What excites about teaching is the organization and presentation of ideas. It always seems like I learned this stuff the hard way and I want to explain how easy (and fun) it really is. There is some self-delusion in this attitude – usually everyone has to learn the hard way – but a little self-delusion can be useful in teaching. Michael E. Gage in Goergen Teaching Award Essay September 1998
In these opening lines to his Georgen Teaching Award Essay, Dr. Gage hits on one of the main pleasures that I too get from teaching, and on the same trepidations.We really do want to make it “easy” for the students. I think this is because we care for them and genuinely want to help. After all we are face to face with them for an entire term or more. More cynically, otherwise they could just read the text or access someone else’s lectures online. The “stuff” is easy for us because we have years of experience trying to teach it to students, exchanging ideas with colleagues, and writing outlines for lectures. When we see a “new” organizing pattern for a series of lectures, our pleasures are similar to seeing a pattern in a mathematical structure. We just don’t have to find a proof. There is also pleasure in finding a style of presentation that suits us and works for students. This pleasure derives from having a “good class” but also from the coherence of the ideas now embedded in our brains. I have gotten pleasure from teaching socratically that is from building a story starting from very basic concepts and ending with a naturally occuring algorithm and from a neat set of a color-coded two-dimensionally organized lecture notes built with Microsoft One-Note and even from from the “dramatic” arc that the typical structure of a beginning statistics course has.
Self-delusion is self-evident. Easy for us is not necessarily easy for students. People have different models in their heads for the same concept and the one we have is probably not the one that they eventually develop for themselves. After all their backgrounds are different – different scholastic background, different culture, different generation. You name it. Here is where compassion and patience come in. Students can not instantly apprehend the material as we do now and certainly not communicate their understanding as well as we do. Otherwise they wouldn’t be students. Generally they are not at the same level of adult development as we are and we can only force the issue so far. It is very easy to write questions at an intellectual level that students are not ready for or grade them as if we were reviewing a PhD thesis for publication. This is the self-delusion of the “Why aren’t they just be like me?” type.
At the level (basic algebra and precalculus) where I teach, my efforts in new “organization and presentation” must confront 400 years of mathematical practice. A study of the historical development of algebra is enlightening. Some of the methods were adopted just to save paper, or because the students then had a no choice but to be good at arithmetical algorithms, or because the notation happened to have been invented first. And the curriculum reinforces itself. The order of topics in an intermediate algebra text builds toward deriving the quadratic formula for instance. My self-delusion says that there is a “simplier” way but but I need to temper by enthusiasms with some cold facts. My students will see and be expected to use the old normal methods in their succeeding classes. If they need help, no one but I can help them with the new algorithms that I have taught them.
One last mention of self-delusion. We necessarily give ourselves or at least our subject a level of importance in the classroom. Yet we are just one of three or four or five professors this term and the class is just one of the many demands on a student’s time. I try to keep this in mind when I devise makeup policies and homework loads.