I agree with this. I can see daily that just by living, she is learning. The problem is her own perception of it because it does not look like compartmentalized 50 minute segments broken down into "subjects" of history, math, science, etc... I know that now at 13 she spent more than half her life in public school (age 5-11) and that is going to have an extremely strong effect on her ideas about life and learning. But for how long?
For several years we were part of a funded homeschooling program which was philosophically very unschooling-like. They recently expanded their programs into secondary education and were very interested in encouraging their adolescent students to really embrace the opportunities for self-determination and following their own bliss. A proportion of these kids had been in school previously. The program encourages such students to create blogs in which to post weekly reflections on their own learning. If kids had writers block, or couldn't think of any interests or anything to write about, the facilitators would give them a bunch of prompts that they could choose from. "Something made me go 'hmmm...' this week was ___, Something that energized me was ____, This week I was surprised by ____, An unexpected conversation I had this week was ___, The song that would make the best soundtrack for my week is ____, etc." Or they would be encouraged to use photos to show what had occupied their interest or made them think. Or use some other medium ... video, audio, cartooning, prezi presentations, whatever.
The idea was that by asking learners to take a little time to actively reflect on what had held their interest over the previous week, they would become more aware of what motivates them, of who they are, of where their interests lie, and more aware and appreciative of their natural learning.
Would something like that appeal to your dd? My kids haven't needed to deschool but even they occasionally enjoy documenting their natural learning as an antidote to the feeling that they have nothing to "show" for their learning, no tidy tick-lists of courses and grades to document that it's happening.