In Wheelock ch. 6 LATINA EST GAUDIUM ET UTILIS, he says that "lingua latina" = latin langauge.
So, would a "teacher of latin (language)" be translated as: "Magister linguae Latinae"?
The reasoning being:
Magister in the nom. sg.
linguae in the gen. sg., since it is "of language Latin" I'm trying to say
Latinae, adj. which agrees with linguae