2. Is this sentence correct grammatically?

[Mad-ox]

Both Robert Frost, through writing poetry, and the teacher, through teaching poetry, want to determine their admirers to observe the world from different perspectives and levels.

[Tdol]

This doesn't work for me: determine their admirers to observe the world
What exactly do you mean by 'determine'?

[Anglika]

Would "encourage" work better?

[Mad-ox]

by determine I mean "to teach"

[MikeNewYork]

by determine I mean "to teach"

For me, Anglika's "encourage" works great.

[Mad-ox]

I see your opinions. But is the rest of the sentence correct gramatically??

[MikeNewYork]

I see your opinions. But is the rest of the sentence correct gramatically??

Yes, it is a great sentence (with the proper verb).

[riverkid]

You must remember, Mad-ox and other ESLs. A sentence can be complete nonsense with no discernible meaning but it still can be perfectly grammatical.