Most journals are written as personal documents and are therefore written in first person. What's interesting about John Smith's General History of Virginia, New England, and the Summer Isles is that it's written in third person. I assume that's what your teacher is getting at by asking about his style of narration.
If you didn't know it was actually written by one of the characters, you'd think the journal is simply an historical narrative. One of the things my students always find striking about Smith's use of third person narrative is how good he's able to make himself sound in every situation--and he was a bit of a troublemaker, for sure. The General History was not published until many years had passed, giving him time to make all kinds of "adjustments" to the writing and the stories. His most famous story, his dramatic rescue from certain death by Pocahontas, was included in this work. By the time he published his account of this story, both Pocahontas and her father had died and there was no one to either confirm or deny his version of the story.
This third-person narrative style allows John Smith to embellish and praise as he sees fit as he tells his own story as if he were a stranger. Good for his reputation, perhaps, but not so good as accurate history.