I believe that Walter's transformation throughout the play is one of internal growth. At the beginning he's like a child, living in the home of his mother (who is still the head of the family). He may have his own wife and child, but he still acts like a child himself. His own son sleeps on the couch, and Walter still fights with his sister like children do.
Throughout the play, he begins to, ever so slowly, become a man. He starts to challenge his life and what it has become. Sadly, he has to hit rock bottom before he can finally start to take ownership over his own life.
There are a few pivotal moments when we see him starting to emerge, although they are not pretty. When he is talking with George, and George is speaking down to him, Walter knows that this kid is not treating him with the respect he should deserve.
When Ruth tells him of her pregnancy, he does not respond in a way that paints him as anything other than selfish.
When his mother finally gives Walter the money for their...
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