Gordon Mackenzie, president of the Headteachers' Association of Scotland, told its spring conference on Tuesday: "The crisis is now affecting all parts of the country and all subjects." And a paper to Aberdeen's education committee the same day detailed shortages in a number of subjects and difficulties with relief cover.
The situation will be exacerbated by the 4,000 extra posts demanded by the post-McCrone settlement, mainly in primary schools.
Mr Mackenzie told the conference, with leading members of HM Inspectorate sitting beside him: "Schools have embraced the improvement agenda. But it is difficult to improve and to raise standards when you can't get the teachers."
He knew of one maths department that should have 10 teachers but is three short and cannot fill the vacancies. "Think of the pressure that puts on the school," Mr Mackenzie said. "Think of the pressure that puts on other teachers in the department."
He added: "The situation is getting worse and it's getting worse at an alarming rate. Those who are makng decisions about schools must take account of that reality with which schools have to struggle."
In Aberdeen, which is experiencing recruitment problems in maths, design and technology, modern languages and drama, difficulties in finding relief cover mean the authority "has very little cover available for illness, vacancy or other absences".
The council's paper states: "Existing teachers of (shortage) subjects are continually juggling timetables and classes to ensure at least some subject teaching for pupils, and are spending time each day on induction of relief teachers who are not qualified in the subject and have been assigned for general cover. School senior management teams are teaching classes and then doing their other work in the evenings and at weekends."
Aberdeen warns that the crisis is leading to more exclusions "because the daily disruption to learning and teaching brings inconsistency and constant change".
The city now plans to advertise on buses, in cinemas and abroad. It will also try to entice teachers from other areas with relocation packages. All posts advertised will highlight the post-McCrone salary levels, which begin to take effect next month