I taught a student a math lesson for the first time in a year.
What I noticed:
1. He was just as quick to pick up on the concepts as students always have been. Me having lost degrees of my touch did nothing to blunt the simple elegance and effectiveness of presenting Math as a language.
2. Today I lacked a long-term vision about where to take this student.
3. I need to speak regularly with people who are also interested in the subject of math -- either teaching it or learning it.
4. My work is no longer one-on-one. If it isn't expanded to something much broader than that, it is dead.
5. The basic tenets of mathematics really can be taught in a matter of months -- it is the presentation of their application that should fill up the majority of a child's educational time. Heavens -- who studies French or German for 12 years? For how many does basic conversational proficiency in Russian require 10 years of regular study?
MATH IS A LANGUAGE, PEOPLE.
6. Words do not give a person understanding of a concept -- experience gives understanding. Words provide tools to communicate and share, especially in the absence of present experience (not the absence of experience at all -- without experience, words can never anything other than sound). A child feels hunger, sadness, and happiness long before it has words to describe them -- language does not teach them how to feel, but how to communicate our feeling -- how to experience feeling in a context over which we have some control, some perspective. Words (spoken, gestured, or quantated) never take the place of experience, but the broader our vocabulary, the closer to real experience hearing becomes -- the greater the likelihood that our hearing the word approaches to experiencing the meaning the word is meant to convey.
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