Arbitrary and Necessary

    This article reminded me of the first assigned reading on relational and instrumental teaching written by Skemp.  I believe that arbitrary mathematical content requires memorization on the part of the student and is primarily instrumental teachings on the part of the teacher. Necessary mathematical content, on the other hand, is about student awareness and is related to relational teachings.

    Since I did not study in English-based education before 18, remembering and understanding math conventions have been a challenge for me at times. Therefore, when planning my lessons, I always try to see the content from the students' perspective first, especially when introducing arbitrary knowledge. As mentioned in the article, covering the history of the content is a good strategy; however, some terms are chosen at random when they were first introduced into an English context. In this case, I think it is helpful to introduce history from other cultural backgrounds. Stories like the mistranslation of rational numbers that I shared in the presentation could help students memorize the mathematical inventions or provide at least something fun to listen to in a math classroom or to share with others later on. 

    As for teaching necessary mathematical content, holding activities to assist students in freely exploring or playing around with math is critical. When planning unit plans, I always try to include at least two activities for a topic. During my short practicum, my SA also inspired me a lot. I am fascinated by Grade 8’s explorations of shapes in 3D in the Halloween cubes activity. Here is a picture of their awesome works!