"Arbitrary and Necessary"

• Dave Hewitt’s article related to “Arbitrary and Necessary” forces me to think that math is not about the memorization of the “arbitrary” terms and names rather than the awareness of the “necessary” mathematical knowledge.  According to Hewitt, “arbitrary” are the conventions, symbols, or the names, which we are using in math. I would say the conventions mean the mathematical language. These conventions are just the choices made at sometime in the past. These did not have any proofs or reasons behind their names or their existence.  For example, why we call tangent as a tangent? We cannot prove the name “tangent” because it is arbitrary. On the other hand, when we talk about the properties of the tangent (it is a line, which touches the given circle at one point), then these properties are the “necessary” for the students. They may have the awareness of this fact or the teacher can introduce tasks, which help students to use their awareness in coming to know what is “tangent”.
• In my lesson plan, I would try to relate the necessary and arbitrary. For example, I would relate the words tangent and touch (the line which touches the circle). Hence, from the word touch they can easily relate the tangent. Consequently, if they understand about the tangent then they would continue to explore about the properties of the tangent. My role is to encourage and scaffold the students to use their own awareness.