Arbitrary and Necessary Reflection

    In his article, He tried to explain what arbitrary and necessary are when we’re teaching math. Arbitrary is something that teachers should inform students and students should try to remember, such as terms and symbols or notions that teachers should mention before letting students try to be aware of mathematics. Necessary is something that students would better use awareness to come up with some ideas instead of teachers giving them “received wisdom”, i think proof of some properties is a good example for “necessary” in mathematics that students do not need their memories to figure out.

    After reading his article, I was trying to think about how my lesson plan could also use these two definitions to apply different ways to teach students. At first, I should have a general idea about what arbitrary and necessary mean in that unit or lesson. Then I could decide whether I should tell students the arbitrary part and let them figure out the necessary part or after the necessary part tell them an arbitrary definition. Also, I realized that having (generating) some effective guiding questions are useful for students to have a deeper understanding and be aware of the “necessary” part in math instead of memorizing the “received wisdom”. But, to be honest, when doing the necessary part, it is hard to get our expected result, since students have different levels. Some of them are easier to understand and generate their own knowledge by appropriate activities or guiding questions, but for some students who don’t have a sensitivity for math, the only way they could use is memorizing the knowledge. So it’s also a problem we should solve as a teacher. Teachers should create or change a different activity or question to let all kinds of students be involved. Moreover, As a higher grade math teacher, how students understand math knowledge also depends on their experience in lower grades. If they already know what is arbitrary and necessary in lower grades then it’s easier to adopt in higher grades, like math is also a language, and when you already know the alphabet and apply them properly then you could make a full sentence when you’re in the next level. However, if you just memorize the alphabet and grammar and cannot apply them, then it’s impossible to make a correct sentence in the future. So, it’s tough to let all students know and apply the knowledge properly. As a teacher, we need to use a lifetime to figure out what is a suitable way to teach math and make connections. But this article indeed makes me reflect on my lesson plan and teaching way (or activities) in my short practicum and make me think more about how to change it and make my lesson more meaningful and useful.