By Brian Simanek
Many mathematicians, both students and faculty, are constantly looking for ways to become more effective teachers. I have attended TA training sessions but much of the instruction was devoted to rules and policies and not effective teaching. I have also been to conference presentations devoted to teaching mathematics where much of the content was devoted to teaching tools (e.g. MATLAB) or how to help students that are struggling. However, I think there is much to be gained by sharing ideas on how to teach a specific topic.
There have been numerous occasions in my own research (indeed too many to list here) where I have read multiple papers, each of which presents a different perspective on the same topic. It is often the case that I am able to pick one of them and say “Aha, that is the right way to think about it!” It’s not that the other perspectives are incorrect or misleading; but sometimes a single observation or example can provide insight in a way that other presentations cannot. So much of higher mathematics is quite specialized and I understand that the number of people interested in new ways to teach some advanced topics may be very small. However, I believe sharing ideas on how to teach any topic, no matter how specialized, is worth the time and effort.