I'd seen the movie when I was a kid on the late show and while it wasn't great it had interesting enough things going on in it that I wanted to read the book.
There seemed to be many movies about school teachers in the 1960s. To Sir With Love, Up the Down Staircase, Goodbye Mr. Chips, The Trouble with Angels. Not all movies succeeded, and most critics agreed that Miss Brodie didn't, but the book is a good one.