable project."
Progress is said to be down to the small classes and the methodology and approaches of the primary teachers, working alongside secondary specialists to ease the often difficult transition to a bigger school.
Pupils have a single social subjects teacher and a single teacher for science. "We are giving them a calmer introduction to secondary and we have managed to cut down the number of teachers in front of them for a third of the week. For most of these kids, the two-year project is necessary for them to consolidate," Mr Dalziel said.
The two primary staff are an addition to the staffing complement and help reduce class sizes in other first-year subjects where the average is 27-28.
Mr Dalziel points out that the maths department already chooses to have larger classes at the top end of the ability range and lower classes at the bottom and that is the flexibility teachers want.
Eastbank argues that work in S1 English and maths is more sophisticated than a simple focus on basics which most pupils have grasped in primary.
"While we are waiting for the effects of early intervention to kick in, we need to place the emphasis on the 10-14 group," Mr Dalziel said.
"It has gone extremely well and it has not been stigmatising like the old-fashioned remedial education. The kids are closely monitored and it's a fairly intensive differentiation across targeted core skills. By the end of second year they can begin to access the full range of courses available through the local authority.
Last year, we found that it not only helped these kids in the Enable project but it had a positive effect on the rest of the first-year programme. The other teachers were relieved of the extra need to target kids with quite significant deficits and the rest of the class could move on."
Without the special focus, some of the pupils might be lost to education, either staying away altogether or causing difficulties, Mr Dalziel contends.
"For class sizes reductions to really work, what actually made the difference were changes in teaching practices."
Ewan Aitken on class size studies by the Scottish Council for Research in Education (TESS, April 11)