PHJim uses the notation that is easiest to make sense out of. It drives me crazy when someone says "First string, fifth finger, fourth fret" or some such thing. It is less confusing if you refer to the strings by their pitch, the frets by their number, and the fingers by their names. Also, be real clear about what you mean when you say "Higher" and "Lower".

Mind you, I am not blaming any of you. The instrument was like that when we got here.