The idea is to start somewhere in the middle of the piece, practice a small part, then select another and start again. It's easy to catch problem spots when you listen to the student playing a phrase, four bars, or even a single bar. The small group of bars can then be played multiple times to perfect them. Intonation can be corrected to remove the guesswork of where to play a note, on a violin for example. Rhythm can be solidified where the note lengths vary, contain triplet or trills. A phrase's dynamics can be emphasized and understood by the student when he only concentrates on a small portion of the piece.
Small parts are easier to repeat than large ones. By separating the piece into manageable bites, the student can work on perfecting only that part. By repeating it they practice efficiently, and quickly assimilate the part. This should be done on pieces the student knows. Even the pieces that he's comfortable with, there is always room for improvement. The student will realize, once he's worked on a section, that the whole piece becomes easier to execute.
By practicing disconnected sections of a piece, the student is able to break out of a cycle where he feels he can only play a piece from beginning to end. The student may be in a situation where he is unable to pick up where he left off after being interrupted. The student will know how each section sounds like separately and be able to recover quicker and adapt to different situations, especially if the student is asked to perform, be it for grandma, the classmates, or a more discerning audience.
To be effective in separating the piece in to small chunks, it's good to be able to identify the phrases. The beginning of the phrase is a logical place to start playing a section of the piece. Each piece is different, and knowing what the whole piece should sound like certainly helps to identify those spots. Often the student will indicate where he prefers to start the small section. Luckily, most pieces the students work on will separate well in four-bar chunks: bars 1-4, 5-8, 9-12, etc. or 1-5, 5-9, 9-13, etc. for those pieces that don't start on the first beat of a bar.
So, how do we break the piece up into bite sized sections? You can choose the bar number to start on with this table and a 20 sided die. You can get a 20 sided die at most games store. Roll the die, find the number on the left, the number on the right is the bar number to start on. Re-roll the die to get a new bar number if it is greater than the number of bars in the piece.
1-1 ... 11-41
2-5 ... 12-45
3-9 ... 13-49
4-13 .. 14-53
5-17 .. 15-57
6-21 .. 16-61
7-25 .. 17-65
8-29 .. 18-69
9-33 .. 19-73
10-37 .. 20-77
2-5 ... 12-45
3-9 ... 13-49
4-13 .. 14-53
5-17 .. 15-57
6-21 .. 16-61
7-25 .. 17-65
8-29 .. 18-69
9-33 .. 19-73
10-37 .. 20-77
The student plays the four bars once to determine what needs to be worked on. Look for the difficulties starting from the most basic and specific, to the more complex and general, so that nothing gets overlooked. Repeat the four bars as necessary to see an improvement, then select a new chunk to review. The student does a set, of these random 4-bar chunk reviews. The whole piece is then played to incorporate what he learned. On the following day, when the student replays the piece, point out to the student anything that improved that is a direct consequence of the previous day's practice.
This technique smooths out rough spots that tend to be forgotten when the whole piece is played through. It distributes the work put into the practice of a given piece, not just the beginning and not only the parts the student prefers or finds easy. It intensifies the practice, concentrating effort on a small section, and giving that section the best opportunity to get better. The student will play better and be more aware of the structure of the piece he's playing.