The shortage is much worse for low decile schools: 62.5 per cent of principals in the poorest three deciles said they did not have all the teachers they needed this term, compared to 39 per cent in the richest three deciles.
The survey is based on responses from 700 (36 per cent) of the country's 1945 primary and intermediate schools, and was organised as the institute campaigns for a 16 per cent pay rise for teachers over two years.
The teacher shortage has been a major justification for the pay claim, as the institute says it has become harder to recruit teachers as their starting salaries, now $49,588 a year, have slipped from 25 per cent above the national median wage in 2001 to 1 per cent below the median last year.
Domestic students starting teacher training (excluding early childhood teaching) have dropped by a quarter from 3590 at the peak of the last economic cycle in 2008 to 2790 last year.
Indicative Ministry of Education numbers for this year are up by 280 but are still well below the same point in the last cycle, in a period when primary and intermediate school rolls have grown by 7.5 per cent.
NZEI president Lynda Stuart said children's education was suffering already and without urgent action, the crisis was destined to become a disaster.
"This is why we had a day of action on August 15 – this is desperate and the Government has to take the bold steps to make teaching a sustainable career choice again. We simply can't wait," she said.
"Teachers' heavy workload and low pay for their qualifications and responsibilities has seen many leave the profession."
She said shifting children or splitting classes was a desperate last resort, usually taken after a principal and other senior leaders had put their usual duties on hold to teach for the day.
"I've never heard of this happening so frequently before," she said.
"It's really disruptive to teaching and learning – for those who are spread around other classrooms, for the children who find themselves with extra classmates, and for the teachers who are trying to continue a quality teaching programme with a significantly larger group of students."
Many principals also reported having to cancel or postpone release time for teachers because relievers could not be found – adding to teachers' stress and workload. A massive 81 per cent of principals said sick teachers had still come to school on occasion because they knew there were no relievers available to take their class.
Almost half (46 per cent) of principals said they had to alter curriculum or programmes because of a shortage of teachers this term.
More than a third (36 per cent) don't yet know whether they will have all the teaching staff they need at the start of Term 4.
The Education Ministry is developing its own set of teacher supply and demand projections. Acting deputy secretary Pauline Cleaver said she expected to make this available "shortly".
"In the past, relieving roles were the entry step into teaching for the majority of new teachers, however, as supply pressures have tightened more new teachers are starting their career in fixed term and permanent positions," she said.
"Schools around the country have reported increasing difficulty finding relieving teachers over the last three years.
"In December 2017, the Government announced a package of teacher supply initiatives to support more graduates into permanent teaching positions, support experienced teachers back into the profession and recruit new graduates into teaching. This package was continued as part of Budget 2018.
"Early uptake figures suggest our teacher supply initiatives have been popular overall."
She said more than 1000 teachers who had been out of the workforce, or whose registration was about to expire because they could not get secure work, had taken up refresher courses since the course fees were wiped for this year.
The ministry has also approved 145 relocation grants for Kiwi teachers returning home and overseas teachers relocating to work in New Zealand.
