Well, of course any work of literature is going to employ a vast arsenal of literary techniques as part of its presentation, and this great short story is no exception. However, if you wanted to focus on one, I would have to pick the way the author contrasts the two...
Well, of course any work of literature is going to employ a vast arsenal of literary techniques as part of its presentation, and this great short story is no exception. However, if you wanted to focus on one, I would have to pick the way the author contrasts the two different worlds of Da-duh and her granddaughter, and the subtle conflict that ensues. The story charts a series of conversations between the narrator and her grandmother where both try to assert the supremacy of their own territory over the territory of the other. For Da-duh, who has never left Barbados, her daughter shares marvels of American city life that she cannot even begin to imagine or understand.
The climax in this conflict comes when Da-duh takes her granddaughter to see the tallest object on the island:
There in a small clearing amid the dense bush, she stopped before an incredibly tall royal palm which rose cleanly out of the ground, and drawing the eye up with it, soared high above the trees around it into the sky. It appeared to be touching the blue dome of sky, to be flaunting its dark crown of fronds right in the blinding white face of the late morning sun.
However, when Da-duh asks if there is anything taller than this wonderful example of creation, the narrator is saddened to have to tell her about the skyscrapers that soar even higher into the sky than this tree. When she hears this, Da-duh initially responds with anger and disbelief, but then, accepting her defeat, she returns with the narrator "triumphant yet strangely saddened" at her victory:
All the fight went out of her at that. The hand poised to strike me fell limp to her side, and as she stared at me, seeing not me but the building that was taller than the highest hill she knew, the small stubborn light in her eyes (it was the same amber as the flame in the kerosene lamp she lit at dusk) began to fail.
So, if you are after a literary technique, this story features a massive conflict between the narrator and the grandmother and the two worlds that they represent. Analysing how this battle is fought and the way it is resolved should give you ample scope for analysis.