Louise Chumlig is a freakin' rockstar.
Okay, she may not look it or sound it. And she sure doesn't get the respect and reputation she deserves: Juan notes that she used to teach at the smart school but "well-documented rumor held that she just couldn't keep up" with the smart kids, which makes her a failure (4.97); and when Xiang mentions her to Miri, Miri's thought is that Chumlig is fine "for the boneheaded classes" (13.64). So yeah, all the teenagers agree that Chumlig isn't so great; and Robert thinks she's a cretin at first. And really, she doesn't show up all that much in the book and she doesn't get any POV sections. So why do we say she's a rockstar?
For two reasons:
"And the amazing thing was, she'd done it in a short pause, when everyone else thought she was just looking at her notes. Juan eyed her with new respect." (4.126)
Now, if Chumlig said, "I deserve respect," we could ignore her. So this respect from Juan makes us reconsider her more… because it comes through someone else's POV.
Similarly, when Robert comes around and realizes that Chumlig isn't a cretin, it's more meaningful coming from him. (It also shows that Robert isn't such a jerk anymore.) He recognizes that she did a good job organizing the students' demos at the end—that she's "exercising each kid to his or her limits."
What really surprises Robert (and us, because again, Chumlig didn't have a POV section where she could reveal this) is that she seems to have known all along about Robert's condition:
Chumlig looked up at him, a crooked smile on her face. She held on to his hand for a moment.
"You! My very strangest child. You were almost the reverse of the problem I had with the others."
"For everyone else, I had to make them reach out to learn what they were. But you... first you had give up what you had been." Her smile was fleetingly sad. "Be sorry for what you lost, Robert, but be happy with what you are." (34.28-31)
So Chumlig—who everyone thought was a failure, cretin, just good enough for the boneheaded classes—Chumlig secretly knew all this time what every one of her students needed. What's even more striking about her is how laid back she is about all this.
Rabbit would form a parade with marching band to say how great he is, but Chumlig denies responsibility and says, "I just showed my students how to use what they have and what the world has" (34. 26). She's not just smarter than she lets on—she's nicer too.