Teddy doesn't accurately fit any of the Booker plots. The meat of the story is the philosophical debate between Teddy and Nicholson – not any action that we could break down into different stages. Very few things actually happen in this story: Teddy talks with his family, then talks with Nicholson, and then dies (in most interpretations) at the end. The story is about ideas, not plot; character and not events. One can even argue that the protagonist remains essentially unchanged throughout the entire tale. He certainly teaches, but he neither learns nor overcomes difficulties himself.