By Chapter 5 of Gary Paulsen's Hatchet, we learn that Mr. Perpich was Brian's English teacher in New York. Though only an English teacher, Brian learned a great deal from him about morale and optimism, two qualities that are essential for Brian's survival. The fact that Brian begins to reflect on Perpich's lessons in this chapter shows that Brian had a great deal of respect and admiration for his teacher.
By Chapter 5, Brian has just woken up for the third time by the lake after the crash. The last time he awoke, he was viciously attacked by mosquitoes and black flies. This time, he is extremely thirsty and hungry. He drinks enough from the lake to make himself sick. But once the sickness has passed, he is no longer thirsty and can think clearly for the first time. His thoughts turn to Mr. Perpich.
As Brian phrases it, Perpich "was always talking about being positive, thinking positive, staying on top of things." Brian also reflects on how Perpich teaches that the way to stay positive is to "get motivated." These thoughts are sufficient to encourage Brian to become enough aware of himself and his surroundings to see what he has that will enable him to survive. He pulls everything out of his pockets and takes an inventory of his possessions. Aside from his clothing and the hatchet his mother gave him that he has looped through his belt, he does not have much to help him survive.
He at first feels desolated by this realization but then remembers another valuable lesson taught by Perpich: "You are your most valuable asset. Don't forget that. You are the best thing you have."
Though his thoughts next become negative as he realizes how far off course the plane went before it crashed, limiting his chances of being rescued soon, Perpich's lessons help him in his time of need. Due to Perpich's lessons, he is able to keep his head on straight, build a shelter and look for things to eat.