No, see, that's telling. Showing would be giving examples of Gwen's drive and intelligence. OK, she has a post as head intern at Oscorp. Why? Do we get any scenes that show off Gwen's intelligence? Hell, I think we get more scenes that involve showing Gwen's, well, stupidity. I mean, she attacks the Lizard with a trophy. She takes the system for delivering the Lizard formula, and rather than tossing it out the window, or hell, DESTROYING IT she hides in a closet and tries to stop the Lizard with... a bunsen burner. I guess if we're supposed to play this character off as intelligent as Parker, there should have been more scenes showing that off. Have them talking in class or something that reflects that. I guess I don't see Gwen as that intelligent in the film.
I see the trophy attack as her being brave, not stupid (though the two aren't that far apart). And she works in the lab, so she obviously knows what the device is capable of, for both good and bad, so trying to save it makes sense. And attacking with the bunsen burner was resourceful. It's better than just standing there scared.