Recently a student of mine, who tried teaching maths to younger brother, narrated the frustrating experience to me - "its so obvious to me, but he doesn't get it. He just doesn't get it".
This is especially true of Maths. Maths is the ultimate compact way of saying things. Obviously a lot of thought is required to unpack all the thought that is hidden in a simple looking maths statement. A teacher can show what happens when different levers are pulled. But to understand how the Maths-machine works a student has to figure it out for himself/herself. Teacher may use various props to nudge a student to think about the inner working of maths. But for the student, think he must.
Maths demands a lot more "willingness to learn" from a student in that sense. The best kind of maths-teaching is when student does most of the thinking and teacher remains invisible.
Some things can not be taught, but can be only be learned.
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