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Clarisse is an odd duck by this new world’s standards. She likes nature, she isn’t into violence or TV, and she’s not into vacant socializing. She’s interested in odd things, which is what draws her to Montag – he’s a fireman without the typical fireman qualities. She gets to ask him questions about his job (How long have you been a fireman? Why do you do it?), questions that no one else in his position would ever be willing to answer.
So Clarisse isn’t trying to teach Montag anything. She’s trying to learn from him. It’s just that her constant questioning ends up pushing the already-doubt-ridden fireman over the edge. Clarisse never tells Montag what to think; she just shows him that thinking is an option. She invites him to do it for himself, and he walks through the door she opens.
Then Clarisse dies (we think). What’s up with that? It could be that, in this world, a girl like Clarisse just can’t exist. She’s incompatible with her surroundings, so she’s not allowed to live. We don’t know all the details of her demise, nor is the confusion reconciled by the end of the novel. But we can’t help but think of Clarisse when Granger discusses the thumbprint on his mind left by his grandfather. Even after her disappearance/death, Clarisse continues to affect Montag. She exists because she changed his mind, whereas someone like Mildred hardly existed at all.