An expert is one who synthesizes fundamentals into a seamless whole.
But as learners, we all start with the fundamentals. When a little kid sits down at a piano, he learns to play the individual notes, and how each of them sound. A budding chess player learns about individual pieces and how they move on the board.
As they progress, musicians think about notes in relation to one another. They learn about intervals – the spaces between the notes, and chords – the harmony of several notes played together. A seasoned chess player evaluates a position not based on individual pieces, but where they placed on the board and how they work with each other. For a chess Grandmaster looking at a single configuration on the 64 squares of the chessboard is equivalent to a beginner looking at a piece in isolation.
Once experts become teachers, they have to move from synthesis to analysis. The way masters construct chord progressions or evaluate chess positions can appear mystical to their students. They need to step back to the fundamentals and explain to their students how they put things together.
The mark of a great teacher is to move from analysis to synthesis like descending a staircase and guide a student through every step of the way.
Inspiration: The art of learning – Josh Waitzkin