What's the most important thing that a student can learn?

I believe that the most important issue involves how to HEAR so that "right" can be discriminated from "wrong".

I learned about this from Mike Cusak. Mike has the "fastest" ears of anyone I've ever met. He knows just what was done right or wrong in each embellishment or note change first time through without even looking. I had a two week summer course with Mike in 1994.  Whenever I'd make a mistake, he could guide me to correct it. He taught me to listen to my own playing and diagnose my own playing. In that two weeks, he taught me how to improve my piping for the rest of my life. If we could all learn this skill, we'd all be better at diagnosing our own playing.

An approach to teaching this skill is to require the student to record their practice and spend time diagnosing it. Some tape recorders will play back at half speed to catch problems. Many computer programs can do the same.

An important point is that no student (no player) ever is "done" improving the accuracy and understanding of basic skills. I've had students who've attempted to literally "cross off" each embellishment or claim to have "eliminated" crossing noises from their playing. A good student of piping will continue to HEAR what they do and to seek improvements.