Gee, we wish strangers would still give us money for being cute. Or, uh, something like that.
Anyway, while giving out a penny seems innocent enough to Julian's mother, there's a much more dire side to it. A tails side, if you will. (Oh, we will.)
Side one. Heads. Julian's mother saw a cute kid. She wanted to give him something. And isn't the act of giving a sort of sacrifice? Remember that she's going to her Y class because it's free and when she searches for a nickel all she finds is a penny that "shone bronze in the dim light" (101). She's not even rich enough to give him a nickel, so this is actually a pretty nice gesture.
Side two. Tails. It's not hard to understand why Carver's mother lashes out at Julian's mother. From her point of view, white people giving money to black people is nothing more than a continuation of slavery and an assertion of dominance. Yeah, we get it. We can't really contest her view of the thing.
Just like the hat, the penny means two different things depending on which side of the race fence you're on. It's a symbol of oppression and generosity—and, maybe more than either, it's a symbol of the fractured nature of race relations.