If you begin piano by learning to read music you may struggle when you try to improvise: after-all improvisation at first never sounds as good as somebody else's idea you can just read. If you learn to improvise before you can sight read, you may struggle to read music: after-all it's way easier to play something of your own that sounds close enough to the real thing then to relate all those symbols to your hands. If you memorize a difficult piece you may find it easier to play it by memory then when it is put in front of you and you are asked to read it. If you learn to sight read everything you see, you may struggle with memorization. Chord theory sometimes comes really slow to the sight reader too, and good chord readers often feel that sight reading is hopeless. Some sight readers can see intervals but not notes. Some note readers can see notes but not intervals. In each case we can beat ourselves up. How often have I heard “I can play the song but I really don't know what I'm playing.” That is a very pregnant complaint! There are so many ways to “know” what we are playing. The chord reader who can't sight read knows what he is playing in a way that the sight reader cannot, and vice versa. My response is always: “Good, you're playing the song.”
It is unfortunate that most musical methods I've used often force a teacher to be choosey about how a student learns, which right away should give us pause and make us reconsider how much stock to put into method. There isn't one true method or way of teaching that must work for every person, and that is why it is so very important to taylor the method to the student, and not vice versa! I am currently striving vigorously to write my own method that will do just that! In Jazz theory we learn that theory (method) is the study of history, not truth. It is an explaining of what happened, and what could happen again. But the truth is in fact what we play. So lets not get too excited about how one thinks or “knows” a song, particularly if they can play it.
This is not to suggest that the student should rest just on what comes natural to them. The fact is with some effort a good musician can “know” music in many complicated ways. The role of the teacher is to encourage you to see it the other way that isn't coming to you easily. If you like Jazz and pop music, I'll encourage you to also read some classical. If you like classical, I'll encourage you to read a lead sheet. If you can sight read anything, I'm going to push you to memorize a difficult song. If you have to memorize a song to play it, I'll push you to read it. I live by the 40% rule. 40% of my practice time is spent doing what I can't do very well. The rest of the time I get to do what comes naturally to me. I find that after a few weeks, what I struggled with seems to come more naturally. If you can read chords, sight read, memorize a piece, and improvise after-wards I'd say you really know the song. But it usually takes many years to be able to do all of that.
If you are good at something don't beat yourself up for what you can't do so well. Lets instead work a little at that part of you that resists, and you may surprise yourself. If you try and fail and it still isn't coming then forget it and just play the song. That's good enough. We'll try again later.
