When I studied Hebrew in graduate school, part of my work included translations from English into Hebrew, and after shorter sentences, I moved on and did parts from Weingreen’s Classical Hebrew Composition, a book rare at the time but which may have been reprinted since then. (See mention of this book, and some remarks related to the theme of this post, particularly in terms of Hebrew, here.) Composition into a language one is learning, even an ancient one, used to be very much the norm, so much so that you would be hard-pressed to find a 19th-century learning grammar (as opposed to a reference grammar) that does not include some composition exercises. I confess that I am not well-read on research (the latest or otherwise) for second-language acquisition and its pedagogical concerns, but speaking merely from personal experience, assuming there are adequate resources for it and a way to check it (preferably by another human being who knows the language better), second language composition is an excellent learning practice, not to mention possibly fun, depending on the material to be translated. Optimally, there should be a “known language” to “language being learned” glossary, with idioms, and a key, and the sentences to be translated ought to be based closely on passages that have been read. Good stand-alone dictionaries will of course also have idioms included.
Exercises for compositions and translations into Greek and Latin abound in classical textbooks, especially older ones. For work like this, a kind of practical vocabulary, one that is often not derivable from dull vocabulary lists at the end of language lessons in grammars, is necessary. Ancient, late antique, and medieval commentaries—there are immediate examples for Greek, Latin, Syriac, Arabic, Armenian, etc.—can be very helpful here, as can even later texts when they are written in an ancient language, as the compilers of the Delphin editions, a number of which, but far fewer than the entirety, are available online, recognized. A similar method was put to good use more recently in Waldo Sweet’s reader of Vergil’s Aeneid, Books I and II, which has the text, a facing Latin prose paraphrase, and commentary on certain passages from Servius and other commentators. Eleanor Dickey has made some material like this in Greek more approachable in her Ancient Greek Scholarship (Oxford, 2007).
Some classicists will also know of the method pushed by W.H.D. Rouse (see especially his Scenes from Sixth Form Life and A Greek Boy at Home, as well as The Teaching of Greek at the Perse School) and latterly the similar work of Hans Ørberg for Latin and the Italian adaptation of Athenaze by L. Miraglia for Greek. These all stress real direct use of the language and reading and composing without translation as an intermediary crutch. For one of the volumes (Sermones Romani ad usum discipulorum) in the Lingua Latina per se illustrata series, Ørberg used to good effect the Latin part of some colloquia (the original also has Greek) published with the Hermeneumata Pseudodositheana (ed. G. Goetz, Leipzig, 1892).
A plethora of English to Greek or Latin exercises exist in (especially older) grammars, and there are many slim volumes for both languages specifically dedicated to composition. Taking a cue from Cicero’s De oratore, Roger Ascham in the 16th century was a strong advocate of double translation in learning Greek and Latin: the student would learn a Greek or Latin passage, translate it into English and then, after a period of time, put away the copy in the original language and translate from his or her English translation back into the original language and finally compare it with the original text. (I can’t at present locate my copy of The Scholemaster, where he discusses this method, or I would cite some lines from it. Those interested may find the work online here and probably elsewhere.) The Gaisford Prize, long a venue for Greek composition at Oxford, is also worth mentioning. Some of these are new compositions (mostly prose), others translations from English literature into Greek (mostly verse). Unfortunately, only a few of these interesting specimens have been published. In prose, the most notable piece is on a trip to the zoo in Herodotus’ Ionic Greek style. As an example of verse, some lines from Henry IV, Part 2 (Act 1, sc. ii, ll. 173-181) were rendered into Greek by George Nutt in 1866. Shakespeare’s words read (Lord Chief Justice to Falstaff):
Do you set your name in the scroll of youth, that are written down old with all the characters of age? Have you not a moist eye? a dry hand? a yellow cheek? a white beard? a decreasing leg? an increasing belly? Is not your voice broken? your wind short? your chin double? your wit single? and every part about you blasted with antiquity? and will you yet call yourself young? Fie, fie, fie, Sir John!
The Hellenic version is:
ἆρ᾽ ἐγγράφεις σὺ τοὔνομ᾽ εἰς νεανίας,
ὅστις γέγραψαι πάντ᾽ ἔχων τεκμηρία
γήρως γέρων ὢν ἐμφανῶς; ἆρ᾽ οὐχί σοι
λημῶσιν ὀφθαλμοὶ μὲν αὔη δ᾽ ἐστὶ χείρ;
ὠχρὸς παρειὰν καὶ πολιὸς γενειάδ᾽ εἶ·
γαστὴρ μὲν οἰδεῖ, τὰ σκέλη δ᾽ ἰσχναίνεται·
φωνὴ παρέρρωγέν θ᾽ ὑπ᾽ ἄσθματός τ᾽ ἀεὶ
πονεῖς· διπλοῦν γένειον ἀλλ᾽ ἁπλοῦς ὁ νοῦς.
οὐκ εἶ σὺ γὴρᾳ πᾶς παρεξηυλημένος;
κἄπειτα ληρεῖς σαυτὸν ὀνομάζων νέον;
A recent example of Greek composition is the brief paragraphs on current events in classical Greek at a site I have from time to time in leisure moments enjoyed for some years.
While Greek and Latin are the languages for which (for speakers of European languages, at least) the most tools in this regard are available, they are not the only languages that have been and can be learned this way. For example, for Sanskrit, E.D. Perry’s Sanskrit Primer (4t ed., New York, 1936) contains exercises, and an English-Sanskrit glossary (but no key). Huehnergard’s Grammar of Akkadian has (generally short) sentences to be made into Akkadian from English; there is an English-Akkadian glossary, and a key is available as a separate volume. I was very surprised to read recently in Budge’s autobiographical remarks in his By Nile and Tigris (London, 1920; vol. 1, p. 60) that at Cambridge, where he read Syriac texts with William Wright and Robert Bensly, with the latter he translated part of The Pilgrim’s Progress into Syriac! In his words, “During the years I read with him, I turned, with his help, the greater part of ‘The Pilgrim’s Progress’ into Syriac, as an exercise in composition.” It is possible that this translation is somewhere among Budge’s papers, but I don’t know where these are located. This was apparently not the only English-Syriac composition Budge did at Cambridge, but this is the only specific project named under this head. When he sat down with Wright at the beginning of his studies with him, Wright
at once sketched out a plan of work, and terrified me with the list of books which he expected me to read. Certain set books in Syriac and Arabic he would read with me himself; Syriac works which were translated from Greek were to be read with Mr. R. L. Bensly, who would help me in translating English into Syriac; and the Hebrew and Chaldee books were to be read with the Rev. W. H. Lowe, who would direct me in Hebrew composition. (pp. 55-56)
Learning a language this way, where possible, is not only effective in improving one’s knowledge of it, it’s also quite fun, as mentioned above, and as, for example, the people at Eisenbrauns know, when they have their annual Valentine’s Day contest for putting together amorous compositions in ancient languages (see the 2011 results here). Well-known songs might also be good practice; I’ve long thought “Hard Rain’s a-Gonna Fall” and almost anything from Dark Side of the Moon would be suitable.
Related to all of this, too, is the place of memorization (of lines and texts, not paradigms and individual isolated lexemes) in language learning. Hopefully, there’ll be opportunity for a post on that in the future. Until then, I would be glad to hear of others’ experiences, both good and bad, translating into and composing in ancient languages.
 These lines are also quoted in the introduction of the new publication of some of Wright’s letters. See my review here.