This semester I have been on Long Service Leave, so I am off the hook for teaching, and can spend more time with my graduate students Ali Alkhaldi and Nguyen Le, do some investigations into hyperbolic geometry and related issues, make more videos, and do some travelling. Ali is in his fourth year of the PhD, and is writing up his work on the parabola in hyperbolic geometry, which is now blossoming into a major re-evaluation of this subject, with dozens of new theorems. Nguyen is in her second year, and is making good progress on various aspects of Euclidean and relativistic triangle geometry, at this point related to the Incenter hierarchy.
Another main pre-occupation in the last few weeks is a large LT (Learning and Teaching) grant that Chris Tisdell, Bruce Henry and I have applied for, in conjunction with other colleagues here at UNSW, and some other universities in Australia. The country’s chief scientist, Ian Chubb, has organized a largish pool of money to be allocated to projects that improve teaching of maths and science in secondary schools in Australia, and our project proposes to address this by creating online professional development courses for high school teachers that teach them more mathematics and science.
Teachers are exposed to lots of in-service development that addresses the educational side of things: how to improve student learning, principles of effective pedagogy, teaching strategies etc. But in mathematics I think the greater problem is that not enough high school maths teachers understand the content of the subject well enough. We hear lots of anecdotal stories of Principals hiring Phys Ed teachers to teach mathematics because of shortages: after a quick 6 week training period the hapless new teacher is expected to inspire and motivate his/her students in a subject many of them already find difficult. Clearly not a very good situation.
Our idea is to make some high quality online courses that lay out the new Australian maths and physics curriculum in an engaging way for Years 11 and 12 teachers. The lectures for these courses would be make freely available on YouTube to anyone. With enough resources, we are hoping to put together videos and other materials with cool graphics, animations, demonstrations etc that will inspire high school teachers (and students too).
In addition to these courses, we hope to also organize a (YouTube) video library of Year 9 and 10 maths subjects, also aimed for teachers, that systematically presents the subject in a careful and fun manner. Let’s hope we get funded! If we do, I will probably be spending more time in the next few years making videos and online courses, and less time doing traditional teaching, which would be a nice change. [As you probably know, I like making YouTube videos!]
On another front, I will be heading overseas soon, visiting fellow geometers at the Universities of Innsbruck and Graz in Austria, and then on to Toronto via Florida to visit my family and friends. I will stop at my old alma mater the University of Toronto to talk maths with my friend Joe Repka and others, and I usually give a talk there.
My daughter Ali loves going to Canada, and she is taking some extra weeks off school to make the trip worthwhile. I will try to give her some personal maths instruction to make up for her lost classes, but that is not always easy! Right now we are talking about Pythagoras’ theorem, and I am trying to get her to see that it is really rather remarkable. I think that possibility is not emphasized in school: that we are here witnessing a small miracle: make a right triangle, carefully draw three squares on the three sides (graph paper is essential for this), compute the areas of those squares, and then notice that the sum of the smaller two equals the third. And if you try it with a triangle which is not right, it doesn’t work! Isn’t that amazing?