Divide and Conquer - The Smartest Strategy for Music Practice

Wouldn't you rather practice a passage for 15 minutes and master it once and for all, than play it over and over for an hour and still make the same mistakes?

Well, then it's time to apply the same strategy the ancients used to solve problems and win wars: Divide and Conquer.
Computer whizzes have actually created an algorithm by that name which works by breaking down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem. (Quote from Wikipedia).

Music practice is in essence problem solving and involves analysing and finding creative solutions. Vain repetition and worse still, the repetition of mistakes during practice needs to be avoided at all cost! Repeating a passage over and over will actually reinforce the very weaknesses and mistakes you are trying to overcome.

Unless you are just scouting a piece and playing it through for the first time to get a feel for it, you should never play over a mistake twice. Do not ignore mistakes,
instead look closely at the passage(s) where it fell apart and analyse what it is exactly you are tripping over.

Is it the tempo? (Can you do it very slowly?)
Is it the rhythm?
Is it visual? (I.e.: is there a line or page break, are the notes written too closely together.)
Is it the fingering? (Investigate other possibilities of fingering. Again, your teacher should be able to help you there)
Is it bad posture? (Guitar players, it pays to check your left hand posture!)
Is it some technique you have never applied before? (Concentrate first on acquiring a new technical skill!)

Once you have found the exact place of bother and have analysed the cause for your struggle choose one or two notes before and after. Now play the passage very slowly at a tempo you can handle comfortably. Analyse the movement of your fingers and find the best possible fingering and posture. It is crucial that you play the passage slow enough not to make a mistake for 7 successive times. Only then increase the tempo just a little and repeat the same short passage again 7 times. Note: If you happen to make a mistake the fifth or even the seventh time you played it, the counting starts again from one - sorry!

It is crucial that you increase the tempo slowly and do not repeat your mistakes! Keep on increasing the tempo gradually until you reach the required tempo. This type of practice is best done with a metronome.
Initially it may seem that this is the long road to success but once you disciplined yourself to actually practice a passage in this manner for about 10 to 15 minutes you will have achieved a lot more than playing through the whole piece repeatedly for one hour.
So why the number 7 ? Well, you can repeat it more often if you like, but anything less is just not as effective. Some say it's a magical number... If you don't believe it try it!