What I'd like to focus on here, though, is a word that was sandwiched in the middle of that previous sentence - "productive." Plenty of students put in their hour or two every day but they feel like they are going nowhere. They honestly feel like they are doing what their teacher asks by getting in the practice room, but when they show up for their lesson every week their teacher (me!) is never satisfied. I would argue that 99% of the time this is because the student has not demanded enough of himself/herself in each practice session.
I grew up a Dallas Mavericks fan. For much of my youth this meant I was a fan of the worst NBA franchise in America. Things turned around when the Mavericks signed Steve Nash and Dirk Nowitzki. One of the things that I admire about both of these players is that their free throw percentage is always around 90%. This means that when they get to shoot the ball with no one flying at them trying to block the shot they make it 9 out of 10 times. This is a very comforting attribute to have on your NBA team. Contrast this with Shaquille O'Neal, who only shot around 50% from the free throw line. This means that when the game was on the line Shaq would miss foul shots just as many times as he would make them.
Why do I mention my affinity for the (reigning NBA champion!) Dallas Mavericks? Free throws should be automatic. No one is guarding the player. The distance to the rim is always the same in every arena and practice facility. Other than people watching and the nerves involved in an actual game, there is no difference between shooting free throws in practice and in a game. Sure, there may be physical differences from player to player that make it harder to be successful. Typically, larger players do not have as many of the fine motor skills that aid free throws, but that hasn't stopped Nowitzki (who is 7 ft.) from shooting well from the foul line. I would say these points are true of a musical performance. Other than having an audience in a lesson or in a performance, nothing should be different between playing in a practice room, office, or recital hall. Some people may be more naturally gifted and can therefore achieve a successful performance with less work than others, but does that excuse a sloppy performance? I don't think it should. Imagine how many more games Shaq's teams would have one if he had devoted more time to perfecting his free throw shooting?
Sure, you can say that nerves play a role in this. I would agree with this, but where I think the issue lies many times is that students have not put enough pressure on themselves in the practice room. It is not embarrassing to mess up in a practice room. No one hears. But suddenly when we are in a lesson or on stage everything becomes magnified. We realize that, "Oh, yeah I guess I never really mastered measure 47."
I don't think it is unreasonable to demand perfection from my students. Now, I must clarify this a bit. Do I expect that my students will perform with absolute accuracy every second of every day. No. That would be hypocritical. I don't play that accurately. But, I do practice in a manner that I expect any performance to be accurate. I am human so I may slip up here or there, but I know going in to any recital that I am more likely than not to play accurately. This is not because I am supremely talented (which I am definitely not); it is because I practice effectively and thoroughly. I also believe perfection can be demanded at each student's unique level of ability. I don't expect my freshman students to be able to play the Cosma Euphonium Concerto perfectly. But, there is no reason why they shouldn't have a Rochut and Herring etude prepared accurately. Demanding perfection also doesn't mean that I expect to agree with everything that is performed. We all have preferences. Someone might hear a phrase as angry while another hears the same phrase as melancholy. Two professionals might perform the same piece very well, but usually I have a preference between the two. There is no perfect interpretation of a piece - that is not part of demanding perfection.
Practicing to achieve perfection is tedious. It takes a lot of repetition of correct playing. But, I also think it is an attribute that, once developed, does not take as much tedious effort to maintain later on. The high school and college years are vital in the development of accuracy. There was a time when I practiced scales religiously for 2 hours a day and I did the penny game (see below) with every solo I worked on. I don't do either of these now, but the time invested doing scales and demanding perfection through the penny game continue to pay dividends in my playing.
A few tips:
1) Have a goal for each practice session. You don't need practice an entire concerto in an hour. Choose one thing to work on and make it perfect. Then, make something else perfect in your next session, and so on... If you string together 10-20 practice sessions like this then you will have your solo learned at a level where you can expect perfection.
2) Don't practice until can play the passage right. Practice until you can't get the passage wrong. This means that once you have mastered a passage you need a lot of continued repetition of correct performances. Another way of looking at it - if you play a passage wrong 9 times and then finally get it right on the 10th try - you only have a 10% chance of playing it right. I guarantee when you show up to your lesson the next day you will play it wrong when the spotlight is on you.
3) Treat the practice room like it is a recital stage. Sure, you are going to have to work out some kinks in your playing. You won't play every second of every practice session perfectly. But, there needs to be a time when you do "turn the red light on" and perform. Imagine that people are watching. Maybe, even bring someone into the practice room. Put pressure on yourself so that when you are in a lesson or on stage you don't feel out of place.
4) Penny game. I learned this from Øystein Baadsvik when I was a student and it challenged me to be as accurate and prepared as I could be. The game is that you put 10 pennies on one side of a stand. Choose a passage and perform it. If you perform the passage perfectly (pitch, rhythm, sound, articulation, dynamics, etc...) you move one penny to the other side of the stand. Do this 10 times in a row, but if you ever mess up you start all over. You have to do the passage perfectly 10 times in a row. This can be a very frustrating process, but it is one that will train you to demand perfection in your playing. It is also a great way to build confidence. After "penny-gaming" a passage you can say to yourself, "I just played that passage perfectly 10 times in a row. There is no reason why I won't play it perfectly on my 11th try."
To sum up, I think all musicians should expect to play perfectly. Just as when Nash and Nowitzki step to the foul line - they expect to make the shot and it is a surprise when they don't. We all need to gear our practice in a way that on a daily and weekly basis we become more accurate players. None of us will ever achieve perfect accuracy, but if we don't strive for it we will never approach it.