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It has asked the Ministry of Education to close the 97-year-old school. A ministry spokesman said a report would be developed for a final decision to be made by the Minister for Education, Hekia Parata.
"This was not an easy decision to make, as it means not only the school closing but a loss for the community. Paerau School is the hub and heart of our rural isolated community," Mrs Elworthy said.
The school in the Styx Valley catered for children from 11 farms. The nearest school, once Paerau has closed, will be about 60km away.
"The nearest school bus stop is about 25km, one way, on roads often impassable to a good 4WD on many winter days," she said.
"Our school roll has always fluctuated but, as the school is such an important part of rural life, the community have always been 100% behind it. Voluntarily closing Paerau School leaves huge implications for our community," she said.
The school opened this year with four children on the roll, all members of one family, and that family had now shifted from the district.
There were six pre-schoolers in the area, ranging in age from a newborn to two 4-year-olds, who were due to start school next year. The preschoolers included the Elworthy's 4-year-old daughter and 18-month-old son.
"So now we have to look at where the decision leaves parents. On talking to the ministry, there are little options available.
"Along with many other rurally-based communities and families we will have some hard decisions to make.
"Do we make our children spend hours every day travelling, to gain the school experience, or teach them at home, with all the drawbacks associated with that?
Mrs Elworthy, who is a teacher, has been the board chairwoman for four years.
Three generations of Paul O'Malley's family have attended the school. His late father, Peter, received all his primary schooling at Paerau, as did Mr O'Malley and his five sisters, and Mr O'Malley's two sons.
During his time as a pupil, the roll reached 42.
All received an excellent education and they also learned socialising skills, because they mixed with such a wide age group, he said. There were far more advantages to attending a small school than disadvantages.
"This is going to be a huge loss to the district. It's a bugger, really, and it'll have a big impact. The school is all we've got. There's always been a school here. There's no easy solution but we're hoping we can at least retain the building as there's no other community building. "
Mr O'Malley farms in the district and said the absence of a school would make it harder for farmers to recruit staff.
He served 10 years as board chairman and has now been co-opted back on to the board.
The board and community had offered free rent for a year to attract families to the area.
Former education minister Anne Tolley announced seven months ago the school would stay open, but its future would be reviewed in 2013.