This blog is me reflecting back after spending nearly a month TA-ing for pre-calculus at NYU. Honestly, the only reason I wrote this was because across the incredibly crazy and somewhat diverse experiences I’ve had in my nearly 2 months in NY City, teaching UGs in a physical classroom maths has been arguably the most rewarding. I’ll explain more at the end why this has been the case for me.

Some boilerplate info : All views expressed are my own, and NYU does not back anything I write here. Also, I’ll be very protective of student info, and this WILL be general. This is more a blog about what I learn’t teaching maths to UGs, and less about how maths should be taught- I want to explicitly state this right here.

Anyway, lets begin.

I have some history with teachers, and more importantly math teachers in general. My mom is a maths teacher- so technically it’s in my genes. My dad thinks he’s a great maths teacher - technically false as corroborated my my sister’s complaints about his teaching. Neither ever taught me maths very seriously- mostly coz I didn’t listen to them when I was younger.

I have another connection to teaching- Richard Feynman remains one of my heroes I admire most, and getting the chance to teach gets me another chance to be as cool as him. He said if you truly understand something you should be able to explain it to a 5 year old. I’ve got undergraduates to teach, so challenge accepted Mr Feynman.

I had some pre-conceived notions about teaching before I plunged in. I had TA’d before in virtual classes, which seemed too impersonal to count as experience. Also, explaining something in your courses one-on-one to your batchmates seemed to be easy enough, explaining the same thing to a class shouldn’t be any different right?

Additionally, there were a few traits I inherited from my consulting background which influenced my teaching style. McKinsey places special emphasis on structure of speech, and the “why is this important” of each topic. Which means I was relatively comfortable presenting to lots of people, and being structured about it. There are a few major differences I’ve noticed between giving an hour long corporate presentation and teaching a class of 40 people math.

1. The students care about understanding things. Usually, clients or business people don’t care enough, they can always pass on work to their underlings- students are naturally more individualistic.

2. Students are at multiple different levels of understanding. There might be a maths major in my class sitting right next to a arts history major- trying to solve the same question. Corporate meetings have far less variance.

3. Teaching means I don’t need to prove to folks how much I know - I just need to help people reach the required level. Corporate presentations mean I’m selling myself while talking- the divergence in motivation means I need to be far more empathetic while teaching to students vs giving a talk to the CXOs of banks.

Now that I’ve laid down how I found teaching different, let’s rewind to how my first class teaching went.

I arrived early in a relatively non-chalant mood for I had prepared 3 hours the night before. My first lecture was hopefully gonna be a choreographed masterpiece. I entered with slides prepared to introduce myself, and a few jokes to break the ice. One major issue in my first class - the classroom projector wasn’t working that day. All the slides and jokes built with excruciating detail were laid waste within 2 min.

I’d be lying if I said I did not break a sweat when the tech-glitch hapenned. But I had to roll up my sleeves and pick up the chalk and head to the blackboard - mustering my inner Matt Damon (from Good Will Hunting - best math movie ever?). I wrote down what I planned on covering today, how these classes would be structured, and finally posted the students a question asking them what they hated about most classes, and what THEY think I should focus on.

I think asking students what they wanted and how, worked wonders. Firstly, it broke the ice and the interaction became less impersonal and one-directional. Two, since we were not discussing academics - it meant both me and the students were more frank about how they should and wanted to make use of my classes. Lastly, I was in rhythm - I knew the pace the students were comfortable with and modified my speech to reflect that.

The rest of the class was more math-y, folks genuinely seemed to be interactive and interested, and each time a student answered a question correctly, or made an interesting point, it made me genuinely happy. Modifying the Interstellar quote - “After some years, we’re only alive to be memories for our students”. Teaching is rewarding, if done well.

Here’s the key takeaways in the about 1.5 months I’ve tried teaching math-

1. Probably the most important : It’s more helpful if you teach students how to think, than teaching them how to solve a question. Solving a question is algorithmic - it’s like giving folks a recipe to cook a dish. Teaching them how to think is like giving them ingredients, and then telling them how they can combine them to make good dishes. One’s domain is constrained to that question, the latter influences every question they solve again in life. And the latter is what they’ll remember when they face it in the exams - which means it’s more impactful.

2. Being structured helps more than being right : It’s the teacher’s job to ensure that the material is written in a way so it’s easily followed. If the students spend ANY time deciphering in what chronology things flow - it’s chipping away precious brainwaves which could have been used up in undertanding a concept. The worst teachers in IIT Bombay I had were unstructured in their lectures- you lose the class easiest if you’re ever doing this.

3. Being prepared for lectures makes a massive difference : I usually spend 3 hours the night before carefully choreographing how I’m presenting material. Even subtle changes in emphasis on words while teaching maths can majorly influence how people understand math. Saying “We divide by 2 here to make the LHS x” vs saying “We want to isolate x to the LHS so we can compare stuff easily, so we divide by 2 to achieve it”, makes such a massive difference to students. I’ve noticed how receptive folks are to phrasing purely by looking at their nods - things like these will take you from a 1x to a 5x teacher. But it all comes down to the prep you put in the night before.

4. Getting students to talk in class helps : I prefer asking small questions each minute, and they crafting a solution to a question based on student responses in my sessions. I’ve noticed this keeps energy in the class - basically keeps folks on their toes.

Why is it rewarding?

I think humans emotions are governed by the impact we have. The impact can be how many percentage points of profit we helped a company save, or how many people we helped become better people. We also perceive impact by how visceral it is- corporate profit increments are essentially numbers, a student pursuing maths in future because he/she/they liked your class is lifetime impacting for someone. It’s so easily perceivable that you feel your time was well spent. Additionally, I’m teaching UGs. I’ve faced UG troubles in the past, it’s quite refreshing to see people worried about math homework than job-interviews. It’s a good breather in between other stuff I’m working on - it takes my mind off things.

That’s about it. Roughly, I don’t think teaching is for everyone, but it’s worth a try. You might not like it, but you will regret it if you never try it. After all, we’re all teachers in someway to someone at most points in time in life.

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