I use your daughter's way for adding 7s and 8s, and your for 9s. It's especially good for subtracting. I think that she probably like to see problems in an abstract way, and just doesn't like 'techniques' as much as the elegance of actually understanding the basis of what she is doing.

As long as she is fast enough for the classroom, I would leave it be.

Smiles,
Grinity

Coaching available, at SchoolSuccessSolutions.com