According to Hewitt, being arbitrary means that something has to be memorized to be known and is informed by someone else/ other sources such as
TV, books, etc,. However, something that is necessary does
not have to be informed by someone else, and it is learned through awareness
based on the arbitrary things. For example, mathematical terminology, names, and
symbols are arbitrary since students have to accept them the way they are in
order to communicate within mathematical community. However, mathematical
properties and relations are necessary since they depend on arbitrary things
that students have already become aware of.
This idea might influence how I plan my
lessons since I would have to consider how to create/ introduce activities for
students to become aware of the necessary things using arbitrary things. Rather
than explaining problems based on my awareness to students (“received wisdom”),
I would have to introduce appropriate activities for them to find out relations
by themselves. In other words, while helping students remember names or symbols that they have memorized before, I should also help them understand relations and properties/rules better and let them know why things work the way they do. This is because students should be the ones who do the
math in math class, not a teacher.
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