"Miss Gladstone" is probably a warrant officer. Warrant officers are specialists who progress through 4 to 5 grades, all of which rank "with but below" an ensign. In today's military services, a warrant officer is a specialist who spends an entire career in a single specialty, but has full command authority does as any other officer. Warrant officers are addressed as "Mister/Miss/Ms." and are saluted by enlisted personnel. Because Ms. Gladstone presumably posesses an exceptional educational qualification for such an important billet, while performing a function that could be considered auxiliary to running the ship (i.e., she is a schoolteacher, not an astronaut), it makes sense that she would be recognized with a service warrant (and possibly an officer's commission as today's warrants from CW2 - CW5 receive). Given the respect that LCDR Troi shows toward Miss Gladstone and her particular form of address (CPOs are addressed as "Chief" not as "Miss") it is likely that she serves at warrant officer grade, as do today's Naval physician assistants and Army helicopter pilots. The Coast Guard, as the smallest American service, makes exceptional use of warrant officers when a billet requires a commission but the job is beyond the capability of a young ensign or lieutanant.
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