For example, I really love chopin etude op 10 no 11, but it's way above my level. So is it recommended to play a piece you really like, but is way above your level? (I have been playing for three years)
Hopefully a personal anecdote as an answer is helpful:
I was forced to take piano lessons when I was young. When I became a teenager, my parents made it my choice whether to continue and I chose to stop piano lessons. I did not find it exciting or fun, it was just pressing keys in a certain order every day and "making music" that I didn't recognize and didn't care about.
At age 19, I had fallen in love with the band Led Zeppelin and just had to try playing guitar. I loved it right away and one of the things that kept me going and learning and playing every day was that I chose the songs and I had fun and did what I wanted. One of the first songs I chose to learn, after playing for only three months or so, was "Under The Bridge" by Red Hot Chili Peppers, which is a very hard song.
In retrospect it took me three to four years before I could really play "Under The Bridge". In the meantime, I worked on it almost every day and I also played around with many much easier songs.
- I was working on music I loved.
- I heard it slowly take shape every day and felt great every time I got even one more note to work than the day or week or month before.
- I was working to emulate a truly great guitarist who demonstrates great touch control, tone, and taste.
- I also had other songs that came along much more quickly that I also loved.
- At one point, I had to quit for about two months because holding too much tension and playing for too long every day was causing me pain in my lower arms. I had to work on my ergonomics and relaxation. I'm not sure this had anything to do with the difficulty of the music I was playing.
Generally, I recommend to my students that they chase what they love, no matter how difficult it seems, but also that they reserve some time for working on techniques and ergonomics so they can play better than they currently play, not just more songs.
A student of mine decided he was going to learn a piece on piano. It's way above his level, and I suggested he left it for a year or so, but encouraged him to have a go, and sorted some tricky parts. Last week he turned up and played, pretty well, mostly from memory. Pedalling needs sorting - he's only just started using it. But, a great effort has paid off, for him, not me, as he managed it without much help at all. He sets himself deadlines, and usually meets them. If only every student was at least similar!
So, in some cases, yes, it's a great idea, if the player has the tenacity to see it through. In others, though, the proverbial brick wall gets in the way, rendering it a bad idea, with a demoralised student.
Only you know which group you are in, but if the latter, there are loads of other pieces that would be far quicker to turn around, until your level is up to the Chopin piece without too much of a struggle.
It's great to set yourself a target. Unless you push yourself, you'll never get better.
I'm a guitar player, and some years ago I decided I wanted to learn "Cavatina". I practised very very slowly for about a year until I reached a point where I could actually hit all the notes. I then found I was being held back by lack of technique, so I went to a teacher to get help with that. Another year later, I had it sorted.
I also worked out my own arrangement of "Take 5" for solo guitar - and then found that it was harder than I could actually play! It took me 2-3 years to get the basic notes down for this one. It is still my test piece for how current my skills are. If I haven't played much for a few months, it'll take me another few months of practise before my skills are up to scratch enough for this one.
The key thing though is practise properly!!! Don't just try to steam through it, miss half the notes, and say "job done". Work at it properly, slowly. Get each note right, and the phrasing right, and the transitions through the passages right. And only when you can hit every note properly, at about one-tenth speed, do you try to speed it up a little. That's how you build your skills up.
While many simplified arrangements of famous pieces are terrible, it may be possible for you to either find an arrangement you like, or study the piece, determine what you like about it, and come up with an arrangement that you can enjoy playing. For Chopin's op. 10 number 11, I would suggest that you replace most of the arpeggios with a couple of notes in the right hand, or (depending upon your skill) perhaps just one the melody note (though adding a parallel harmony part would almost certainly make things sound better). If you keep the arpeggios that fall on downbeats, you could probably end up with something you can enjoy playing that would capture the essence of Chopin's piece.
I play guitar, and I tried out songs that where above my level. I managed to learn a few parts, other parts where still far from perfect, or I could not do altogether. Then I put it aside, and came back a few months later and I recognized that suddenly the whole song, also the former difficult parts became easier, and I progress faster as I am continuing learning the song.
I have not done this on purpose, or this was not a "method", but I had this with a few songs (fingerstyle guitar pieces) I came back later. But you can built a method out of it: You like a song, go for it, practice it some time, some parts you will learn, other might drive you crazy, stick to your song 1-2 weeks (or whatever timespan you like, but I think just one evening will not be enough to make this "effective"). Then after you clearly reached your "limits" step back, practice something different (I guess there is not just one single song you admire...) and come back when you feel ready, and hopefully everything comes out easier and fresh ;)
Side note: Just reminds me as I am writing, as a theoretical computer scientist I am much into mathematicics, and I remember the famous Henri Poincare (one of the core figures behind the ideas made famous by Albert Einstein about space and gravity) once said that he was doing a similar thing with mathematical ideas and problems and beliefs in some "subconscious processing" of them. Google his name and terms like "creativity" and "subconsciousness" to find out more about him and his "psychology of creativity" if you like to.
There is a chance you would then give up and lose interest in the song because of its difficulty. You should find songs that are maintainable to learn, but sound really nice to you.
Someday you will get to that level and play your favourite song, but you need patience :)
Is it recommended? I don't think so. Recommendations focus about efficiency in acquiring skills. Messing around with stuff beyond your paygrade is not efficient. Obsession may often deliver results in the end, but one cannot control obsession. And obsessive work on a good lesson plan will generally deliver more than obsessive work on something inaccessible.
So you won't likely get recommendations about obsessing about something too hard for you. That doesn't mean that it cannot work in some respects. If you do stuff like that, it still makes sense to let a teacher look over it from time to time to avoid establishing bad practices.
That can be tricky since of course a teacher may take it personally when he finds you working more on stuff he doesn't recommend for you to work with than on things he finds sensible at your stage.
Also take a look at good players occasionally in order to see what your work (which tends to focus on producing the right notes in the right order rather than actual music) is lacking yet.