Practice: what does this mean exactly?
Students often ask "how much" they should practice. I am sure they mean "how many minutes"?
You may ask: What's the difference?
Some students may take hours to master a particular piece. Some students make find that they master the same piece in 30 minutes. It's not the time overall, it's HOW the time is spent. AND the students practice habits up to that point.
Simply playing through a piece, whilst ignoring incorrect pitches, rhythms, or chords, while perhaps satisfying: "I played my piece!", this method of "practice" falls short. Every time that problem spot is played incorrectly, that sequence is further ingrained in the brain. Overcoming the mistake becomes more difficult because of this. In effect, students have to re-learn that part. Or, they become frustrated and quit.
How much more effective, rather than only playing the piece, is taking those problem areas and isolating them. Three things should be done:
1) STOP playing! Back up a few notes, and figure out the correct pitch, rhythm, fingering.
2) SLOW it down. Play just that sequence of notes, a part of a measure only in most cases.
3) REPEAT correctly!
In my personal practice, I mark (in pencil) the areas that need work. I make sure to write in fingerings so that I am training muscle memory. I isolate and slowly play through the part, first right then left hand (if we're talking about piano) Then, I gradually add the few preceding notes/measures, and the following notes/measures, in order to put it all in context.
This process can take several minutes. For less experienced students, this process becomes boring. Students do not want to practice this way! I acknowledge this. And for this reason, I try to keep most the pieces which students are working on within their current ability. Most method books are graded well for this process.* In order to grow, I emphasize technical studies: scales, finger patterns, cadences. These can then transfer to new pieces.
Playing through pieces is indeed satisfying. I recommend that students spend part of their practice session playing pieces which have already been mastered. Keeping skills which have been learned is very important for the layering of proficiency. The building blocks of music mastery is a slow and steady type of endeavor.
Therefore, in order to progress; isolated, slower repetition with repertoire selections should take about 1/3 of the practice session. Another 1/3 should be spent on technique exercises. Uniformity of pulse and accuracy are the goals of this portion. The final 1/3 of the time (no matter how many total minutes we are talking about) should be spent enjoying pieces already learned in previous lessons.
I hope that this article has been helpful. The TED talk linked below explains the science behind practice.
*Trying to explain to a student (or their parents!) why Jonny can't study Fur Elise, or Moonlight Sonata yet is a subject for another post.