This is an odd question. But I think I can use some wisdom from teachers and other experienced individuals.
Now, most of the instruments have method books, and many teachers follow them as well. My question is, how are these method books structured? Why do they have exercises the way they do? I'll detail my questions(s) below:
1. Practising exercises
Now, method books seem to have a series of exercises. In Berklee's Modern Method for Guitar, it is said that you should not be "stuck" on an exercise. Just try your best, move on, then come back and review.
My question is, what's the difference between trying to master a particular exercise completely, and improving on it a little bit and coming back later. What are the benefits?
I believe the benefits would depend on the how the book is structured, and the purpose behind each exercise. I, as a student, wouldn't understand that. But I'm curious to know.
One explanation (for guitar) can be that it takes time for your muscles to develop. So it makes more sense to master, say a new chord form, over a period of time. But I don't find this to be true with the Piano. Maybe for major techniques, but not the minor ones.
2. Technique vs. Repertoire
I was following Alfred's All-in-one Piano for Adult Vol 1. I learned a lot of new things. However, as things progressed, the book seemed to move slower. It did introduce a lot of new songs, but many of them were not something I wanted to learn. In the end, I spent my time learning some songs I'll never play again, and didn't learn any new technique too.
So, how is that you guys keep your learning rate constant?
3. Exercises vs. Learning new things
There can be countless method books for, say, guitar. Since I've been playing for about 3 years, I've developed a good foundation of the basics.
Let's say I pick up a random method book and open the chapter that emphasizes the key of C. There is a good chance that I might not be able to play everything perfectly in the first try. There can be things I'd have problem with.
Now, my impression is that every "piece" is different and has to be learned. The learning rate depends on you. So, even if I do master that chapter of the method book, it'd only "validate" my skills, not add to it. (At least that's what I think).
Of course, I'm a bit confused as to how method books work, and how I should use them. Can anyone shed some light? I do agree that this is a long and annoying question, but it's just my curiosity.