Although I might live to regret mentioning this in case any potential employers find the blog, there is an area of music theory in which I have not had much teaching experience.
I haven’t taught aural skills/musicianship in a while, and I’m rusty.
What is the pedagogical purpose of musicianship/aural skills? We require aural skills because – and this is not meant to be sarcastic or obvious – it makes a musician better. The ability to sing a melody at sight will improve performance accuracy. The ability to internally hear intervals, chords and progressions will improve analysis, which in turn will lead to a performance that is a better reflection of the composer’s intent.* A musician needs to hear a piece internally before he or she plays/sings it.
What is the proper balance of theory/analysis and aural skills? Whoever unties that particular Gordian knot is going to be the King/Queen of All Theory Pedagogues. Even though I don’t officially teach the Aural Skills classes at my current institution, I do incorporate hearing and singing intervals/chords/bass lines into my theory classes as well as a small keyboard component. Music is, after all, an aural art.
Fellow theory teachers – what sorts of materials and techniques do you use in your aural skills classrooms?
*Ah, yes, “composer’s intent.” That old canard.
WF
Wes Flinn Music 
I always told my students that aural skills is the single most important class that they’ll ever take (despite its lowly 1-credit status). I’m playing a gig today for which I got the music a week ago: Dvorak Czech Suite, Rachmaninoff Paganini Rhapsody, and Tchaik symph. 1. The Dvorak and Tchaik I’ve never played before. I learned the parts mostly on the bus (!) commuting to and from work, thanks to aural skills. Listening around me in rehearsal helps quite a lot in that regard, too.
Having said that, you know my thoughts on the aural skills business–witness my “Listening” blog (which hasn’t been updated in some time…)