I shared some thoughts the other day On the Pedagogical Advantages of the Q Hypothesis, suggesting that it can act as an appealing and tangible symbol of participation in academic study of the New Testament. There is no Q in the Bible, but there is a Q in the scholar's canon, and it quickly and effectively makes the point that Higher Education is not about Bible Study.
I have also noticed other pedagogical advantages in teaching Q. The architecture of the Two-Source Theory has an elegance, a simplicity that lends itself very nicely to teaching introductory students. The genius of the theory is that it is able to assign a document to each major type of tradition. People find it difficult to grasp the complexity of the Synoptic data, but refracting the data through the theory can be helpful and clear.
If one is looking to simplify the data, there are broadly two key types of material in the Synoptics, triple tradition and double tradition. The Two-Source Theory enables the teacher to link a documentary source with each of those basic data sets. Triple Tradition is essentially Mark's Gospel -- Matthew and Luke are copying Mark. Double Tradition is Q -- Matthew and Luke are copying Q.
The same essential elegance is taken a step further in Streeter's classic Four-Source Theory, according to which one adds in Special Matthew and Special Luke and assigns a document to each, M and L, so that we end up with four types of material -- triple, double, Special Mt and Special Lk -- and four documents -- Mark, Q, M and L.
In fact, the model is so elegant and straightforward that I enjoy teaching it myself, and explaining how the Two-Source Theory nicely maps onto the data that it is isolating and describing.
The difficulty with the model is, sadly, that the data is not quite as simple as the model requires. Triple tradition is contaminated throughout with material that should not be there, with major and minor agreements between Matthew and Luke against Mark. Double Tradition is not its own unique data set but often flows into Triple Tradition, requiring the postulation of Mark-Q overlaps in order to make sense of the evidence.
Luckily, at an introductory level, one does not need to introduce the complications like the Minor and Major Agreements, and the discussion can remain on the kind of general level that keeps the model functional. The genius of the Two-Source Theory is that it works so well on a general level. It's only those who linger for a little longer who find out that the devil is in the detail.