Answer: it shows that the narrator knows her feelings of shame are inappropriate.
In this story, the narrator is ashamed of her working mother. She wants to own an umbrella that she saw during her piano lesson, and becomes obsessed with it. Finally, her teacher gives it to her, and she wishes that her teacher were her mother. However, the speaker ends up hiding the white umbrella from her mother. This is likely because the narrator knows that her feelings of shame are inappropriate.