I have heard it said that a student is only as good as his teacher; but that has never rung true to me. The Psalmist reaches higher: "I have more understanding than all my teachers: for thy testimonies are my meditation."
I found another quote today that shows the 'how' of a student advancing past his teachers.
"Do not seek to follow in the master's foosteps; seek what he sought." --Vladimir Horowitz, quoting a Chinese proverb.*
This idea fills me with hope. I want to seek what is worthy, and teach my students to reach beyond what I know. I want them to seek the Lord in everything they do, whether that involves finding Him in the expression of a piece of music, or the rationale of a scientific conclusion.
*from _Great Pianists Speak for Themselves, Vol. 1_ by Elyse Mach