I don't believe in traditional exercises for the piano such as Hanon and Czerny. I believe there are several problems with them. In order of importance, these reasons are:
1. They encourage un-musical, mechanical playing. It is very unlikely that the student will play these exercises as beautiful music. Most teachers will say that does not matter, that you are only practicing "technique" and it does not have to be musical. I believe the opposite, that EVERY time you touch the piano you should be practicing playing with full emotional involvement and commitment. As one practices, one becomes. You will get good at whatever you practice. Do you want to become good at playing mechanically? The physical coordination you will use when you are playing with involvement is different than when playing without it, so you cannot practice anything, even "technique," without the full force of your emotions behind it, and then expect that will transfer over to playing your pieces.
2. They kill the enthusiasm for piano. It is very rare to find a student who loves these traditional exercises and can't wait to practice them! More often the student hates these, and for good reason. They just aren't that interesting or fun. Worse, students are often told to practice these first, at the beginning of the practice session, so they start their practice with something unpleasant and this feeling may carry over to the rest of the session.
3. They don't cover the full range of technical challenges. Many of these were written in an era when music was less technically demanding than it is now. Czerny, for example, lived and composed his studies during the time of Mozart. Nothing in his exercises prepares the pianist for the big chords and octaves of Brahms, the lush chords and arpeggios of Chopin, or the shimmering effects of Debussy.
4. Exercises which promote "independence" of the fingers are very detrimental to good playing. We want the fingers to work within the hand and within the arm, not independently. You cannot play a chord, for example, with absolute evenness or extreme softness, if three or four fingers are all trying to do their own thing. The chord must be a unit and must be played by the hand using the power of the arm. This myth that a long arpeggio or even a scale is achieved through each finger acting independently is very insidious. Watch and listen to a great pianist and you will see that a long arpeggio is played with a masterful sweep of the arm, within which the fingers play their part by simply being in the right place at the right time, so to speak.
5. Exercises given to the student may not apply to the pieces he or she is working on at the moment, so maximum efficiency is lost, practicing something that may not be used and applied for months or even years.
Instead, I create my own exercises, which I call "set ups," from the technical challenges of the piece the student is working on. They are done in small amounts and then applied directly to the piece. The set-ups themselves are varied so as to be kept interesting, so the student does them with pleasure.
Sometimes, what seems like a technical difficulty is really a different problem, most often, of not really having the passage "in one's ear." In other words, you do not have a clear auditory image of the passage. To strengthen this, I use various methods, including transposing the passage to other keys. Invariably, when the ear is strengthened, the passage always becomes easier from a technical standpoint.
The area of technique is difficult to grasp by reading about it. It needs to be shown, and then felt and experienced by the student. My lessons are very "hands-on" so the student can sense and experience a new way of doing something. When the body experiences it, and the student knows HOW he or she got to that experience, it will be more likely the student can re-create that process at home. It just cannot be done by mechanically repeating a canned exercise over and over.
When I first started my studies with Joseph Prostakoff 37 years ago, I asked him what I should do with my books of Hanon, Czerny, and many others. "Burn them!" he said. "Burn them immediately!" I give my students the same advice.