In To Kill a Mockingbird, how does Scout look up to Jem?
For one thing, in To Kill a Mockingbird, Scout talks about Jem constantly. This book is about Scout growing up and she frequently compares changes in her own life to Jem's progression. She looks up to him and she's also empathetic and genuinely interested in what he's thinking. In Chapter 22, just after the guilty verdict, Scout narrates, “I stole a glance at Jem, but he was not listening. He would look up at Atticus, then down at the floor, and I wondered if he thought Atticus somehow responsible for Tom Robinson's conviction” (113). Scout often learned from the way Jem interacted with Atticus and other adults.
In Chapter 4, Scout narrates, “Jem was a born hero” (21). She is referring to his courage in portraying Boo Radley and keeping their game secret from Atticus. This is the most direct statement of Scout's admiration of her brother. Later, Jem would show much more courage in defending Scout from Mr. Ewell.
There are plenty of examples that are less direct. When Jem got to the second grade (Chapter 7) she noted that the only good thing was that she got to walk home with Jem. Overall, the evidence that Scout looks up to Jem is shown by how often she wonders what he's thinking. In fact, when she senses Jem is in a mood, she'll avoid him until the mood has passed. She does not agree with everything Jem does or says but she constantly cross references her feelings and thoughts with her guesses of what Jem is thinking. This preoccupation with Jem might be the initial model of how Scout learns to see things from the perspective of others. It was Atticus who taught her to put herself in other people's shoes.
Scout naturally looks up to Jem. After all, he's her big brother. She may be smarter, and generally more perceptive, but Jem has street smarts. As a streetwise kid, he's better able to look out for his sister. But, he's still an older brother, and older brothers can sometimes be a bit of a pain. As Jem gets older, he starts to assert his alleged superiority over Scout, treating her like a little kid:
"That's because you can't hold something in your mind but a little while," said Jem. "It's different with grown folks, we—"
His maddening superiority was unbearable these days. He didn't want to do anything but read and go off by himself. Still, everything he read he passed along to me, but with this difference: formerly, because he thought I'd like it; now, for my edification and instruction.
But there's more to Jem than meets the eye, and Scout senses this. He's nothing if not courageous. Although, in the case of the Boo Radley game, Scout realizes that Jem's acting tough more than anything else. At the same time, Scout's seems fascinated by what's going on inside that mind of his.
However, as Jem matures over time, so does his courage. And when he saves his little sister from the evil clutches of Bob Ewell, his status as a hero, not just in Scout's eyes but also in the readers', is confirmed.