I think the right environment can bring out your best talents, making you appear 'genius'. Some people can be true geniuses but never have it brought out.
For example: Mozart was brought up in a musical household.
It's an awful way of testing intelligence. All it really shows is how good you are at IQ tests.
If you're intelligent, you'll have something more important to show for it than a stupid IQ test score.
Seriously .. I do not think Genius can be taught, I think genius as such, as a concept could only be genetic or inherited (possibly) or something a person is born with.
What I think a person can be taught are some super skills or performance, maybe an Application of their Genius so to speak. I think a person can be taught to use their energy, their potential, their skills and abilities more or less to the maximum, or be stimulated into doing that, they can probably be guided towards channelling their abilities that way or to that level.
So like.. in a way, I think Genius can be assisted or its application enhanced if you like.
But also - with respect - what is Genius anyway? (not trying at all to diminish this concept or such people). What constitutes it? How is it defined? Is it somehow different from Talent? Or the same?.. Anyway, something to think about too probably.