i also need quotes
You don't need people to provide quotes, because you are studying this book in your class. Don't try to avoid spending time with the book. In the days before TV was invented, literature was important for entertainment, and you would have enjoyed it! :-)
how important is an understanding of how christopher thinks to our understanding of the way he acts and relates to those around him?
the teacher wants you to write an essay that explains why it is important to understand Christopher's personality.
What if your little brother has to read this book in a few years? You would have to explain to him why it is important to know how Christopher thinks in order to appreciate the book. You want your brother to be able to appreciate literature, right? So write an essay that is like an email message to your brother, and use a few paragraphs to give examples of times in the story when, in order to appreciate the theme, you need to know how Christopher thinks.
To get you started, google this:
The curious incident of the dog in the night time haddon analysis
Don't forget to enjoy writing the essay! Talking about art and literature are some of the most important aspects of life.