My students are often capable of more than they are ready to give themselves credit for. It's easy to underestimate your abilities, especially when you are new to music or are struggling through a difficult piece. Sometimes you have to be shown your own greatness. You need a teacher to hold a mirror up to your talent so you can see how your hard work has paid off.
One way that I like to encourage my students is by having them learn a song at a slow tempo. Then, during a lesson I will use the metronome to speed up their tempo (I usually go up two notches at a time) and I have them play faster and faster, until we reach the ceiling of their actual ability to play. All this is done without showing them the speed at which they are playing. Then, I announce the tempo ("You just played that song at 176!") and this is a happy surprise for the student. It's always nice to know you are doing better than you anticipated and this is motivation to keep learning and working towards the next big thing.