This is a good question with several possibilities. When your teacher asks you to be specific and original it is probably because the entire novel treats the theme of whether the Governess is insane, or whether the ghosts are playing tricks on her. Moreover, we cannot assume that this is,...
This is a good question with several possibilities. When your teacher asks you to be specific and original it is probably because the entire novel treats the theme of whether the Governess is insane, or whether the ghosts are playing tricks on her. Moreover, we cannot assume that this is, indeed, affecting their reader's perception because there is no way to prove that unless you conduct a study on several readers.
Keeping your line of thought, how about you consider focusing on how specific Gothic elements in the story contribute to the formulation that the main character is in fact insane. For example, the Gothic element of "isolation" is surely a factor that could trigger the exaggerated reactions of the young Governess because her time is wholly invested in the care of the children. Furthermore, when the Governess decides to keep the children in the household altogether with no communication with the outside world, she is actually bringing her own sense of isolation into the lives of the two children. How else can isolation affect her mood, behavior, and logical thinking?
Another Gothic element is the atmosphere of coldness that permeates the environment. Could the eternal winter in the novel be so nerve-wracking that it also contributes to the mental state of the Governess. Is she insane, or merely seasonally depressed? What do her actions say for us to be able to answer this?
Finally, the Supernatural is the ambiguous, and yet pervading, Gothic force behind the plot. The Gothic setting- an isolated manor- could trigger the imagination of anyone who inhabits it. The Governess, young and in charge of two children, certainly must feel the stress of being a mother-figure as well as a teacher. Could the house simply be triggering the Governess's own fantasies? What evidence can we find in the novel that shows that it is more feasible for the manor to be haunted, than for the Governess to be losing her mind?
The three points above should serve as your supporting details and you will find a number of facts that should help you support this main topic.