Teaching students math after COVID.
I want to discuss my experience teaching at Duke and Princeton and the trends I’ve noticed. I have been an academic teaching assistant for the better part of 10 years. It goes back to my senior year at NCSSM, where I chose to be a Physics TA. I continued during my undergraduate years at Duke as a Computer Science TA, and I have now been a graduate TA at Princeton for four years. I’ve seen, taught, and dealt with many students in different ways, whether it be one-on-one, small discussion sections (about 20 students), or teaching a full lecture (80 students).
I will focus on one particular course that I have taught three times: the Princeton undergraduate optimization course. I was a graduate TA for this course in each of the Spring 2022, 2023, and 2024 semesters. From a scientist’s perspective, teaching the exact same course three years in succession is a nice control variable to look at the student performance trends over time.
The first two times I taught the course, I was getting accustomed to teaching the material and figuring out the right approach. By the third time, I was extremely confident that I had figured out the best way to teach the material. I felt I had optimized the teaching, if you will. For the first exam for the ‘24 batch, I wrote a question that looked roughly like this:
- Part a: Start with a basic problem copied exactly from the lecture slides. It is a specific example of the overarching theory that they are to learn.
- Part b: Take the basic problem from (a) and apply a formula from class.
- Part c: Apply part (b) to a real-world setting.
Seems straightforward enough. (Or so I thought…)
My intention when designing the problem was: part a) will be free points if they paid attention, part b) should be an application of the formula, and then part c) will be the differentiator to assess who understood the material. I made one terrible miscalculation: almost half of the students got stuck on part a) of all places! The lack of fundamental mathematical knowledge and what they were coming up with was baffling to me. It was like asking for an essay and they wrote words on the page with no grammatical structure. The overall ideas were at least on the right track, but the details were nonsensical. Of course, without the answer to part a), the rest of the problem was completely hopeless. For comparison, I used a similar question structure for the ‘22 and ‘23 semesters and the students performed as I had expected.
I cannot express just how flabbergasted I was when grading and seeing the results. To be completely clear, this is a sophomore level undergraduate course with a strong mathematical background requirement. The complete lack of fundamental mathematical sense from so many students was troubling, to say the least. Not only that, but the problem in part a) was copied word for word from the slides.
As a side note, I want to reiterate that the part a) example was just a specific case of the more general theory. If they didn’t remember that example? No problem. If they understood the general ideas, then they should have been able to easily work it out.
I spent days racking my brain and talking to students trying to understand one (seemingly) simple question:
‘What went wrong?’
The conclusion I came to was shockingly simplistic, if not a bit reductionist, but I think tells at least a little bit of the picture. This is a mostly sophomore level class, but some students take it in their junior or senior year. The key thing I noticed is that almost all of the juniors and seniors were able to make it through parts a) and b) with little trouble. What separated them from the sophomores?
COVID-19.
If we rewind, then the Spring 2024 batch of sophomores were high school sophomores when everything shut down during the pandemic and schools were jolted into online learning. More specifically, their entire junior years were spent entirely online. I would argue that junior year of high school is the most important for college. From my experience, students tend to take their hardest courses, work on extracurriculars, and take standardized tests. It’s a lot to juggle, but I would argue that juggling is extremely transformative. Something of extreme value was lost here when, suddenly, all students were thrust in front of screens and learning just became an endless information stream. Through a firehose of information from the internet, their main takeaway is that they can always find the information they need and not need to actually learn it. Well, at least until push comes to shove and the exam rolls around. It’s the crucial ability to synthesize new information that has been lost.
The question then became: how do we fix this? One issue with the word ‘fix’ is that technology development is not going to slow down; it will likely continue to accelerate. That being said, I do not want to sound as if I am advocating for the removal of technology or the information highway in classes. When I was in high school, I remember using a TI-84 calculator and having our teacher tell us about the tedious nature of numeric calculations with slide rules. I also remember being incredibly grateful that we did not have to do those by hand anymore. One could argue that modern technology information access is the natural evolution from calculators. Nowadays as a researcher, I am also grateful for seamless access to the newest research and methods in my field. So, it’s not as simple as trying to revert to teaching methods we used before as they are no longer built for the modern age of information. But we also cannot lose track of the benefits of older methods and having to think through problems ourselves. There’s a balance to be sure, and one that even now I am trying to find.
I do want to end on a positive note. If the experience taught me anything, it is this: first, these are unbelievably bright and driven students; second, with all the information students consume every day, they are incredibly intuitively sharp. Like anything else, creating something new or applying an endless information stream to a new task is a skill, and thankfully, one that can be taught. So, I changed my teaching style accordingly. I modified my discussion materials to focus on the application and transferring of ideas to new settings. I found the students really enjoyed this new approach.
And yes, the results did speak for themselves in the second midterm.
– Vinit