Alan Kennington wrote about the "asterisk method" to learning mathematics [0]. There is a line that I'm thinking about in particular when you mention the utility of paper and pencil over reading on screen (or solving problems in general): "Copying material by hand is important because this forces the ideas to go through the mind. The mind is on the path between the eyes and the hands. So when you copy something, it must go through your mind!"

Maybe there is something about owning a problem that is more personal when writing it down and working it out by hand versus reading it on a screen.

[0] http://www.geometry.org/tex/conc/mathlearn.html