Quote 1
"I'm wondering what to read next," Matilda said. "I've finished all the children's books."
"You mean you've looked at the pictures?"
"Yes, but I've read the books as well." (1.20-22)
You can't really blame Mrs. Phelps here, for being a bit skeptical about Matilda's abilities. She looks like a five-year-old, so she must read like one, too, right? What's so awesome about this little scene is that we get the sense, early on, that Matilda will keep defying the expectations of her teachers and the other adults in her life. They won't be able to educate her in the way they typically would teach a student. It's a different ballgame altogether.
Quote 2
There was a moment of silence, and Matilda, who had never before heard great romantic poetry spoken aloud, was profoundly moved. "It's like music," she whispered. (16.43)
You can tell that Matilda loves learning and stretching her mind. She doesn't just try to learn things to get good grades or to please other people. Far from it. (After all, the more she learns, the more her parents seem to hate her.) Instead, Matilda likes learning for the sake of learning—it moves her, brings her joy, expands her world.
Quote 3
"I know it's a ghost!" Matilda said. "I've heard it here before! This room is haunted! I thought you knew that." (4.56)
While this seems like a supernatural moment to everybody else in the chapter (the Wormwood parents and Matilda's older brother), it totally has a logical explanation. There is no "ghost." It's a parrot. But, because the other people in the room don't know the logical explanation, they have to believe that it really is a ghost.