Privately, some heads suggest that pressure to meet the Scottish Executive's target of 53,000 teachers by 2006-07 in order to cut English and maths classes to 20 in S1-S2 may be causing a relaxation in standards, and that the universities are passing the buck to schools to fail poor probationers.
They say that the small numbers of unsatisfactory probationers teaching in schools has still meant that around 200 pupils are receiving "unsatisfactory teaching for a year" until action takes place. The association wants more information on the past performance of probationers to help gauge their mentoring requirements.
Iain Smith, dean of the faculty of education at Strathclyde University, responded: "No student can obtain his or her initial teaching qualification if they have been 'considered unsatisfactory during their school placements', and the judgement of 'satisfactoryunsatisfactory' is made by a combination of TEI and school staff.
"There are indeed a very small number of probationer teachers who have been graded satisfactory during their ITE experience and are then graded unsatisfactory in their probationer year; but that is a different issue.
"According to the General Teaching Council for Scotland, the number is very small. Any system is bound to have some such cases - that is one of the things that probation (as its name implies) is about. It is only if we had anything other than a small number of such cases that we should get alarmed."
Lindsay Roy, president of the HAS, acknowledges that the induction scheme set up under the national teachers' agreement is a vast improvement on what went before. But the association wants it to work better. Top of the wish list is earlier allocation of probationers so that schools can, if necessary, recruit permanent staff in time for them to start in August. It suggests notification to schools six to eight weeks earlier, a move supported by Mr Smith.
Heads point out that a small but substantial minority of new probationers end up refusing their fourth or fifth placement offers, usually for financial or travel reasons. But this information does not reach schools until late June.
The association claims there is a "lack of clarity" over how probationer teachers are allocated to local authorities, with some taking a substantial number of placements while others fail to meet their minimum requirement.
It also calls for better support for teachers from other countries who, it says, struggle to enter the Scottish system because of red tape surrounding work permits and visas. It calls on the Executive to do more to reduce these barriers by making contact with foreign students in TEIs.
Other suggestions include accommodation or a cash sum to buy a car for probationers who have not been offered a post near their home, and cash incentives to make remote and small authorities more attractive.
The HAS calls on local authorities to think out training procedures more clearly. It cites one that gives training to probationers three days before other staff arrive in August, with days off in lieu during exam leave. Bad practice is where authorities remove all probationers from classes on the last Friday of the month, causing major cover problems, discontinuity for pupils and substantial supply cover costs.
Roy Jobson, president of the Association of Directors of Education in Scotland, supported many of the headteachers' suggestions, as did Mr Smith at Jordanhill.
A spokeswoman for the Executive said it had yet to see a copy of the HAS's proposals, but added: "As they stand, their suggestions are a bit of a mixture. We have discussed some of the issues with them before, and thought they understood the factors involved, and why seemingly attractive, but simplistic, solutions would not actually address the concerns they have raised. We will certainly be happy to sit down with them.
"The minister has made very clear to HAS that he values its input. But he would rather hear from HAS direct than through intermediaries in the media - even the ever-responsible TES Scotland."