If you recognise yourself in the description above, this is how you should practice a difficult passage or etude.
First of all, you have to decide that perfection is your aim, and you are not going to be satisfied with less. Saying to yourself "it was nearly right, and I'm sure it will be OK next time" is the greatest enemy of progress.
Second, when you notice a mistake, STOP, immediately, before you have a chance to forget what the mistake was or where. It might be a piece of awkward fingering, it might be a short passage with a high note that you mispitched, it might even be a slur that wasn't sufficiently clean. Go back a bar or two, and practice just the fragment that contained the error. If you still get it wrong, go about 30% slower and do it again. Keep slowing down until you find a speed at which the error goes away.
Then, having found a speed that is OK, repeat several times at that speed. If you find yourself still making regular errors, slow down even further, until you find a speed at which you can play the fragment at least 3 times in a row (and preferably 6 times) with no error at all.
Resist the temptation to go any faster in the later repetitions. What you are doing is practicing getting it right, and the only way you can practice getting it right is to practice at a speed at which you know you actually can get it right!
Once you have managed 6 error-free repetitions, try the fragment just a little faster, 10% or so. If all is well, repeat 3 times at that speed, and then go a bit faster still. If you make a mistake, immediately drop the speed by 30% and do the 6 repetitions at the slower speed.
Gradually, you can get the speed back up to concert speed. Having done that, go back a few bars and put the fragment back into context. Hopefully it should now be fine. Carry on until you come to the next difficult bit, and repeat the process.
This practice technique is very hard work if done properly, and is very tiring, but there is no more efficient use of practice time. This is because of two things.
- You spend most of your time practicing the difficult bits, which after all, are the bits that need the practice!
- You spend most of your time practicing playing those difficult bits right (albeit slowly to start with).
You might notice that the techniques described here bear a remarkable resemblance to those I described in The art of sight reading a few weeks ago. That's because they essentially are the same. Whatever you are practicing, you learn faster if you practice getting it right, and you practice getting it right by practicing slowly.
In fact, getting good at sight reading is a very efficient use of practice time, because it means that you start from much further on when you have to learn a new piece.