Communicating Understanding

What I got most from Thurston’s article is encapsulated in the following line: “The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics.” I could easily identify with the image Thurston describes of an audience getting lost in a colloquium talk within the first 5 minutes and sitting silently through the remaining 55 minutes. I can see how effective communication of mathematics with students has does not depend on how big your words are or how vast your vocabulary is but depends solely on how you are able to connect to students in a way that they can understand. We must be able to see the diversity in our schools: diversity in ability and diversity our ways of learning. Considering this, we should see that the language we use should be understandable by students, not only by you. Furthermore, our teaching must accommodate all learners - visual, auditory or kinesthetic. I enjoyed the example of the various ways that the derivative could be understood and how spending time connecting these ideas promoted a fuller understanding of the topic. 

I must keep this in mind: As I work to become a teacher, I must not forget how a student thinks. Put myself in their shoes and remember what it is like to not know.