1. always memorize everything possible, it speeds up the learning process so much. To memorize something you don't just have to remember the notes, you have to remember the music. So, in a short amount of time, as part of the memorization process you end up doing harmonic analysis, motivic analysis, structural analysis...
2. always make your young students memorize everything: even more than speeding up their learning process, it'll help them when they turn 40 - that stuff is still somewhere in the old brain!
3. writing short little Lullabies (Lullaby Project) in the style of Bach has really helped my understanding of actual Bach. So maybe that should be a part of the instrumental training, writing little pieces in the style of whichever composer you're studying at the moment? Or at the very least, in the style of the biggies for solo cello rep: Bach, Kodaly, Britten? And probably Popper and Piatti...Definitely slower in the short term, but maybe faster in the long term? The ability to see the stylistic specifics of any composer is really handy, especially when playing new music. I feel like this should be taught as part of the comprehensive theory curriculum - but those idiosyncrasies are so instrument specific that it should probably be taught by the instrumental teacher rather than the theory prof who doesn't play your instrument...
Maybe people do it on their own and I'm just so dumb that I didn't realize? I guess better late than never.
Katri Ervamaa, cellist