I was thinking that it might have been token ring, but they appear not to have ever used that type of connector. It does look like a mini 10-BaseT connector, but that seems really improbable for a school application, as those were very limitted.

One other option comes to mind, especially since there doesn't appear to be a central post in that picture: Fiber optic connectors. That would be contemporary with Ethernet cabling, would be in keeping with the location, and they roughly match pictures of the connectors that I have seen online. Furthermore, that would fit with the fact that they look like BNC, but are somewhat smaller.