> Although the term scolae grammaticales was not widely used until the 14th century, the earliest such schools appeared from the sixth century, e.g. the King's School, Canterbury (founded 597) and the King's School, Rochester (604). The schools were attached to cathedrals and monasteries, teaching Latin – the language of the church – to future priests and monks. Other subjects required for religious work were occasionally added, including music and verse (for liturgy), astronomy and mathematics (for the church calendar) and law (for administration).
I am not knowledgeable enough about the topic to say how efficient or helpful medieval Latin schools were at teaching Latin as a second language, but the idea of “grammar” as part of the “trivium” (alongside logic and rhetoric) meant something substantially different than the modern usage of the word.
Maybe we need to bring back grammar school.