An almost three year old's logic

When not visiting hospitals, our youngest has discovered the joy of jigsaws. A month ago she could not even do a four piece puzzle, but suddenly she is doing, unaided, 40 piece jigsaws. These are the type that have the shape of the pieces marked on the backing piece, as an aid. My usual method is one of the following: a) do the corners and edge and work inwards; b) take a random piece and attempt to fit it in by shape, according to the backing piece. This does not suit her majesty, and I am frequently told that I have the wrong piece. She has a very particular order of doing the puzzle row by row, and carefully picks the next piece from the pile. This is quite the opposite of what I intuitively expected of her, and I don't think it's something we have 'taught' her, even by example. Time to reconsider my theories on development of 'intelligence' in children. They're a lot smarter than we think (Or should that be, we're a lot smarter than we think?). This came to mind because we have been discussing this in one of my classes (mentioned earlier), and it was an interesting phenomenon. Any thoughts from the professionals (and/or mothers/fathers)?