I figured it was a mode of G because it is the second scale form of G major. But it's interesting how my teacher is teaching me the modes. Because simply playing the A major scale starting on B and playing all the same notes of A major does not get you Dorian. There would still be 3 sharps in that case. As you said, A Dorian has 1 Sharp. Hence position 2 of the A major scale played starting on the 5th fret and not the 7th, Kinda makes sense to me.. As you can tell, I am a positional player.. forms and patterns for this feeble mind.. but it works for me. Any of this make any sense ?