It is particularly interesting to examine the stage directions of this section of the play, as it reveals crucial information regarding the conflict that Walter is experiencing and how he makes his decision. If we look at the way he is described as acting towards the beginning of the conversation with Lindner, we see that he is walking "slowly and awkwardly, rather like a small boy, passing the back of his sleeve across his mouth from time to time." Having just lost the remainder of the inheritance thanks to his own foolishness and naivety, and planning to accept the money from Mr. Lindner as a way of trying to regain that money, Walter is literally described as having regressed. He is not a man, and only appears as a child.
However, it is when Mama openly challenges Walter to show his son what kind of a man he is that he begins to "man up." Note what Mama says to him:
And you make him understand what you doing, Walter Lee. You teach him good. Like Willy Harris taught you. You show where our five generations done come to.
Mama in particular makes him think about what he has learnt from the steadfast hard work of his father and his father's father, and how accepting Mr. Lindner's offer would represent a slap in the face of all of this legacy. As Walter begins his speech to Mr. Lindner, he continues to be presented "really like a small boy, looking down at his shoes and then up at the man," therefore metaphorically rejecting his ancestors' efforts to achieve self-respect and equality, until he mentions his father, which makes him look at Mr. Lindner with "sudden intensity" and begin to stand up for himself. Therefore Walter's decision to reject the money is a symbol of his maturity and becoming a "man," the man of the household that his father was.