In "The Whipping," we can assume something that we normally should not: The speaker is the poet. The transition from the use of the words, "the boy" and "him," to "I" and "my" in the middle of the poem illustrate this fact. This is an important change. The poet makes us take notice of the story through the different point of view. Normally, this change would be seen as an error, but in the case of a poem, in which every word is carefully selected for its meaning, this change is extremely significant. Further, Hayden goes back to the original point of view at the end. It's almost as if he slipped in letting out the fact that the subject of the beating was him.
If you're looking at the poem from the biographical approach, then you can make this connection and support it using the rest of the poem. The old woman becomes Hayden's grandmother; the woman who "leans, muttering against a tree" becomes his grandmother muttering against a tree. Using a biographical lens, Hayden is the speaker who has suffered the beatings of his grandmother.