Article Reflection: Arbitrary And Necessary

Article Reflection

1) What does Hewitt mean by "arbitrary' and "necessary"? How do you decide, for a particular lesson, what is arbitrary and what necessary?

In his article, Hewitt describes the terms "arbitrary" and "necessary". By arbitrary, he means this is something that a student learns and is told to memorize. There aren't good explanations for these things that would make sense to the student so they are always told to memorize. Necessary refers to something that a student would be able to figure out on their own. These are things they could teach themselves with the proper "awareness" - proper background in order to understand and answer these questions.
In order to decide what is arbitrary and necessary, it is important to note what you intend for the students to know and learn by the end of the lesson. Once you do this, you can split the points into either arbitrary and necessary based on whether a student would be able to figure it out on their own through "awareness", or whether they would just need to be taught it and told to memorize it.

2) How might this idea influence how you plan your lessons, and particularly, how you decide "Who does the math" in your math class?

This idea is a major component that can be considered before creating a lesson plan. It is important to understand which parts of your lesson will be merely "memorized", and which parts will force the students to think for themselves and figure out the questions on their own based on the background they have been taught. When the teacher is deciding which aspects are necessary, those will entail students "doing the math", whereas arbitrary aspects will just entail memorization.