Tomson, Pieter J. "Chapter Seven: The Halakhic Evidence of Didache 8 and Matthew 6 and the Didache Community's Relationship to Judaism." in Van de Sandt, Huub (editor). Matthew and the Didache: Two Documents from the Same Jewish-Christian Milieu? Minneapolis: Fortress Press, 2005, 131-141.
Tomson evaluates the Didache and Matthew in regards not to doctrinal considerations as such but rather from the perspective of Halakha, roughly akin to civil, moral laws (Tomson 2005, 131). The basis of his exploration is the fact that it was cultural rules, rather than doctrinal stands, which routinely distinguished groups.
The Didache is normally accepted as having extensive roots in Jewish thought (Tomson 2005, 132). Studies of the Halakha have been engaged in over the years, though it has not been a very crowded field of expertise. Tomson observes that halakha has strong practical and social applications (Tomson 2005, 133). Observance of these social customs defines one as a character in the community. It is also something which may change over time and space. We would expect some distinctive features in Jewish Christian communities which may serve to identify the community more clearly. It is important, in Tomson's opinion, that the Didache and Matthew have some halakhic elements in common (Tomson 2005, 134).
Didache 8:1 gives an instruction about the days appointed for fasting. While Monday and Thursday can be identified as the typical fast days for Pharisees, it calls for a fast on Wednesday and Friday (Tomson 2005, 134). Monday and Thursday were typical market days, when there would also be prayers and public Torah readings. Engaging in a fast on such a day makes sense. Tomson identifies a 364 day solar calendar which had all the festivals on Wednesday, Friday, and Sunday as a probable reason. The Pharisees avoided special observances on those days, but the earliest Christians may have placed their fasts on those particular days due to the message that fasting made about commitment to God (Tomson 2005, 136). The calendar of festivals which was adopted by the Pharisees was rejected by the Sadducees and the Christians.
Didache 8:2-3 instructs the community in prayer. The text of the prayer given is almost identifcal to the words in Matthew 6:9-13 (Tomson 2005, 137). The custom is stated clearly, that we pray three times in the day. Tomson notes this daily calendar was considered normal, and included three daily times of prayer (Tomson 2005, 138). What to pray was a matter of debate, but when to pray was not. The prayer we recognize as the Lord's Prayer fit the structure of several other ancient prayers which were used (Tomson 2005, 139). Because the prayer in Didache 8 is so similar to that in Matthew, Tomson takes there to be a high level of agreement in the type of social teaching used (Tomson 2005, 140). The Christian practice draws away from that of the Jews at this point.