Response to Thurston's Article

After Reading Thurston's article I think the main thing I appreciated was his emphasis on communication. Not only in the way we present mathematical concepts but also in a social setting. As Thurston says “Human thinking and understanding do not work on a single track” Different methods of communication benefit different types of people in different ways. I will definitely try to utilize different methods of communicating into my classroom by adding visuals, using metaphors, analogies, and incorporating “motion.” Another point made by Thurston that stood out to me is that its important we don’t assume prior knowledge as this may cause unwanted barriers. Not everyone has the same “mathematical mental infrastructure.” We as teachers need to identify and react to this accordingly by putting a greater emphasis on educating the basics of math and using effective means of communication. Also we need to enjoy the social settings of mathematics! I think too often we get into a narrow minded way of thinking and we treat math as a solo project. We should be expressing our ideas to other people and digesting theirs. Using a social environment to our advantage.

One of the big points that caught my attention was how Thurston implied that most people didn't really care much about the actual proof itself, or rather the results. However it was the understanding that played a greater importance. I’m on the fence to agree if that is still true in an elementary or secondary setting? In my experience, a lot of students just simply want to know the answer :)

Nonetheless I have a different outlook on why we teach and how we should teach mathematics. Putting more of an importance on things that I otherwise would have neglected.