I've been teaching knitting off and on for about twenty years. Over that time I've changed my techniques as I learned more about the best approaches. In my previous career I often taught software applications to others and I generally would show one method to accomplish a goal even when it was possible to demonstrate a method from the menu bar, a method using an icon as well as a keyboard shortcut. In small groups I would take a poll as to what methods the users preferred and then teach to that preference set.
I often adjust my teaching for the audience when I teach knitters. New knitters don't have the same established set of muscle memory that long time knitters have. I am much more likely to show only one method to them. Frequently they can't see the difference between two ways of reaching the same goal that they will later in their knitting lives. I've heard the same thing about experienced dancers in that they can quickly reproduce complex movements in a long sequence with a single demonstration.
Lately I've had a lot of highly skilled knitters in my classes and I teach differently to that group. I find that due to variations between knitting styles that often one version of a technique will speak to a specific knitter much more than another technique that accomplishes the same final goal. When I first started teaching I always loved the reaction when a student had a light bulb moment during a class. I was thrilled when it happened because I knew I'd really moved their skills forward and what teacher doesn't want confirmation that we are offering the student real value? More recently I've noticed that many very knowledgeable knitters will sample the two or three possible techniques I give them. When they find the right one for them that for some reason speaks to them I hear an audible... aah! How cool is that?