Review the original item:
Professor Britton was grading papers at her desk,
her students were slaving over their in-class compositions, sighing
heavily and flipping through their dictionaries for the correct spellings
of words.
You chose the correct way to fix the error:
Professor Britton was grading papers at her desk while
her students were slaving over their in-class compositions, sighing
heavily and flipping through their dictionaries for the correct spellings
of words.
Professor Britton was grading papers at her desk is a main clause. Her students were slaving over their in-class compositions is the second main clause.
To subordinate the second main clause with the subordinate conjunction while is a perfect way to fix the problem.