- Edited
Taushi Teach a student basic fundamental theory - scales, note values, keys, keyboard layout, time signatures
Teach a student to read sheet music
Plus listening exercises, and listening to pitch sequences and translating it to keyboard exercises (developing hearing and music memory), and also intervals/hearing training, and some pedal exercises, and finger sequencing problem-solving exercises, and chord work (how it 'fits' with melodies, and how to select/detect/determine workable chords). With some composition theory to come at some stage later as well.
As for the original post at the start of this thread ... regarding the person hypothetically wanting to have piano lessons purely for some other genre ..... eg. pop etc. People most likely assume that lessons will all involve beginning studies and playing of 'classical music'. And that probably is the norm ..... traditional.
So the person just needs to communicate with teachers, which might involve the teacher customising the course to suit. Or the teacher may know other teachers that suits the request, or meets the request nicely etc.
And of course ... if they can't find anybody ... then use online tutorials until there is (if any) a time where a workable solution is gained.