My daughter has got a new piano teacher this year and has started learning the oboe.

In September she was learning by ear, convinced that note reading was a waste of time since her old teacher wanted her to play everything from memory and in her solfege classes they were doing "relative" note reading where the teacher decided which note the bottom line was supposed to be and the children then worked all the other notes out from there.

Having discovered that she could read the oboe music, and play while reading the music, she tentatively started reading the piano music and discovered, to her surprise, that she could read that too. Over the past couple of weeks she has become quite manic about sight-reading. She has been playing her way through a collection of tutor books which I bought cheaply from e-bay a couple of years ago to try and give her some practice at note-reading but which she has refused to look at until now.

Last week she decided she wanted to play some of the pieces from her oboe tutor book on the piano and discovered that they had no fingering. Usually she ignores the fingering that is written in and uses her own weird (and as I keep trying to point out to her) counter-productive fingering which changes every time she plays. Anyway, she asked me how people decide which fingers to use and I suggested she try to move her hand as little as possible, to look for groups of notes which fall under her five fingers and and to turn the thumb under to be able to reach a few more notes. To my utter amazement, she has learnt a couple of pieces with consistent, logical fingering which she worked out for herself.

Sounds like she's someone who likes to know the why of things rather than just being told thar's how they are.
Happy to hear that she seems to have sorted out the mysteries of note reading and piano fingering. The note reading approach for oboe seems to have been the missing piece of the jigsaw.
Maybe given the time and the tools an interested child will get there even if it's not by the route we expect?

You're a lucky mum to have such a keen and persistent daughter! And she's a lucky girl to have you as a mother, too, as you seem to be nurturing her in just the right way - allowing her a free rein to explore and discover for herself, and giving good advice when needed. Providing a child with the wherewithal to work things out for his/herself is worth a thousand dictatorial lessons. Long may you both continue!