Arbitrary vs Necessary Article

"All students will need to be informed of the arbitrary. However, the necessary is dependent upon the awareness that the students already have"
Arbitrary facts are things that a student would not be able to figure out on his/her own. Necessary facts are things that a student MIGHT be able to figure out on his/her own. Certain conventions, such as the (x,y) placement of coordinates on the Cartesian plane, are arbitrary. A student would not be able to come to the same conclusion on his/her own. However, a student might be able to figure out a calculation of a side length of a triangle without guidance from a teacher; this is a necessary fact, according to Hewitt.
In a particular lesson, deciding what is necessary depends on any particular class on a given day. The arbitrary things are probably things that I don't even really know why the convention is there, or how to explain. The arbitrary stuff, I will "do the math", and teach explicitly. The necessary stuff, I will guide the students into figuring out themselves. That's the plan, at least.