The Path of a Mathematician: Good Bookkeeping
Among the great many pieces of advice my mother gave me was one that tested my patience. Every Friday afternoon after 4PM, unless I am engaged in a special task, she asked me to collect my thoughts on teaching experience and on new insights into mathematics for the week. “Write it down, save it on a flash drive, put a date on it.” For a person who values his freedom far above discipline, this maternal advice was antithetical to my nature. But immediately I recognized its potential.
For the past two years, I followed this advice on and off. There are many Friday afternoon distractions – sometimes I was at seminar all day, sometimes I was doing my daily laps at the pool, still other times I was traveling and could not avail myself. The collection is not always a weekly recollection albeit they were mostly done on Fridays. It could be a useful observation of the subtlety of students’ cognitive obstacles to a new concept, or it could be a new approach to an old theorem that challenges students and educators alike. All in all, I compiled some 80 entries on teaching and the nature of mathematics.
This past Christmas, my mother reminded me of the “Friday Collections” and asked me if could organize them for publication. As I browse the entries, I began to see the rich layers of thoughts, the structures of reasoning, and the connections within. It is more than good bookkeeping, it is a mathematician’s stream of consciousness – ready to be shared with the other educators. Think of it as an investment in yourself!