Scholarly Reflections
Garrow, Alan J.P. "Chapter Nine: The Full Extend of the Peri Layer." The Gospel of Matthew's Dependence on the Didache. New York: T&T Clark International, 2004, 142-149.
Garrow previously (ch. 5) considered what he refers to as the peri layer of redaction. In this chapter he considers whether this layer would include Didache 1.3-5a. Here, he finds statements which he considers to be "Q" material, and numerous similarities to both Matthew and Luke (Garrow 2004, 142). However, because he sees 1.5b-6 as characteristic of the modifying teacher, a source he considers to predate the written Gospels, he also sees 1.3-ba to predate the work of the modifying teacher. The text does provide a reason for the beharioral demand, καὶ ἔσῃ τέλειος, which suggests the modifying teacher (Garrow 2004, 143).
The title also suggests to Garrow that there was redactional activity in play. Garrow suggests rather than the short title appearing originally on the outside of a scroll and the longer one as the first line, the title may have been a later addition provided for the convenience of the reader (Garrow 2004, 144). In this scenario the shorter title would be an abbreviation for further convenience. The specification "to the Gentiles" suggests to Garrow the peri layer, since here he finds limitations of the applicability of the text (Garrow 2004, 146). Garrow sees this as the earliest layer of compilation which made the Didache a clearly defined text, so he considers it appropriate to treat the title as a part of that material.
Finally, because Garrow has previously identified 16.1-2 with the peri layer, he makes the additional step here of treating 16.1-6, 8-9 as a part of the layer, as it treats the members of the community as a particular, identifiable unit, in a similar way to the other statements of the peri layer which make some limitations on the scope and participation of Christians (Garrow 2004, 148).