Presentations based on my sabbatical work in 2012
In March I spent a month at Quest University in Canada teaching a mathematics course for liberal arts students. Quest students do just one course at a time, with each course squeezed into a three and half week block, so I had the whole course to myself. This style and the actual course content was all new to me, so it gave me a chance to re-think how I teach my own courses. I was particularly interested in how Quest promotes active learning among its students. On my return to Canterbury I gave a seminar about the way Quest achieves better student engagement.
Quest for engagement (PowerPoint slides, 1.3MB)
Teaching linear algebra: experiments and written reports
In November I talked to the 16th Haifa Matrix Theory conference in Israel. Here I tried to convince an audience of research mathematicians that students will achieve deeper learning of their favourite subject if the mathematicians enrich their traditional definition-theorem-proof style of exposition by letting the students engage in computer explorations followed by written reports on the results of the experiments. (This is a continuation of joint work about teaching linear algebra with Mike Thomas, from Auckland, and Sepideh Stewart, formerly from Auckland and now at the University of Oklahoma.)
Learning the language of linear algebra (PowerPoint slides, 150kB)
History of algebra: diagrams, the binomial theorem and induction
In December I talked to the New Zealand Mathematical Society's annual colloquium in Palmerston North. In this presentation I discussed joint work with my colleague, Clemency Montelle, and our student Sanaa Bajri, about the 12th century Islamic mathematician al-Samaw'al and his possible use of mathematical induction in his proofs of two algebraic results, including what we now call the binomial theorem. My theme was that al-Samaw'al's algebra would have been very difficult for his readers to understand, because it is written entirely in words, but that the proof would have been much easier to understand if readers follwed the diagrams he supplied alongside his proofs. It seems that these diagrams almost made up for the lack of a symbolic algebra, which was not invented for another 500 years.
Diagrammatic reasoning in pre-symbolic algebra (Presentation PDF slides in black with my commentary in red, 400kB)