OK, I'm going to get a lot of flack for this,but both movements are an interegal part of PMTS's Direct Parallel beginner methodology. The steps are taught with landing the inside ski on it's little toe edge (LTE). I this is done on very little slope, as to not frighten the student. Once the student gets comfortable doing left and right stepping turns, it is time for more of a challenge, ie, first lift ride. Up to a fairly flat green run. Then it is time to do the first traverse. Three steps up and three steps down untill it is time to turn. At this point, the bullfighter turn is introduced. Once the turn is accomplished, we go back and forth untill the student is very proficient and step turns. The key here is to stay out of the falline.
At this point, the shuffle is introduced. The key to the shuffle is to keep in inside ski on it's LTE. It does not take many turns and the student begins to glide through the turn, both skis parallel. On an average, I have taken never-evers from stepping turns through gliding shuffles in 2-2 1/2 hour lessons. At the end of the day, most are doing a rough parallel.
The crux of this is step turns and shuffle turn helps a student to learn about their edges and balance. Done in the sequence I described, can help the student achieve parallel in a short period of time.