Headteachers say primary schools should be kept locked during the working day, while the union to which murdered teacher Gwen Mayor belonged has warned against a "fortress mentality". The differences emerged in submissions to the Cullen inquiry.
Better security can never prevent a similar attack, the Association of Head Teachers in Scotland admits, but it points out that few people nowadays like being in their own home with outside doors unlocked.
So although tighter security will affect the "openness, accessibility and flexibility" which primaries have tried to foster, restrictions on pupils and parents will have to be accepted. At present the heads say that "many parents expect simply to walk into school at any time and receive immediate attention for often the most trivial matters."
Among the measures suggested are keypad locking, entryphones, automatic-locking doors and security cameras. Alarm buttons should be installed, and where necessary linked to the police. The Education Institute of Scotland agrees, calling for more attention to be paid to school design, better access control for visitors including entryphones, and the use of personal alarms and panic buttons.
The heads are concerned about security when schools are used in the evening when there should be patrols and playground lighting. Caretakers should be trained in security patrolling. In larger primaries, there should be at least one able-bodied employee on duty at all times during the normal school day.
Education authorities should draw up policies to formalise school contacts with parents and other visitors, and they should be required, the heads believe, to publish an annual security audit of all their primaries.
The Educational Institute of Scotland urges "a balance to be struck between the competing demands of personal and collective security and the relatively recent developments which make schools more approachable and more welcoming places."
But, in its initial submission to the Cullen inquiry, the Institute says the safety of pupils, staff and legitimate visitors must be given higher priority than in the past.
It suggests that the General Teaching Council for Scotland, with which all teachers must be registered, should be a model for those involved in running out-of-school clubs for under-18s. Such a national register should be in addition to mandatory vetting of individuals working with voluntary youth clubs through the Scottish Criminal Records Office.