Who is Perpich and why does Brian think about him in Hatchet?

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Perpich was Brian’s English teacher, and Brian values his advice.

Brian is involved in a plane crash in the Canadian wilderness.  The pilot has a heart attack and dies, and Brian goes down with the plane but survives.  In the beginning, Brian is stunned.  He has nothing with him but a hatchet, and he has to figure out how to survive on his own.

In this time of difficulty, Brian grasps at straws for ways to help him survive.  He remembers the advice of one of his teachers, a man he seems to respect.

Brian had once had an English teacher, a guy named Perpich, who was always talking about being positive, thinking positive, staying on top of things. That's how Perpich had put it—stay positive and stay on top of things. Brian thought of him now— wondered how to stay positive and stay on top of this. (Ch. 5)

It is difficult to stay positive when you are a kid all alone in the wild.  Brian has only the clothes on his back and the hatchet.  He has a few survival skills, but most importantly he has cunning and ingenuity. 

Brian’s teacher Mr. Perpich also taught him the value of staying motivated.  Of course, survival is a good motivator.  You stay motivated or die.

I have to get motivated, he thought, remembering Perpich. Right now I'm all I've got. I have to do something. (Ch. 5)

Brian realizes that no one is coming to save him, at least not soon.  He has to rely on himself.  This requires remembering his English teacher’s advice about life. He must stay positive, because it is easy to get overwhelmed with fear and worry.  He must also keep motivated to survive.  Without motivation he will just give up, and giving up means he will die all alone out in the wilderness.

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