I've been teaching for almost 25 years now- hard to believe for a lot of reason. Many people people have profoundly impacted that teaching style, but I'd like to call attention to four in particular for very different reasons. I'll also try to leave a very specific thing I learned from a particular class with the person.
I'll list them chronologically, though I
many of the lessons that I've subsequently learned have come in retrospective meditations. First, I'd like to talk about my undergraduate mentor, Dr. Kunisi S Venkatasubban (Venkat). He, as everyone on this list does in one way or another, taught me the kindness is the most important element of education.
He treated every student with extraordinary kindness and deference. Moreover, if students criticized him or his teaching he always looked for the honest grain of truth in the criticism and took it not just constructively, but jovially. That's an extraordinary quality that too many people neglect- never take yourself too seriously or you will forgot how to take criticism and grow.
Dr. Helena Noronha taught me two important things. First, students need to understand
that you as a teacher are on their side. Sometimes you need to go out of your way to reinforce this. Secondly, you need to help students set goals that take into account where a student is and where she or he can realistically achieve in a short/medium/ and long term and grades out to reflect this progress. Venkat also really agonized over the right grading schema for a class. You don't want it to be arbitrary, but too often we focus on collection of points and exam performance. A really good teacher in a right-sized class can know her students and understand their effort and growth and that is more important than point collection.
Aaron Todd Herbig taught me very specifically about high school students during my time at Stanton Preparatory High School in Jacksonville, Florida. They like to push boundaries because that is generally in their nature so you have to establish rules and stick to them. Moreover, the rules can't be arbitrary, they have to be coherent and reflect standards of excellence. That is a very important point. A good teacher needs to get his students to buy into the rules. A great school needs to make sure they employ consistent rules and that the teachers are genuine role models for the students.
Finally, Dr. Krishnaswami Alladi, has taught me a great deal of mathematics, but more
importantly, he taught me the importance of patience. You need to have patience with your students and constantly encourage them. You also need to have patience with any worthwhile problem. You don't have to solve every problem, but need to be willing to sit with it and let it teach you what you are ready to learn. He has also taught a lot about creativity. This is maybe the most important part of being a mathematician. You need to find the right perspective on a problem to construct an elegant solution. The particular genius that he brings to math though is that many mathematicians understand this- but they focus all their efforts on the most complicated frontiers of mathematics. There's a great deal of extraordinary mathematics hanging around the doorsteps to well-trodden fields that simply needs the right perspective to unlock. In mathematics, we often talk about the low-hanging fruit being well-picked, but I've learned that this is not the case.
I've integrated all of this into a teaching philosophy that is built around examining the student as a whole person and communicating with her or him with kindness. I set high goals and high expectations and I explain those goals and expectations. I think very hard about what a grade often means and what it ought to mean. I work with students to create a path to excellence in a step-wise manner and I explain why this is more important now than ever.