I never thought I would be on the other end of the classroom. Prior to this endeavor, my confidence in my abilities to explain otherwise unknown concepts to non technical audience was marginal at best. I did have some odd experiences tutoring students as a grad student though.
I happened to tutor a very good septuagenarian friend of mine for a graduate control systems class. He ended up securing an A in the course and did much better than some of his classmates who were the age of his grand children. Sometimes you realize that the only prerequisite for being a good student is the willingness to learn. And age has nothing to do with one’s ability to grasp new concepts and apply them to new scenarios. This friend of mine was so old that last time he was in school (1960s), logarithmic tables and slide rules were the pinnacle of computational power (not even handheld calculators). I also found out that he was a fellow alumnus of IIT Madras. I applaud his perseverance, hard work and above of all willingness to learn from any source he could find.
In my limited experience as a student and a professor at different parts of my life, I have my own assessment of my teachers as well as my students. My ideal teacher needs not be all knowing, he/she should be well aware of their boundaries of knowledge and should not shy away from saying “I am not sure” or “Let me find out more and get back to you”. I have always expected inspiration and guidance from my teachers rather than exhaustive coverage of what needs to be taught. Methodical and exhaustive coverage of syllabus is a good starting point. But I always expected something more from my teachers. I wanted them to show a glimpse of how impressive you can be after you master the subject matter. Leading by example is always more effective than leading by command. My first computational fluid dynamics class comes to my mind.. in the first class, the professor pulls out his laptop and starts writing a incompressible flow solver for a very specific case. He was writing code extemporaneously in a python prompt. Once he was done, he scooped all the lines into a script and made it a python program. This demonstration was deeply impressive, and gave the students a skill level to strive towards. Keep in mind that planning and teaching a class is a laborious task in itself. But including an extemporaneous activity with inputs from students is exponentially more complicated and keeps students involved in the class much better than sticking to n-pages a day teaching plan. I have noticed that all great teachers inspire the students to learn more than what is taught in a classroom setting. They leave some questions unanswered in the class to keep the student’s curiosity primed. Don’t misunderstand my notion.. I do not advocate leaving a student’s questions unanswered. Best efforts to answer the questions with the scope of the class need to be made. But sprinkling some details which are beyond the scope is always a delightful addition which primes the student’s imagination.
I have been fortunate enough to have had some great teachers during my graduate and undergraduate school. Though I was more appreciative of them in my grad school. All of them cant be great… some were marginal and some I consider unsuitable to teach. Funny enough, I was never critical of my teachers in undergrad school. Grad school was a different ball game… I butted heads with a couple of professors due to disagreements on what was taught (All of them were fair… I did not lose my grades because of my disagreements which were sometimes in front of the whole class).
Even though I had a clear picture of the kind of teacher I wanted to be, nothing could have prepared me enough for a live class. I wanted to try something new for my first class. It was an Engineering Statics class for freshmen and sophomore Mechanical Engineering majors. My first class started with introductions of all the students and I moved onto a brief synopsis of the course material and the course plan for the rest of the semester. I did not want to dive right into the subject matter on the very first day, since I knew most students would be absent for it. Instead I decided to teach them a test topic which is not a part of the course in order to familiarize myself with the class and find out their level of understanding. ‘Tensors’ was not my first choice for a class of undergrads. But it turned out to be a great exercise in teaching a one-off topic which is closely related to the subject matter. Since the very next class involved basic vector operations like addition and products, a generalized definition of a tensor would give them a bigger picture, while they studied vectors. This first class showed them what vectors were among other entities, and where they stand in grand scheme of things. I also threw in a bit of historic trivia, and showed them Einstein summation notation. This first class definitely got some mixed reactions from students.
Through the rest of the semester, I dedicated a portion of the class to extemporaneous solving of statics problems. The students were free to pose an unsolved problem from the textbook or elsewhere related to the course, which I would solve in real time. I considered this a very important part of the course, where the students learned how one tackles a problem. In my opinion, this helped them see how you solve a problem without resorting to a algorithmic cookie cutter approach. This also shows how to approach an otherwise unknown problem starting from known information. I hope this was the part that I led by example.
I look back at teaching as a very fulfilling experience. It taught me how to have a dialogue with and pay attention to a group instead of one individual person. I have improved greatly in my ability to spontaneously respond to questions and perform calculations in critical situations when all eyes are on me. I definitely miss my students… my audience for extemporaneous problem solving. Most of all.. I miss being a teacher.