02.29.08
In the days of teaching
I had a dream about this last night, so thought I’d blog the memory (of the actual events, not the dream).
About 35 years ago, I was teaching at a small private liberal-arts college and was asked to take over a Freshman Math Tutorial at the beginning of their second semester.
A word about class format: the college used the “Great Books Program”, and Freshman math was devoted for about the first two-thirds to the study of Euclid’s Elements (in translation) and then the Almagest of Ptolemy (also in translation). The tutorial consisted of the tutor (in this case, me) and 10-12 Freshmen (co-ed). The tutor’s job was to ask the right questions so that the students, in discussing the answers and thinking about the implications, would develop an understanding of the focus of study.
In studying Euclid’s Elements, there would occasionally be a general discussion, but mostly a student would go to the board and “demonstrate” one of the theorems or constructions: stating the proposition, setting out a diagram and stating what specifically is to be proved or constructed, doing any necessary construction, and then going through the proof. The student demonstrating could be asked questions by the other students (or the tutor): to clarify a step, to explain why something actually followed from what had been said, etc. Questions such as those were common.
Demonstrating the theorems led to a deeper understanding for all, and provided the student doing the demonstration with useful practice in presenting abstract material, answering questions, thinking on his/her feet, etc.
