Arbitrary and Necessary: Nov. 15th

 Hewitt provides an interesting analysis on the arbitrary nature of many of the ideas and arguments that might be made in a mathematics classroom. Much of what we learn is based on the decision, for one advantage or another, of someone decades, hundreds, if not even thousands of years ago. I also like what Hewitt says about the necessary elements of the mathematics curriculum: "all students will need to be informed of the arbitrary. However, the necessary is dependent upon the awareness students already have" (pg. 4). As a teacher, this informs how my lessons would be planned and especially the type of information that I would want to convey to students. Arbitrary things have to be conveyed to students, they are arbitrary and often there is not much logic behind the choice of one convention over another apart from historical reasons. In terms of the thinking classroom, I think this framework of arbitrary or necessary is a really good way to inform what should be taught in the classroom and how the teacher can ask classroom during practice and production segments of the lesson. It's very important not to simply tell the students what the right answer or method is and instead make them think about what they are doing and why their answer is correct or not, so when you are asking students questions, as an educator you can think about what is arbitrary that they may need to be reminded of, and how you can guide them towards necessary knowledge and understanding.