Please note that Mommsen uses the AUC chronology (Ab Urbe Condita), i.e. from the founding of the City of Rome. You can use this reference table to have the B.C. dates
From: The History of Rome, by Theodor Mommsen
Translated with the sanction of the author by William Purdie Dickson
In consequence of this progress of jurisprudence and grammar, elementary school-instruction also, which in itself had doubtless already emerged earlier, must have undergone a certain improvement. As Homer was the oldest Greek, and the Twelve Tables was the oldest Roman, book, each became in its own land the essential basis of instruction; and the learning by heart the juristico-political catechism was a chief part of Roman juvenile training.
Alongside of the Latin "writing-masters" (-litteratores-) there were of course, from the time when an acquaintance with Greek was indispensable for every statesman and merchant, also Greek "language-masters" (-grammatici-)(27)--partly tutor-slaves, partly private teachers, who at their own dwelling or that of their pupil gave instructions in the reading and speaking of Greek.
27. -Litterator- and -grammaticus- are related nearly as elementary teacher and teacher of languages with us; the latter designation belonged by earlier usage only to the teacher of Greek, not to a teacher of the mother-tongue. -Litteratus- is more recent, and denotes not a schoolmaster but a man of culture.
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Reference address : https://www.ellopos.net/elpenor/rome/2-09-art-science.asp?pg=31