Take a look at the original sentence again:
Mrs. 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 to fix it the correct way:
Mrs. 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.
Mrs. 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.