Often it actually HINDERS physical and mental learning when you practice something slow and then gradually speed it up. There are 2 main reasons:
1. There has been conclusive research that brain function for slow practice is quite different than in fast practice (the brain activity actually occurs in a DIFFERENT place in the brain for slow and fast practice).
2. Muscle use is different for slow practice and fast practice. Think of a horse's different gaits: walk, trot, gallop, run, etc. a gallop isn't just a sped-up walk, the motions are actually quite different; if a horse tried to just trot really fast, it would trip over itself.
In piano playing, this is more obvious with some gestures.
Try playing RH fingers 1, 3, 4, 2, 5, 3, 2, 4, 1 on a C pentascale or just on the table. Try it really slow first, and notice the circles that your wrist makes and how you have different "turn around" points.
To play it very fast, notice that it's more like one big motion. To practice it fast just do 1, 3, 4 really fast and relaxed, and then add the next one: 1, 3, 4, 2, and then 1, 3, 4, 2, 5, etc. If you practice it really slow and then gradually speed it up, it starts feeling awkward, doesn't it?
I find that it is more effective to figure out how to play something FAST and RELAXED rather than slow and then gradually speeding it up. Granted, when you're first learning a piece, you can't play it fast yet. So, isolate a very small section, and work on playing it fast and relaxed as SOON as possible, then do the same with the surrounding passages to put it in context, and continue this process.
Anyone else?