Would it be acceptable if I omitted 'written' (between 'poems' and 'by') in the following sentence?

Would it be acceptable if I omitted 'written' (between 'poems' and 'by') in the following sentence? 'Poems written by the students' and 'poems by the students' mean the same thing, don't they? Have I correctly used 'required expectations' (which refer to the professor's criteria for judging a poem)? 

If the poems written by the students fall short of the required expectations, their teacher will definitely frown at them.