Hewitt - Arbitrary vs. Necessary

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I really enjoyed this article! I have always enjoyed working things out from a minimal set of given truths or conventions; perhaps this is one of the reasons that I fell in love with math, particularly in university. I just never had the eloquent words of Hewitt: "If I'm having to remember ..., then I'm not working on mathematics". In a sense, this article equipped me with some language and examples to better illustrate ideas that I have been thinking about as long as I've been a student of mathematics.

Reflecting on Hewitt's article will help my teaching practice in a number of ways. Most importantly, the discussion has highlighted for me the domain that I need to focus on improving my abilities as a teacher the most: creating or finding activities/resources that will enable students to learn necessary concepts through awareness, and learning how to conduct better formative assessment to more accurately take stock of students' current awareness levels and mathematical skills/competencies (as well as prior knowledge where applicable). It is also difficult to get students to want to figure out on their own that which is necessary; often, many students just want to be told what the algorithm is, or the theorem, or what the answer to a problem is. These are the problems  that I want to find better solutions for as a teacher.

On the other hand, I think that I already do a decent job of explaining why certain conventions or definitions are chosen by the mathematics community to be the way that they are (I actually make a point of this when tutoring). This is a practice that I adopted rather subconsciously because I hate remembering arbitrary things, so as a student, I would have to figure out why conventions were the way they were in order to remember them. That learning strategy/adaptation just spilt over to my teaching in many ways.

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