I agree with what Birba says on his video, except that my teacher always told me that when you are still at the learning stage of a piece you should be always practicing slowly and heavy, you should not care about interpretation at this point cause what you are trying to achieve is getting all the notes ingrained into your fingers and your brain, its very mechanical, if you try to do little nuances and dynamics without having the notes really under your fingertips, your going to start making mistakes or you will not be able to make the dynamics right at all. So, after you can play the whole piece, or a whole section of a piece on a technical level, up to speed, them you go back and start the "Details phase" where you get the dynamics, the articulations and all that into your playing, as well as pedaling, this is where you get the sheet music and start reading paying attention to what you missed the first time. After that you go to the final phase that its interpretation phase, where, knowing the limits you cannot cross on the piece, you find your own way of playing it.