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In an article on the University of Otago's Public Health Expert blog, they say the government should take more precautions against the virus during winter.
The group, which includes Amanda Kvalsvig and Michael Baker from the University of Otago, said actions should include requiring the use of masks indoors and ensuring classrooms are well-ventilated.
They also want a push for high vaccination rates among teachers and students, isolation for all close contacts of positive cases, and a commitment to closing schools if case numbers reach a particular threshold.
The group says the United Kingdom's experience shows trying to keep schools open leads to high numbers of cases and absenteeism.
The Primary School Teachers' Union says teachers would need more sick leave to complete proposed Covid-19 isolation requirements.
Union president Liam Rutherford says already teachers are struggling to take the mandated time off for household contacts.
"What we're starting to hear regularly from the education sector, both in schools and early childhood centres, are some of the inadequacies of sick leave provision. We're only a quarter of the way through the year and we've got people already use their sick leave."
Rutherford says the union would ideally like to see special pandemic sick leave introduced for the next 12 to 18 months.
He also said the proposed school covid-19 action plan should be applied more widely then schools. "It doesn't make sense that we've got these restrictive supports going into just schools alone.
"This is something that we need to see echoed across the entire country."
Secondary Principals' Association head Vaughan Couillaut said schools were struggling to cope with high numbers of staff away.
"When the grown-ups go down, then they have to stay at home and care for their own children or isolate or whatever it may be, well replacing them is proving very problematic because the relief pool is very shallow. We do have quite a shortage, particularly in the secondary sector," he said.
Couillaut said at his school on Friday, 20 staff were away due to illness and they were considering putting some classes online again to cope.
He said there were other schools around the country also using a hybrid learning model.
Meanwhile, the Post Primary Teachers' Association (PPTA) said it is worried about teachers suffering burn-out and post-virus illness.
President Melanie Webber said it was difficult for teachers to return to work slowly after infection, particularly if they don't have much sick leave.
"I'm really concerned that teachers trying to do everything they can for their students are going to burn themselves out and it's going to have huge implications down the track."
She is calling for clear advice about how to manage Long Covid in the workforce.
Webber said a shortage of teachers had exacerbated the problem.