My Reflections on the Arbitrary and Necessary Article

 In the categorization of math concepts by Mr. Hewitt, Arbitrary represents the concepts constructed by humans for the sake of common communication, while Necessary represents the concepts which can be naturally derived from the Arbitrary concepts.

The one intuition I have built is that the derivation of Necessary should have very little dependency on the Arbitrary. The Necessary concepts like Pythagoras theorems have been discovered by people around the world at different time and with different culture. Their agreed Arbitrary concepts were likely different.

In light of my intuition above, the focus of my lesson should emphasize on the importance of Necessary concepts. Students should be encouraged to inquire through challenging problems to naturally reach the understanding of Necessary concepts. I am not diminishing the importance of Arbitrary concepts, they do serve a role for communication. However, it will be my goal to introduce the Arbitrary concepts once I can illustrate students the beginning of Necessary concepts. For example, the definition of reference angle should be introduced once they learn through examples of what they are. Typically, I should start with a set of examples to introduce the Arbitrary concepts before asking students to work on them and truly pave the own path to reach the understanding of Necessary concepts.

This approach paves a more efficient way for students to tackle both the memorization of Arbitrary and understanding of Necessary concepts.