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The average house price growth in Auckland in the year to September was $54,000, while the average annual wage was $51,116.
The situation has become so bad Post-Primary Teachers Association Auckland western ward executive member Melanie Webber said a colleague told her: "I wish I'd studied harder at school and become a house."
Drumm said young teachers wishing to settle down, buy a house and start a family, could not hope to pay a hefty mortgage and raise a family on their salary - even at the top of the teacher pay-scale at $75,949.
The sector was starting to see a trend - young teachers a few years into the profession, who want to settle down, are choosing to leave Auckland. The city had become "out of the question" for them.
"They can see it's unsustainable, and they're taking their skills elsewhere", he said.
Such migration out of Auckland was "shrinking the pool" of quality teachers, he said, especially in high-demand science, technology, engineering and maths (STEM) subjects.
Owning a house in Auckland 'not realistic'
Teacher Steve Sharp, 31, is one of the MAGS teachers leaving at the end of the year.
He and partner Laura Robinson, 26, are moving to Dunedin, where she plans to study and the cost of living is cheaper.
The couple - who have been living in Auckland for two years - would like to buy their first home and settle down. But even with Sharp earning close to the top of the teacher pay-scale, at around $70,000, their dream was "not really realistic, particularly if we go down to one income".
Teachers get paid on the same pay-scale all over New Zealand, so his pay cheque would go much further in Dunedin than in Auckland, he said.
"At the moment we live in a share flat ... but we want to move into our own place, and realistically that's a bit more challenging if we want to live in Auckland and save for a house at the same time.
"Whereas in Dunedin we could start renting our own place and then even potentially look at buying our own one, so it just makes sense to be somewhere else."
Starting a family in Auckland 'completely unachievable'
His colleague Jenny Bates, 28, is also leaving the city of sails in pursuit of a home where she could start a family, which she said was "completely unachievable" in Auckland.
"If we were going to go down to one income the kind of mortgage we'd have here would just not be possible."
Physics teacher Bates admitted that her and engineer husband David, 30, have a combined income that is "pretty good", but said it still couldn't compete with Auckland's overpriced housing market.
House prices were "ridiculous", she said, and anywhere in reach would either be a long commute to central Auckland, or take every cent they earned.
"It would leave us in a situation where we couldn't do anything else with our money, it would all be tied up in the home."
The couple are relocating to Hamilton, where there's a demand for engineers, and Bates has lined up a job at St Peter's, Cambridge.
She believes there's an argument for an Auckland accommodation supplement - like London - and a pay increase for teachers.
For Drumm, the answer "is quite simple".
"It's about pumping up the top of the [pay] scale significantly," he said.
Schools poaching young STEM graduates for in-demand teaching jobs
School principals are scouting teaching colleges to poach in-demand science and maths teachers before they graduate.
With only two physics graduates leaving the University of Otago College of Education at the end of the year, schools are already approaching them for jobs.
Drumm said he had recently visited the college scoping out soon-to-be graduate teachers to replace the three science teachers who are quitting because of Auckland's overheated housing market.
"We're happy with getting a physicist, but I do know that people are quite envious of us, getting her," he said.
"There's a lot of principals down there looking for physics, science teachers, maths teachers."
Schools were in desperate need of science, technology, engineering and maths teachers, he said, and had got to the point where they were now "robbing each other of teachers".
It was a "significant Auckland issue", he said.
"We've got a perfect storm brewing of this high growth, high student numbers, immigration ... and a diminishing pool of quality applicants.
"If you have any physics of any sort ... you'd be able to waltz through the doors of a training institution, regardless of how good a teacher you were, there's such a desperation for those STEM subjects."