Imagine you are struggling with a fast sixteenth-note passage. Your fingers are always getting "stuck". You practice it over and over again. Slowly, with exercises, quickly - nothing seems to be helping. Often your body and mind will try to solve the problem in a way consistent with the notation: in groups of four, 1-2-3-4. However, musically speaking it is likely that the grouping should be: 2-3-4-1. This creates direction towards the beat and not from it. This allows the muscles to relax at a different time in the beat/measure/passage and thus will (hopefully) allow you to master it. A more musical approach will almost always solve a technical problem. Another example would be leaps. If they are causing you problems in a certain direction, turn it around! If the score calls for leaps from bottom to top, try skipping the first note and leap from top to bottom. This re-directing of the muscles and the mental outlook will allow you to be relaxed in places where you weren't until then.
A further advantage of observing problems from a variety of viewpoints: One actually has a better shot at truly understanding what the problem is. Too often, whether it is in politics, relationships, or piano playing, we simply do not understand the problem. Unfortunately, we also are not aware that we don't understand it, or we are unwilling to admit it. But truly understanding a problem is usually a surefire way to solving it. The solution is the easy part.
In the examples above, we thought we knew that the problem was a certain leap or passage, when in reality it was an incorrect musical outlook on the passage. Another "favorite" problem students have is in memorization. They come to their lessons, mess up the memory, and invariably say: "It was perfect at home." And I believe them! So what is the problem? There are actually two of them. First of all, students trust themselves too much in their practicing. When they are playing through their pieces, from memory, they are not second-guessing themselves. They are simply playing. And when they do have small slips, they happily play through them, assuming that it will be better next time. However, when they show up to their lesson, they suddenly start to question their preparation. They start to worry about what comes next. The little devil on their shoulder taunting them all the way through. This will invariably lead to a collapse. In these cases I am always reminded of a German saying, which pertains to relationships: "Vertrauen ist gut, Kontrolle ist besser" - (I paraphrase) "Trusting someone is good, but checking up on them is better." While I do not subscribe to this saying as it pertains to relationships, I do like to use with practicing vs. performing. When you're practicing, trusting yourself is good, but checking up on yourself is better. When you are performing, trusting yourself is the ONLY way to go.
The second part of the equation once again takes us outside the box and we realize that we might not completely understand the problem. We spend all of our time memorizing the notes, the rhythm, dynamics and articulations. We know the harmonies and melodies. And yet, we still have memory slips. What we have forgotten to memorize is WHEN to recall the music. It is just as important as WHAT to memorize. The image I instill in my students is the following: imagine walking down a long hallway with many locked doors in your way. It is dark, with the exception of lights over each door. You have the keys to each door. They are numbered and there is absolutely no secret as to which key fits into which lock. As you walk towards the door and enter into the halo of the light, you pull out the key, slide it into the lock, and open the door all in one motion. And then you continue on to the next door. If you pull out the keys too soon, you can't find the right one, since it is dark. If you do it too late, you will walk into the door. Like everything else, these moments of recollection need to be consciously decided upon so that in performance they are recalled subconsciously.
The next time you encounter a problem (in any environment), see if you can look at things differently. Students, become your own teacher. Teachers, become your own students.