Many skills we learn in and out of school do not translate very well to other aspects of life. However, for me, playing the piano seems to be the exception, and I can show you how.
Since most of us have to learn the instrument here in the former British colony (I live in Hong Kong), I've felt ambivalent towards the piano for a long time until recently, when I took part in a piano competition and came up with my own training schedule for the event.
When I first started playing as a child, I didn't know why I had to play the scales and arpeggios, or why I had to "keep on going" when I made mistakes, but when I practiced the piano on my own, I came to understand why my teacher said I had to do such things.
1) Basics matter.
Scales and arpeggios hone players' sense of progression. Many pieces require nimble fingers that play long flowing passages, which are precisely the sequences of notes in scales and arpeggios. By knowing these notes well, we also become more aware of the different kinds of chords and broken chords used in the accompaniment to enrich the listeners' musical experience.
Being taught calculations before moving on to noticing patterns in mathematics is like learning scales and arpeggios before getting our hands on wonderful musical pieces that amaze, awe, and inspire, like Chopin's fabled Fantasie Impromptu. For students to see the point in learning the "boring" fundamentals first, they need to appreciate what those bricks can build. Of course, it would be best if students could first see examples of beautiful houses -- by this I mean musical pieces, mathematical results, plus other marvellous things -- and not begin the music, maths or some other lesson with painting a fence. We learn effectively when the things we learn are relevant to us.
2) Focus is everything.
Thinking about other things while playing music has often led to more careless mistakes than merely thinking of how to present the music. As leisurely as it appears on the surface, musical performance is rather demanding on the players. We have to be agile and flexible. We need to know the next note to play, the style of playing it, the devices to use, the force to apply to notes, special fingering techniques, and the list goes on. Our capacity for remembering all these little pointers only improves with practice.
We also need to concentrate when we are doing mathematics or learning other things in life, because then we get into what is known as "flow" where everything suddenly clicks and falls into place. Relentless concentration is key to perfection.
3) Keep on going.
The performer cannot go back and change his or her notes without disrupting the show, but he or she can fix the notes that are going to be played, and, provided they excel in the remainder of their performance, they can expect applause in the end. By observation, a musician who keeps playing despite his or her mistakes appears more professional than one who tries desperately to correct them.
Whatever one's vocation is, many agree that persistence is key to success. (No, I'm not saying that one shouldn't check their work in mathematics, because they do need to persist in finding out the most appropriate answer.) Therefore this lesson in music shows us that whatever mistakes we've made, whatever irrecoverable territory we've lost, we are compelled to get on with our lives, to silence the inner critic, to work out our future, and to change the things that we can change. As it says in the serenity prayer:
Grant me the serenity to accept the things I cannot change,
Courage to change the things I can,
And wisdom to know the difference.