It was a great question as I don’t think it is understood enough how much this varies from teacher to teacher. I’ve had 7 teachers in my career now, and each one had a different approach it seemed like when it comes to speed of progression through music. I had one teacher that I would be on the same piece it seemed like for months–by the time she was ready to move on to the next song, the music had so many fingerings and marks you could barely read the music. On the other hand, I’ve had some teachers that wanted to move on very quickly, not writing much in the music at all (suggestions/fingerings).
I really think it is a balance that is hard to manage. I think having the student tell the teacher that they want it a certain way helps. Otherwise the teacher can interpret things you say and do for going too fast or too slow. Tell them you have an expectation and don’t be afraid to veto them if you feel they are one one extreme or the other.