It is simple. The fastest way to acquire technique is to identify the most difficult bars of a piece and work on them first of all. Any experienced pianist /teacher knows (or should know) that. Most inexperienced pianists/students ignore this (even if they have been told many times).
So, imagine for a moment Professor Czerny trying to teach his young and headstrong pupil, 10 year old Franz Liszt to play a Beethoven sonata. Franz is impatient. He wants to start at the beginning and go to the end of the piece (he can already sight read well). He does not want to spend time repeating over an over that single bar with arpeggios in the left hand. What is more, Professor Czerny is never happy. Not only he wants to Franz to repeat the arpeggio endless times, as he now wants him to do it with different rhythms, different accents, transposing in all keys. And this is just one bar, for crying out loud!
Professor Czerny is not indifferent to young Franz predicament. He remembers his own lessons with Herr Beethoven, the famous musicus. No exercises. Just a piece thrown onto his lap and the direction: Bring it ready next week. Not much discussion of technique at all, but oh! What interpretation insights! Yet he was grateful for his previous teacher to have told him many of the little practice tricks he now tries to impart to his own students and that allowed him to master the difficult pieces Herr Beethoven assigned to him. Has it to be like this? Dry technical tricks on one side, and beautiful interpretation on the other with no middle ground in between?
That is when he has an epiphany: The left hand has to endless repeat that arpeggio, so why not add a simple melody on the right hand to make things a bit more fun? Yes, why not write a little piece that will incorporate all the repetitions, all the rhythm variations, all the accent variations and so on? Yes, little Liszt will be so excited when I show him this!
And so professor Czerny sets to work. He believes Herr Beethoven’s 32 sonatas to be the pinnacle of piano music. So he sets out to identify and isolate every single difficulty he can find in these sonatas. And around each difficulty he builds up a little pleasant tune so that the task of learning these monumental works of music will be nothing but fun!
And he proceeds to compose over 50 000 of those fun pieces. For generations of students to come to have fun in the process of learning the piano.
Unfortunately for Professor Czerny (and all music pedagogues that came up with the same ideas) there are a lot of problems with this approach:
1. No one finds Czerny (or technical exercises) fun. Granted, they may be more fun than the alternative approach (work on the difficult bars without musical context), but this is more or less like saying that going to dentist is fun since he has all those nice magazines on the waiting room.
2. A Czerny study is completely specific to the Beethoven sonata difficult passage it was meant to conquer. Just playing any exercise – or set of them – will not help technique in general, because there is no such thing as technique in general. Technique is always specific to the piece you are working on. True, octaves, trills, scales and the like are common enough in most pieces, but even then they may have to be played differently according to context.
3. Czerny left no instructions on how to use such exercises. This is of course part of a tradition of secrecy amongst guilds of musicians/teachers in past centuries. You may buy the scores, but you still need the teacher to make it work. So once you have played all the 32 Beethoven sonatas perfectly and acquired all the technique, if you go back to Czerny it will be pretty obvious which exercises are taken from which sonatas. But then you will not need them anymore anyway! So if you are to benefit from them you need a knowledgeable teacher. But this is almost impossible to find since the knowledge was passed from Czerny to his pupils, and as the emphasis on teaching went from technique to interpretation at the start of the 20th century, the tradition was lost. Leschetizky may have been the last one who really knew this stuff, but since he never took on beginners, and since he rarely taught technique (Although Paderevsky was put on a regimen of Czerny for a couple of years) it all died with him.
4. Therefore, most likely your teacher will be giving you a Czerny exercise that has no connection whatsoever with any difficult passage of specific pieces. Go on, ask your teacher: Why am I doing this study? If the answer is: because your assigned piece this summer is the Moonlight sonata, and this particular exercise will get you through bars 1 – 4 of the third movement, the teacher knows what s/he is talking about. If the answer is on the lines of: “It is good for you, it will develop your technique” s/he knows nothing. (S/he can still be a good teacher, but you will waste a lot of time doing things for no purpose whatsoever). What if the teacher reply is: “This study is good to develop your facility with double thirds”. That is better than the previous answer, but then you must ask (most of all yourself): “Does any of my pieces requires double thirds?” If you have no piece currently on your repertory that requires double thirds, why should you be doing this exercise? This may uncover the teacher’s hidden philosophy that one should spend time acquiring all kinds of irrelevant (for the moment) techniques to be (or not to be) used at a later date. And this is really bad philosophy.
5. Although Czerny is better than Hanon (which in my opinion is not only useless but also completely misguided – don’t get me started on that one!) the sad truth is that as music, Czerny studies are crap. Would you perform them for friends and family? Would you like to share them with anyone? Actually there are a couple of them that I actually like, but I never played them for their “study” value, but simply because I like the music. Compare with Chopin etudes. Yes, they are studies, but they are also superb pieces on their own right (and in fact you probably need easier studies to acquire the technique to play them). And if you want easier studies, then go for Burgmuller, Heller and Eggeling which are actually musically satisfying.
6. But now not only you have to learn your assigned pieces, as you have to learn studies that may or may not have any relevance at all to the technique you need in your pieces (more often than not they will be irrelevant).
So what is the alternative?
1. Find a piece you desperately want to be able to play. This is your job . It is not your teacher’s job. Your teacher cannot divine your tastes. If you are assigned pieces you don’t like it is your own fault. Notice that a piece you want desperately to be able to play may or may not be a piece you like. But want to play it you must. Simply because without such compelling inner need you will not be bothered to learn and practise it.
2. Identify the most difficult passage in the piece: all the technique you will ever need to acquire to play the whole piece will be in that passage. It is usually short, and it does not occur too often in the piece (this is true even for advanced pieces). This is your teacher’s job . This is what you pay him/her for. S/he must be able to point out to you straight away the difficult passages. S/he must be able to show and teach you all sorts of practice tricks that will assist you in mastering the difficult passage as quickly and painlessly as possible. S/he must be able to provide you with a choice of movement patterns that will get the job done. S/he must be able to observe your playing and tell you exactly what you are doing – if it is right or wrong – and to assist you in correcting the wrong stuff. With such an approach technical exercises may not be needed at all. The technical exercise will actually consist on the several ways you are working on the difficult passage. If a technical exercise is assigned (and in some circumstances they are helpful) it must have a direct bearing on the difficulty you are trying to master.
3. It is your job (no one else can do it for you) to follow your teacher’s instructions in  above to the letter.
4. Therefore you must trust your teacher completely. You must admire him/her. You must worship him/her. I expect nothing else from my students (not that I get it though ). And the reason for this is simple: you will not follow instructions from someone you do not regard as a master.
We are talking of course of beginners or intermediate students.
The difference between beginner/intermediate and advanced level is not on the difficulty of the pieces one can play, but on the ability of the student to do all the above work without the close supervision of a teacher.
If your teacher still needs to tell you where the difficult passages are and how to work on them you are still a beginner and not ready for advanced classes. On the other hand there is something very wrong with a teacher that treats you as an advanced student (by dropping a piece in your lap and telling you to bring it ready for the next lesson) when you are not one