Interesting things happen when you confine your study of “teaching” (διδάσκω) to Matthew. Jesus has a three-fold ministry of preaching, teaching and healing. He involves the 12 in preaching and healing in Matthew 10, when he sends them out two by two. But only Jesus teaches in the first gospel. Matthew 28:20 is the first time (in the first gospel) where the disciples are included in teaching. Even then what they teach is restricted to teach the disciples they make to obey all of Jesus’ commands.
My study of Matthew leads me to the conviction that Jesus is the only teacher for disciples. As sent out disciple makers we are to point others to Jesus. What we teach them is to obey Jesus’ teaching. It is Jesus who defines what disciple making looks like by the way he makes disciples. His disciples are contrasted with those of John the Baptist and the disciples of the religious leaders. The disciples at the heart of the first gospel are people who have responded to Jesus’ call to follow. It is at its basic core a submissive relationship with the Son of God. Jesus provides the content for all his disciples.
You don’t get this nuanced perspective from the other biblical authors, but only Matthew uses that phrase “make disciples.” We need to be sure we use that phrase in ways consistent with what he reveals about what that entails. Don’t begin by going to Luke-Acts, Mark or John.
I originally posted most of the preceding comments in a discussion area considering the question, “How are we to define the word ‘teaching’ in the Great Commission?” The query sparked much dialogue. My desire was to answer the question by looking to the context where the word “teach” appears. The immediate context of the last four verses is significant, but it is inadequate to know how the term is used by the first evangelist. You only get that from what Jesus has already said and revealed through his actions about the nature of disciple making
From the Desk of John King 
John, this is fascinating. I have come to many of the same conclusions but from a different perspective. I especially like the way you traced the word “teaching” through Matthew’s gospel. I had never seen before that Jesus was the only one to teach in that book. Is the same true in the other gospels? Excellent thoughts!
Felicity, I have not spent as much tracing out these matters in the other gospels, yet. Each of the four has its unique ways of shining the “center-stage light” on Jesus. I believe the Holy Spirit used the diverse personalities and intended audiences of Matthew, Mark, Luke, John, Peter, Paul, James, Jude and the author of Hebrews to give us a manifold presentation of what gospeling looks like.
Paul’s use of “teaching” is certainly not nuanced in the same ways as Matthew’s. They never contradict each other in the use of this term, but they get the message of Jesus’ supreme authority across by different means. I grow more confident that the exclusive presence of the term “disciple(s)” in the narrative sections points to the powerful issue of characters in any story. “Jesus’s disciples” is a short-hand way of referring to people in transforming relationship with this teacher. At times individuals in this group step out, but often they are described collectively. Their words, actions and experiences are compared and contrasted to other groups (e.g., the disciples of John, the crowds, the religious leaders).
What an awesome God we serve. The story of his Son is too significant to confine it to one telling. The diversity of the people groups he has created are too vast and their need to know this Person too significant to not pull out all the stops and use multiple genres, personalities and arrangements! This dovetails well with your recent insights on the calling of leadership to equip the body to do ministry. What God calls us to do will demand everyone prepared and walking out their function.
You’ve helped me (on several occasions) see the emphasis on “obedienced based” disciple making in Matthew 28:18-20, John. I always try to stress the same in teaching others.
Thanks, Mike. Just passing on what others have passed on to me. Thankfully I have been allowed, encouraged and expected to do my own digging into these matters, also. Such discovery approaches have brought me to explore these matters further. Blogging gives me an avenue for engaging others in the process.