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.

http://www.youtube.com/watch?v=pnd6JIdbxjA