What Makes For Really Good Teaching?

I’ve had several good teachers, but a few of them were really good. I often think about separated the Really Good from the merely good.

The first Really Good teacher I had was before I went to college. His name was RN Arora, and he was an expert assassin of maths anxiety. This is what he would do: he would ask a maths problem, and give us a few minutes to take a jab at it. Immediately, our minds would get to work. Some students would stare at the whiteboard, deep in contemplation. Others would scribble furiously in their notebooks. Since the problem would always be at the border of our competence, and our minds always eager, restless and seeking instant gratification, we would be inclined to give up after a feeble first attempt, thinking the solution beyond us.

This habit, of letting self-doubt get the better of us when it shouldn’t, is what RN Arora would then take aim at. “Tum log analyse nahin karte…” (You guys are not thinking, analysing!). This would make us meditate onto the going-ons in our mind. We would realise that our minds had slowly drifted, from the ego-less, vast mathematical space of the problem, to the anxious, inward-looking worry of whether we were capable of solving the problem at all. A few more minutes would then pass. If a student got to the answer, RN would ask them to reveal their insight. If not - which was often the case - he would siddle to the whiteboard, raise his marker, and, with a mischievous glint in his eye, write down the first step of the solution. “Agar main yeh karoon toh? (“Here’s a thought. What if I do this? Will it help?”). That would be enough to nudge us in the right direction and get us going. Ask, not tell, was RN’s mantra, and the mantra of all really good teachers I’ve had since.

While good teachers would focus on the syllabi and the nitty gritties of content, Really Good teachers pose questions, and join the students in the search for possible answers.

Oxford’s tutorial system is designed around this. One of the things that struck me while writing essays at Oxford was how simple and jargon-free the questions used to be. One could pose them to someone who is still in high school, and they would still understand the gist of it (To answer it well, though, was another matter).

When it comes down to it, all knowledge is not equal. Some of it is timeless, some of it is a fad. Really Good teachers distill knowledge which is timeless from knowledge which is a mere fad. The reading lists curated by tutors at Oxford included some of the finest writings by some of the finest thinkers on a subject. It made a real difference. In the same spirit, the computer science (CS) professors at IITD would dismiss the technicalities of programming (languages, frameworks, best practices etc.) as irrelevant in the larger scheme of things. It is the thought that matters, they would say.

One of my Really Good teachers was Naveen Garg, under whom I studied Algorithmic Game Theory, did a minor project and also my masters thesis. Instead of covering the syllabus in the form of polished, finished, well-presented material, he would ask basic questions, and then walk hand-in-hand with the students as he sketched out the answer.¹ Sometimes he would make mistakes himself, retract, and then continue. It didn’t matter: even dead-end paths and fallacious reasoning were something to be learnt from.

While good teachers often present material as-is, which often looks impressive and sophisticated and intimidating, Really Good teachers deconstruct sophistication. Often what looks complex on the surface is made up of simple thoughts layered over simple thoughts.² A particular concept might look complex and intractable, but in the end it was thought of by people very much like you - and Really Good teachers like Naveen Garg make you feel like you could be one of them.

Not all my teachers were like that. I once studied under someone who made me realise I was not cut out for their trade. His name was Domotor Palvolgyi, and he was trained in the Hungarian approach to mathematics. The course he taught was Combinatorial Geometry.

In his first lecture, the grading scheme was announced: at the end of each lecture there would be a homework problem. The points rewarded to each student for solving the problem would be the 100 divided by the total number of students who solved it. And there would be ten homework problems in total throughout the course.

Maths whizzes as we were, we quickly worked out that the scheme was such that if all students solved all the problems, then the whole class would fail. Or that a minimum number of students were required, by mathematical necessity, to fail for other students to get an A. Or some would have to do really badly for others to do well. And so on. You get the drift. Inevitably, almost everyone dropped the course. Ultimately, only four students remained, including me.

The course turned out to be nightmarishly difficult. Domotor, eager to test the mettle of IITD students, would pose tough, advanced-level problems in his homework assignments. Most problems would require a leap of creativity which always seemed beyond me, and even after being revealed the answer, I would find it difficult to imagine how I could have ever come up with the solution myself. He would often jokingly slip in unsolved research problems in his lectures. I struggled through the course, realised how terrible I was at research-level Maths, and never looked at Combinatorial Geometry since.

Domotor was actually a really good mathematician. Probably one of the smartest in his field. And in many ways, he was also a good teacher. But for that particular course and for me, he wasn’t a Really Good teacher.

Really Good teachers leave in their students an everlasting interest and attention for the subject. They follow the Socratic ideal of education as the kindling of a flame, not the filling of a vessel. The best example for me for this was Rukmini Bhaya Nair (RBN), who permanently changed my relationship to language. It is not uncommon for me, when listening to someone, to simultaneously find myself unpacking the metaphors their speech is couched in, or spend a lazy Sunday afternoon reading an article on how language affects thought.

The way RBN used to treat any disruptive behaviour from her students - not with irritation but curiosity - also left an indelible impression on me. Where a conventional teacher would be inclined to say “I will not tolerate this buffoonery!”, RBN would say, “That’s an odd, interesting contribution to the class community. What does it say about human nature and the workings of our mind?”. She perfectly demonstrated how curiosity and attention can kill the human instinct towards judgment and intolerance (Really Good teachers can influence your attitude to life that way). To the students themselves, her classes were therapy.

Another unique aspect of RBN’s courses were her exams and assignments. They never felt like an adversarial challenge, but rather a meditation on the basics. Instead of making you feel inadequate, they conveyed a feeling: “It might be an exam and the question long but its okay and you’re okay and everything is alright. Have a cookie and give this a thought, will you?”

Lastly, one of the underrated aspects of Really Good teachers is that they act like a beacon that attracts other colourful, interesting personalities as students. Purely in terms of your learning, the contributions of your fellow classmates (discussions, collaborations, friendships) could surpass anything that you might learn from the instructions or the course material itself.

There were other really good teachers I have had that I might have missed or haven’t mentioned here. But almost all of them shared one or more of these qualities.

05 September 2020