What it Means to Understand Something

My Struggle with Learning

I'm currently in my first year of studying Computer Science at Cambridge, and have the privilege of being subject to consuming a term of content every single week. A course spans four weeks, twelve lectures, and each one covers the basics of an entire subfield. Operating Systems? Easy, twelve hours is all you need.

What this means is that I've had to scramble to find a way of learning that would work for myself. And that proved to be much more difficult than I expected.

I wouldn't say that I did really well in my academics in high school, but I found enough things intuitive such that I only had to focus my efforts on learning a few particularly difficult topics (organic chemistry ahem). This meant that A levels didn't really put a strain on my mental capability to learn, and I could take things at my own pace. If I wanted to write detailed notes on every single subtopic that was on the curriculum, that was what I did. It didn't matter how much time it took, because I had enough. I could spend half an hour drawing a single equation:

Now that I'm at university? It's a whole different story.

There isn't the luxury of being able to truly understand something before you're forced to hand in supervision work for the week. I've had to resort to keeping my notes open, reading my lecture notes and twenty other different resources while I'm working on the problem sets, fully knowing that this is compromising my own learning as I'm not attempting the questions based on the knowledge within my brain.

When I look around at the people around me, they seem to be able to take in knowledge and apply it quickly, and seemingly without issues. Which leads me to think: what makes my learning process different?

My mental model for having "understood" a topic is reaching the point where I can rederive everything on the spot. If I'm in the process of learning something and a question pops up in my head, no matter how irrelevant it is, I need to have it answered. It's a painful learning process, and often quite frustrating.

I describe it to people as needing to construct a narrative, such that I am able to follow that narrative to derive everything there is to know about the subject. Things don't exist isolated in my brain, they exist as part of a thread, a chain of thought that comes from one place and leads to another. And when I require that bit of knowledge, I pull on that thread and follow it through until I get what I need.

And so the struggle I'm having right now is that I don't have the time to understand everything, yet it's the only way I know how to learn. With most courses and topics, I find that I'm no better than a blank slate - I haven't bothered to anchor the knowledge to anything, so I have no means of finding it within my brain. It's as good as gone.

I don't know how other people learn so quickly and so well - if you don't learn the same way as I do, how does it work for you? I would be very curious to know.

My Approach to Learning

Over the years, I've created a system of learning that meshed well with my personality and characteristics. I'm a naturally curious person and hate to memorise things, so much of my learning stem from trying to gain an intuitive understanding of a subject, then relying on that intuition to help me remember the details and solve problems.

Here are a few things that I found helpful:

1. I make use of multiple resources.

Often times, when I don't understand what the lecturer is saying or what the textbook means, I turn to the internet and try to find alternative explanations of the same concept.

Resources that I found particularly helpful:

• YouTube
• ChatGPT (more so that I can dissect how it's wrong)
• other textbooks
• my own lecture notes, as well as lecture notes that were provided

What I don't do is rewatch the lectures. If I didn't understand it the first time, I'm not going to understand it the second time.

2. I make notes.

This is a bit of a controversial one, given all the evidence with "active learning" and how "making notes is useless" and whatnot, but the way I make notes is slightly different: when I'm typing up the notes, I'm not looking at any other resource, and I'm only relying on what's inside my brain.

For convenience, sometimes I write down everything I know on paper before typing it up on my laptop, but the point of the matter is that I'm not simply copying stuff from one place to another, I'm offloading the knowledge that's already in my brain to see what I already know, and crucially, see what I thought I knew but didn't.

Then, I go and refresh my knowledge, relearn what I didn't manage to learn the first time, learn the derivations, and try the offloading process once again. This means that I end up having a better understanding of the concept and how it fits into the wider picture.

The typing up itself isn't actually where the learning takes place, but it's important to me that I keep a record of the narrative that I've constructed. This means that when I forget the concept again (and I will), all I need to do is go back to the notes I've typed up, read it once, and have everything fall into place really quickly. And this works because I've phrased things in a way that is naturally intuitive, because I've written things down the way I've learnt them. If there's a particular explanation of a concept that worked for me, it's the one that gets written down over the alternative explanations that I've previously found.

Things that I think can be Improved

1. Being more "active".

This includes things like doing past papers, actually coding out the algorithms (maybe in different programming languages), testing myself, trying to explain a concept to someone else, asking questions etc. These are all things that would test my knowledge and help me realise what I haven't learnt properly.

2. Time!

Making notes, and making sure I understand a concept the best I can before making notes, takes up a lot of time. For the content covered in a one-hour lecture, it most definitely takes me more than one hour to understand. Even for a concept as simple as the Fundamental Theorem of Calculus, it took me an hour of crawling through random web pages just to form an intuition and get the definitions right.

If I could somehow cut down this time but still gain a good enough understanding, that would be great. An idea I have is to be more rough in terms of notes and not feel like I have to record the entire narrative down. If I can just get the intuition on rough working then make a short note on how I managed to understand the topic (just the outline of how to go about learning the concept, not the actual information), it would probably reduce the amount of time I need to learn each concept.

3. Spaced Repetition?

To be honest, I'm a bit skeptical of spaced repetition. I don't doubt that the concept works, but I feel like the evidence often used to back it up is limited to rote memorisation (which happens to be something I'm really bad at and therefore actively avoid doing). This is why I haven't tried using flash cards.

However, I do think that there are benefits to revising a concept once in a while. I naturally prefer to focus on learning one topic at a time, and therefore can spend days solely studying a single course, but it means that I often forget about what I've learnt in the other courses simply due to a prolonged lack of exposure. Reading the notes I've made previously helps, but I would also have to do some testing to make sure that I've actually relearnt the knowledge.

Therefore, I might try a hybrid technique of learning a single topic at a time, but testing multiple topics at once. This would ensure that I get the benefits of spaced repetition in that I test myself on the same knowledge every once in a while, but I can enjoy learning the way I like to learn: one concept at a time.

Conclusion

The topic of "how to learn effectively" has always been one of my interests, and I've read more books on it than I'd like to admit. How that has translated to my own system of learning, I'm not sure. But it's an interesting topic to reflect on, and if you've never thought about improving the way you study, I encourage you to do so. Who knows, maybe you'll find something else that works much better. Even if you don't, knowing that what you're doing right now is the most suitable way for you can help to ease your stress and boost your confidence.

How do you learn, and what do you do to help yourself learn better?