Hewitt describes something as being arbitrary is was given through external sources such as teachers, books, the internet, etc. To be learned, it must be memorized and when a person is challenged by the question "why?" to that arbitrary knowledge, they are stumped.
Necessary aspects of math are things that can be figured out on your own, unlike the arbitrary aspects. Using prior knowledge, new information and concepts can be worked out to be true because of the process one goes through.
I think it is problematic if students start seeing all math concepts and terms as arbitrary. When students stop questioning and stop being curious about the "why", math becomes abstract and meaningless. Students can't make personal connections to the material they are learning and this may negatively affect their understanding and interest. I believe it is important to constant question students' thinking process when looking at math concepts and terms to encourage inquiry.
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