My practicing has evolved quite a bit since my beginner days. In those earliest days as a middle-school band student, my idea of “practicing” amounted to playing the scale/piece/etc. through from beginning to end, generally with a number of mistakes, and then (optionally…) doing it again. I did manage to make some progress, but the results were far from ideal: few problem spots ever really got fixed.
As my musical standards, maturity, and commitment to practice time improved, it became clear that beginning-to-end practicing was not the best use of my time. As I started taking private lessons during high school, and transitioned into university music studies, I began spending more of my practice time focusing on the problem spots. With some work, at least some of those spots got solved, and my rate of progress ramped up noticeably.
At that point, I found myself in the same situation that my own university students now sometimes complain of: they successfully improve the problem spots, but, frustratingly, the “easy” parts fall apart under pressure (in a lesson, a performance, etc.).
For me, the third stage of my practicing development began when I realized the obvious: every part of what I am practicing needs concentrated, methodical practice. If the “easy” parts are falling apart, it’s because I have essentially been sight-reading them in the practice room, and under pressure my sight-reading ability suffers a bit. Instead I need to know every note, rest, and expressive marking intimately. Problem-spot practicing gets me up close and personal with the “hard” parts, but neglects the rest.
So now I practice, and encourage my students to practice, phrase by phrase, measure by measure, even beat by beat, through every bit of the music, regardless of difficulty. Some parts might require more work, but every part needs work.
When I explain this to students, I sometimes see in their faces the same hesitation that I initially had: this is going to take forever! It does require serious commitment, but isn’t it worth it to play the lesson or performance with confidence and control? Besides, it might not take as long as you think. Sometimes I walk through the math with a student to show them that it’s actually pretty doable. For example, suppose the student’s assignment includes a 50-measure etude. If the student spends two focused minutes on each and every measure, that only adds up to a bit more than an hour and a half of practicing, but begins an intimate acquaintance with the entire etude. That’s less than one day’s worth of practicing for most college-level music students, leaving quite a few additional hours in the week to shore up the hard parts plus practice other assigned materials.
I think that, at least for me, this progression through three different stages was necessary; in other words, I don’t think it’s necessarily wise or feasible to push all beginners straight into something as intensive and committed as third-stage practicing. Your results may vary.