In the story, the narrator goes into school and doesn't do something that normal school children do, yet leaving school he feels different. How?
After the bell sounds and the speaker leaves school, having said goodbye to friends, he is puzzled because he can find no trace of his father, who had promised to meet him at the end of his day. He is confused by meeting a middle-aged man who he realises that he knows, and then even more shocked by the changes that he sees in his surroudings. Note the rhetorical questions that are used to emphasise the speaker's feelings of amazement, confusion and feeling overwhelemed:
Good Lord! Where was the street lined with gardens? Where had it disappeared to? When did all these vehicles invade it? And when did all these hordes of humanity come to rest upon its surface?
The sights that the narrator sees cause his head to spin and he feels "in a daze", until a young man comes across to him and says "Grandpa, let me take you across", ending the story and clarifying what the reader has by now already guessed - much more time has passed than in the "Half a Day" of the title.