Tonight I listened to a recording of a lecture given by the late Irving Kaplansky, who was a mathematics professor at the University of Chicago from 1945-1984. The lecture, entitled "Fun with Mathematics: Some Thoughts from Seven Decades", is a fascinating combination of personal anecdotes/memoir/autobiography and advice on how to do research and advice on how to be successful in general. The lecture is available from the Mathematical Sciences Research Institute site.
The four main pieces of advice that he outlines are:
I. Search the literature (he spends a lot of time on this topic and much of what he says has probably changed in the past few years with the introduction of Google Scholar)
II. Keep your notes (write a bound notebook and date your stuff)
III. Reach out (talk to people)
IV. Try to learn something new everyday
R. L. Moore
During the lecture, Kaplansky mentions R. L. Moore and his teaching style. Moore discouraged literature search by his students. He wanted them to be able to come up with everything on their own, even if the work had already been done before. I did a quick Google search for Moore and found the main site at the University of Texas. The methodology is called Inquiry-Based Learning (IBL) or, sometimes, Discovery Learning. The concept is that the instructor guides the students to develop the concepts, solve the problems and create the proofs themselves.
Fascinating! I really like this innovative teaching concept and the way it ties the teacher and student together more closely than the typical lecture does. There's lots of material on this method on the UTexas site that I'm going to delve into. I think part of the reason I'm writing this blog is because I feel like if I can say something back in my own words, I didn't really learn and understand it in the first place. Or, as Richard Feynman is said to have said "What I cannot create, I do not understand."
A good background article on Moore and his method was published in 1977 in The American Mathematical Monthly (vol. 84, No 4, pp. 273-278) by F. Burton Jones. It's available on JSTOR via the Depaul online library.
My initial take on the Moore Method is that it works well in courses in which the main focus is development of a system of theorems, starting from a set of axioms - like geometry or topology. However, for branches of applied mathematics such as statistics, the implementation of the method will not be as straightforward. However, I've briefly seen an article (I think it was a PhD thesis) on applying the Moore Method to teaching calculus. If it can be used to teach calc, it can be used for stats!
And the reason I was listening to the Kaplansky lecture - in fact, the only reason I had ever heard of Kaplansky - is because he is the father of one of my favorite singer/songwriters, Lucy Kaplansky. If you want to listen to some of her songs on YouTube, check out the playlist I put together. In addition to being a top-tier mathematician, Irving Kaplansky was also a musician and wrote a song about pi entitled A Song about Pi. I heard Lucy perform that song on a radio event that was recorded in Chicago this summer. It's very cool. I'm anxiously awaiting the release of the CD from that performance.
Sunday, January 27, 2008