November 6 - Arbitrary and Necessary

 In the article Arbitrary and Necessary Part 1: A Way of Viewing the Mathematics Curriculum, Dave Hewitt argues that a lot of the time in a mathematics classrooms is being dedicated to teaching conventions rather than doing actual mathematics. I have always been aware of this and my approach so far has been letting my students come to their conclusions where conventions are concerned and then I tell them the agreed upon conventions by society. This makes the students realize that their method was perfectly acceptable and a lot less time is spent on memorizing the arbitrary.

One thing in the article that caught my attention was when the author says that by simply telling the students that the sum of interior angles of a triangle is equal to a half turn, we communicate to them that this is arbitrary information. They may or may not remember this in the future. I have had students struggling to remember this piece of information, quite possibly because of this same reason that Hewitt mentions. When I plan my lessons, I focus a lot on the contents covered in that specific unit that sometimes I do not pay attention to  what arbitrary memory informations students are bringing with themselves and if it even belongs in the realm or arbitrary. In my future lessons, I am determined to let students work out on their own the concepts that belong in their realm of the necessary, so as to avoid accidentally letting students simply receive information and potentially forget it right after my class.