Give piano melodies room to sing while your hands manage the surrounding texture

Andres tutored me through a linear algebra unit on eigenvalues, where I could grind through the characteristic polynomial but had no real sense of what an eigenvector was doing geometrically. Before any computation, he'd have me sketch what direction a vector might stretch toward under the transformation. I guessed wrong basically every time for the first couple weeks. Eventually the pattern started showing up before the math did. He also caught an arithmetic slip on an old exam that I'd assumed was a conceptual error.