When I look at certain sites of music schools where piano teachers present themselves, I am astonished to learn that some of them have embraced a "modern approach" that makes practising scales superfluous... calling the traditional way "old-fashioned" and a "waste of time".
I am inclined to think that those modern teachers are totally denying one of the truths of fine piano playing: without a flexible, clean and fluent technique, artistic playing on a high level is simply not possible. And practising scales in an intelligent way is one of the best ways to develop an all-embracing technical grasp.
Especially in the first years of learning to play the piano, but also later on when one has a more advanced level of piano playing, it is indispensible to practise scales in all forms, preferably on a daily basis. I give just three of many important reasons:
1. It is the best way to get acquainted with tonality (key, major and minor) and intervals, and in general with the total range of the piano.
2. It is a perfect way to train both the ear and all the fingers by listening very attentively to the exact dynamic value of the tones, so that the result sounds smoothly and accurately.
3. If one has memorized the exact fingerings of all the minor and major scales and if one can reproduce them all without much trouble, it is of incalculable value when studying new pieces of Mozart, Beethoven, Schubert, Chopin etc. that are full of scales in whatever form or key... it also saves a lot of time!
It is very difficult in the beginning to judge the correct volume of sound when one starts practising scales (because the fingers are unequal in strength), that's why I would recommend to start with hands separately.
Special attention is needed for the role of the thumb, because it is often causing a jerkiness or unrest of the hand. This is usually because the thumb is too late with moving towards the proper key. To put the fingers in time on the right keys without any jumpiness while playing scales with great speed is not an easy task! That's why it needs so much practise, too. One should always listen with a lot of concentration to the sounding result, but at the same time one should also foresee and prepare all the correct movements.
The right hand of Thedor Leschetitzky (1830-1915), one of the greatest and most important piano pedagogues in history, playing a scale:
Heinrich Neuhaus (1888-1964), in his extremely important book "The Art of Piano Playing", gives this exercise to train the thumb in anticipating the next key:
Marguerite Long, "Le Piano":
J. Pischna, Technical Studies:
Franz Liszt, Technical Studies:
Eventually, a good touch has been formed, and the thumb will be fully prepared. Then one can start practising more advanced scales, using the entire range of the piano.
Of course it is of the utmost importance to study very carefully all the right fingerings. An excellent compendious survey of all the major/minor scales with added fingerings can be found in the book of Marguerite Long ("Le piano"),
but there are many other well-ordered piano methods, suchs as "Le Pianiste Virtuose" by H.L. Hanon.
The "secret" of thoroughly enjoying practising scales is, of course, to vary as much as possible. Chromatic, diatonic, major, minor, in groups of three, four or six notes, in contrary motion, in thirds, sixths and octaves, in different rhythms, with accents, crescendi, decrescendi, piano, forte, legato, staccato etc. etc. There are endless combinations possible... no need to ever work mechanically! There is a great deal of fun in inventing new exercises with scales. It's also nice to just improvise using as much scales as possible. Why not try something à la Prokofiev, who wrote polytonal passages like this (combining an A major scale with a D flat major scale):
Also, it is a very good idea to collect and memorize a repertoire of passages of scales from famous pieces, as there are literally hundreds of them in the piano literature that one can use for practise purposes!
Depending on one's mood, one day one can choose Liszt's Mazeppa to practise (starting slowly and gradually working up to speed):
Or if one feels more like E major, one could spend some time practising this passage:
Sometimes, a fingering may deviate from what is "normal", because a composer/pianist had a certain pianistic style, or he had a certain musical effect in mind. For example we can find in some of the Liszt Rhapsodies rapid scale passages that are supposed to be played with a rather unorthodox fingering:
To end here, I would like to quote one of the greatest technicians in the history of piano playing, Wilhelm Backhaus (1884-1969):
"Personally, I practice scales in preference to all other forms of technical exercises when I am preparing for a concert. Add to this arpeggios and Bach, and you have the basis upon which my technical work stands. Pianists who have been curious about my technical accomplishments have apparently been amazed when I have told them that scales are my great technical mainstay—that is, scales plus hard work. They evidently have thought that I had some kind of alchemic secret, like the philosopher's stone which was designed to turn the baser metals into gold. I possess no secrets which any earnest student may not acquire if he will work in the laboratory of music long enough. There are certain artistic points which only come with long-continued experiment."
(From "Great pianists on piano playing", James Francis Cooke