What type of homework could be interesting to study the elements of gothic literature?
The posing of the question makes me think that you are looking for Gothic literary assignments which students would find interesting. Therefore, this is the way the question will be addressed.
Gothic literature is a genre which encompasses the darker, irrational, and frightening side of literature. Famous Gothic writers are Mary Shelley (Frankenstein), Edgar Allan Poe ("The Raven," "The Tell-Tale Heart"), and Horace Walpole (The Castle of Otranto). Depending upon what Gothic text is being studied, the following assignments can be given.
-Frankenstein: A Comparison--Have students compare and contrast the novel to one of the films.
-Frankenstein--A Metamorphosis--Have students follow the media's representation of Frankenstein's monster over time.
-The Tell-Tale...--Have students create a new story based upon Poe's "The Tell-Tale Heart."
-Poe Animated--Have students act out physically or make a film of one of Poe's stories.
-Otranto's Giant--Have students create a visual of the giant.
If you are looking for assignments which address Gothic literature without being tied to a text, you could have students watch a horror/scary movie and identify the Gothic characteristics the movie includes.