According to Hewiit, arbitrary facts of mathematics are similar to postulates. The facts and concepts with which we assume to be true but which you need to be taught before you can thoroughly explore any deeper meaning within. They are concepts which must be stated and are not able to be found, and are not consistent through different frameworks.
On the contrary, necessary aspects are, according to Hewitt, those facts and ideas which can be constructed through our arbitrary concepts. These are things which everyone will find to be true when based on the same framework of arbitrary ideas and through which are able to be known without being told. They are able to be 'discovered'.
His idea is obvious in retrospect, but makes you become aware of something important in the classroom. You need to teach arbitrary ideas and let the students become aware that these are not capable of being discovered and need to be memorized. This will avoid frustration when students don't understand the idea or can't reproduce it. In addition, you should let them see which ideas are necessary and show them the steps to creating them using your arbitrary set of ideas.
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