November 5th-Homework reading and response: Arbitrary and necessary

In the readings, students have a question about the number of sides in a square, and the answer of four is reminiscent of a definition from long ago. Because of its four-sided shape, it has to be called a square. This is a necessary condition for students to learn, and it provides essential information to continue learning about geometry.

Arbitrary means that there is no requirement for a particular name. Anyone is free to call based on their own understanding of the thing. However, if something is arbitrary, it affects everyone involved in the same community. However, in mathematics, the term "arbitrary" is very tricky. Students may question some definitions or labels, but these math terms are merely conventions. Within the BC curriculum, some aspects of mathematical knowledge are not required to be known. There are specific topics that, as teachers, we must inform or educate our students about. However, at some points, although it is necessary, it does not imply that all students have the awareness or ability to work it out.

The main difference between arbitrary and necessary is that in arbitrary, it is based on the realism of the memory; students are informed of the arbitrary by someone else. In contrast, necessity is based on awareness; a few students can be aware of what is necessary without being informed by others.

In my future lesson plans and unit plans, it is essential to consider the goal that we want students to achieve first, then work backward to identify what parts of the topic are arbitrary and what parts are necessary. Although mentioned as necessary, it is better to encourage students to discover it for themselves rather than being told by teachers.