Miss Brodie is a spinster school teacher at an exclusive school for "young ladies" in Scotland (The Marcia Blaine School for Girls). Her fiance has been killed in World War I, so Miss Brodie has devoted herself to "her girls" - the Brodie Set, as they are called. She is a non-conformist teacher who believes the curriculum at Marcia Blaine is dull and boring, so she teaches her girls much more exciting things - like theatre, poetry, history, art - all with a flair for the dramatic. The girls learn to pretend to be doing "maths" or some dull history lesson when the headmistress walks in, when in fact, they are studying something much more avant garde and exciting.
She is also non-comformist in her personal relationships. As a single, female teacher at a girls' school in post WWI Europe, she would be expected to be prim, proper and chaste. Miss Brodie is none of these things. In fact, she has sexual relations with two male teachers at the school, one of whom is married. She is fond of telling her girls that she is "in her prime" which has much more of a sexual meaning than the girls realize at first.
Miss Brodie is also somewhat nonconformist in her political views. She is very naive. She admires the order that she sees in the fascist countries of Spain (under Franco) and Italy (under Mussolini), but is apparently ignorant of the oppressive nature of such governments. While the rest of Europe was looking in fear at the rising powers in Spain, Germany and Italy prior to WWII, Miss Brodie has just the opposite views of these regimes, which ultimately proves her undoing as she is dismissed from her position because of her views.
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