But Youthtown chief executive Paula Kearns, who runs after-school programmes in 12 locations around the country, said even the usual after-school programmes would be cancelled at 10 locations because parents had made other arrangements.
"We have only seen an increase in demand in Christchurch. We are running a full-day programme [at two locations] in Christchurch," she said.
"Other than that, we are closing our after-school programmes in the rest of the country on the day of the strike. We haven't had the demand. If the children were there, we would open.
"So I guess parents have had family members or other arrangements that they can fall back on."
MacGregor-Reid said all NZEI members would have their pay docked for a day regardless of whether they worked or not.
"Union members who do not strike will be deemed to have taken strike action and not be paid unless boards confirm that they are absent for reasons such as sickness or bereavement leave," she said.
South Auckland principals Sonia Johnston (Roscommon School) and Karen McMurray (Randwick Park School) said groups running after-school care at their schools had also closed their programmes on Wednesday to support the teachers.
"They want to support the teacher action as well because they know how problematic it's been," Johnston said.
Waikato Principals Association president Hamish Fenemor said he did not know of any schools planning to open. His school, Cambridge East, decided against opening for supervision only for health and safety reasons.
"We have 95 per cent of our staff who are union members, therefore we would have only support staff and learning assistants available to provide an alternative programme, so just due to health and safety we can't put that pressure on our support staff," he said.
Te Tai Tokerau (Northland) principals president Pat Newman and Matt Simeon of the Western Bay of Plenty Principals' Association said they did not know of any schools planning to open for supervision.
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Red Beach School principal Julie Hepburn said her school would be open for supervision using 10 teachers who are not NZEI members, but a survey of parents found that fewer than 40 of the school's 590 students would actually turn up for the day.
"By offering to be open for supervision and having many parents saying they will keep their children home, there is quite a clear message that they support the profession," she said.
"It's pretty humbling actually to get that kind of response from parents."
Dr Cathy Dewes of Te Kura Kaupapa Māori o Ruamata in Rotorua said her kura would open for teaching as usual because most of her teachers did not belong to the NZEI.
"There may be one or two who belong but the majority do not because mainstream schools look after mainstream Western pedagogy, Western policies, Western processes, so there is no benefit for us to be derived from aligning with the mainstream," she said.
"We do support the protest action, and I think there are benefits to be derived for us as well, but that struggle is not a priority for us."