"It's important not to underestimate Covid-19 transmission in schools," Kvalsvig said.
Concerns have also been raised about the lack of data relating to Covid cases in schools, with one expert saying it's difficult to get an accurate picture of the impact.
University of Otago public health researcher Dr Julie Bennett said without contact tracing within schools, it was likely that children who had unknowingly come into contact with a person who tested positive were attending school without knowing they were infectious.
"In schools that haven't reported many cases, the use of RAT tests may help to delay the spread. However, given how much infection is occurring in schools, it's hard to say what impact they may have at this stage," Bennett said.
She said until more was known about the long-term effects of Covid-19 infection in children, we should try to minimise the spread.
"Online learning in schools and children working from home should be supported."
Meanwhile, some schools have resorted to collecting their own data.
Henderson Intermediate shut down two weeks ago after cases were shooting up. While they were home, she tasked her teachers with analysing all the Covid cases in their classes and found there were 105 among the school's 720 students. Of those, 53 were clustered in groups of close friends.
Principal Wendy Esera it was hard to know for certain whether some of them could have caught it from one another outside of school - but there were instances where children with no positive household members, who had been nowhere but school, had brought it home.
Some staff had also "absolutely" caught Covid from their students.
"Children are very social creatures ... it's the sheer nature of children. Children touch one another. Children hug each other, children sit close and lean up against each other and, when they're outside, they rough and tumble with each other."
The school had been doing all the things right, such as staggering break times and getting all kids wearing masks, but it was impossible to stop the spread.
University of Waikato researcher and public health physician for child health at Waikato District Health Board, Polly Atatoa Carr, said while the rapid rise in cases in children was not particularly surprising, the burden faced by families and schools is real, and is not felt equally.
"Schools are not equally resourced. Families are not equally resourced, nor are all families equally able to cope with the challenges of home isolation. Those who need more support are more likely to be attending schools and learning centres that are also less resourced."
She said policies such as job protection, extended paid sick leave, wage subsidies and hardship grants were crucial to supporting vulnerable parents, families and communities.