She met with local authorities and teaching unions on Monday after concerns were raised that the Foundation Phase, which would need one teacher for every eight pupils, is underfunded.
"One of the principal concerns that men considering teaching feel is the worry that they will fall foul of rules which make normal contact between adults and children a legal minefield, " he said.
The image was posted on 18 April, four days after staff at the school called for Dr Luckcock's resignation in an eight-page collective grievance document which included concerns about the axing of eight teaching assistant posts.
As in other nations, there is a growing recognition in the United States that issues of access cannot be separated from concerns about the quality of the teaching and learning to which students are gaining access.