Some piano teachers prefer to improve a student’s technique by selecting difficult passages from the mainstream piano literature rather than assign a load of scales, arpeggios and chords that journey around the Circle of Fifths.
I still believe the best foundation upon which to build a solid understanding of the piano repertoire is by studying scales, arpeggios, in legato, staccato, with all possible combinations: in 3rds, 6ths, 10ths, rendered in parallel and contrary motion.
In addition, once a student has a well rounded exposure to theory, harmony, and understands the physical demands of playing with a focus on relaxation, using a full arm, supple wrist follow-through motion, then he is best equipped to tackle some of the more challenging passages as they appear in Beethoven sonatas–even those, like the Pathetique, from his first period of composition.
In the video below, I selected a section of the composer’s Sonata, op. 13 in c minor, that requires lots of chord blocking and voice tracking. I demonstrated in steps how to best untangle a very tricky group of measures spanning bars 89-113. A parallel section in c minor, measures 253-277, would benefit from the same layered approach.