Rabbis would, of course, also occasionally address the public, whether on the street, in the market or synagogue. But it is unlikely that they did so by using the literary forms which are transmitted in the written documents. Neither the brief exegetical comment nor the longer midrashic proem are imaginable as actual sermons delivered in synagogues. Even the parables usually presuppose a certain amount of Biblical knowledge which the ordinary person is unlikely to have possessed. They may have served rabbis to clarify certain aspects of biblical verses during the oral instruction of their student rather than providing moral and theological instruction to the populace. Apophthegmata or pronouncement stories memorialized rabbis’ wit and wisdom. Again, later generations of students would have been most interested in transmitting and preserving such stories about their teachers to make these teachers immortal and to maintain the reputation of their “schools”.
Catherine Hezser, “Form-Criticism of Rabbinic Literature”, in The New Testament and Rabbinic Literature, eds. Reimund Bieringer, Florentino García Martinez, Didier Pollefeyt and Peter J. Tomson (Leiden & Boston: Brill, 2010), 108.