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Having a good practice routine is the key to learning any instrument. The piano is an instrument that is easy to get a good sound out of - just press a key - compared to say a violin. But the sheer weight of notes in piano music makes it hard to learn a new piece, and wrong notes are just the tiniest of slips away.
So you go to a piano teacher, they tell you to start with the right hand alone, then the left hand alone and come back next week.
Then they tell you to practice both hands together. See you in seven days...
Yes, it's coming on a little, you need to practice harder. But what exactly does 'practice harder' mean? They never tell you that.
The key to successful practice to to recognize how the brain works. We learn by doing, and if you do something repeatedly enough times, it becomes automatic. So all you have to do to learn a new piece of music is to play it enough times.
Yes that will work, but only slowly, and you will probably be unable to play the piece all the way through without making mistakes.
There is one 'secret' to successful practice - never make a mistake.
That's right, look carefully at the notes, center your finger on each key individually, and press each key firmly. Go as slowly as you need to to be sure you never make a mistake. Don't start with the right hand - start with the left hand. The left hand gets less exercise in piano playing so it is always weaker, even in left-handed people.
And don't start at the beginning. Mark out a section at the end. Practice that, then work backwards. Otherwise you will learn the beginning well, but the end will always be shaky.
When you feel you are making progress, start to practice the difficult sections more. Choose short sections and repeat them many times. Never go faster than you are capable of without making mistakes.
Press the keys firmly, so that each note rings loud and clear. Contrary to piano teachers' advice, you do not put the 'expression' in at this stage. If you can't play the notes perfectly, there is no point in concerning yourself about the finer aspects of the music. Playing firmly will also strengthen your fingers. You don't need a book of exercises (that probably only covers the white notes anyway).
Clearly though, playing for pleasure is why you are learning the piano in the first place, so you can't neglect that.
But often people will practice first and play for pleasure later. So you end the session with wrong notes. That leaves the brain with the wrong information to process overnight. Effectively, you are learning your mistakes!
So play for pleasure first. That will also give you a guide to where the problem areas are that you can work on.
If you apply this method of practice, you will get startling results amazingly quickly. And you can, if you wish, cut the duration of your practice in half, because now every note you play is part of the learning process.