a teacher's idea

A goes with teacher’s: it’s a teacher’s + idea (not a + teacher’s idea), so a teacher’s is a noun phrase functioning within the structure of the larger noun phrase a teacher’s idea.

then what should should is to refer to idea

a idea of the teacher ?

navidre a teacher's ideawhat is 'a' referring to ? teacher or idea or the context clarifies this

Context will usually make it clear.

"Mainstreaming autistic children is an administrator's idea, not a teacher's idea." (The article goes with "idea".)

"A teacher's idea of a good day is one in which nobody bites her." (The article goes with "teac

navidrethen what should should is to refer to idea
a idea of the teacher ?

I can’t understand this. You’ll have to be clearer.

enoon"Mainstreaming autistic children is an administrator's idea, not a teacher's idea."

Still goes with teacher’s.

It seems quite an interesting question. I don't personally see how it can go with (just) "idea". I think the choices are "teacher" or "teacher's idea". In cases where "possessive noun + noun" is strongly bound, it seems the article can apply to the whole thing, as in "a rat's nest". I'm not sure how possible that is with "teacher's idea".