[from JPSL No. 9]
By practicing these scales in contrary motion in 12 keys you'll develop an ability to finger improvised passages readily, even in seemingly awkward ways. The contrary motion sharpens the mind and develops the instinct for "grabbing" the right notes of the scale in both hands without thought.
I recommend studying these scales as Dan Delaney presents them, mastering one form before going on to the next.
Each scale is continued to the end of the piano. Like all exercises, they should be played as fast and loud as possible, consistent with good, even time. Aim for automatic mastery.
[Note: I no longer believe that exercises should be played "as fast and loud as possible". I changed my mind.]
These fingerings will seem strange and uncomfortable at first, but that stage passes quickly; soon they become quite enjoyable. As shown, the 12 major scales are fingered 1212..., and then 4545...; it's a good idea to master these to a degree before going on to 123123... (ex. 3.1) and 345345... (ex. 4.1).
Subsequently the following fingerings can be added:
No. 5: 12 123 12 123... (2 directions)
No. 6: 345 45 345 45... (1 direction)
No. 7: Classical fingerings.
As if that weren't enough, you can play all the same scales twice as fast in one hand than the other (2 against 1, i.e. eighths in the RH and quarters in the LH or vice versa). Dan likes to introduce the stages of this exercise gradually, over a period of months, which is an excellent idea.