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As a feat in itself this is definitely very impressive, but I wonder if it's really worth anyone's time to spend precious lecture time with your mind fully occupied in the mechanical task of taking notes rather than actually absorbing and engaging with the content. Especially for an extremely content-dense subject like Mathematics, where you need all your concentration just to process what you are reading and follow along the logic.

There is absolutely no dearth of study material on the internet. It's one thing to take notes as part of your study process. There it helps solidify your understanding. But surely taking notes on the fly when you have been barely introduced to the subject isn't going to help with that.




> mechanical task of taking notes rather than actually absorbing and engaging with the content

The mechanical task of taking notes is one of the most important parts of actually absorbing the material. It is not an either-or. Hearing/seeing the information, processing it in a way that makes sense to you individually, and then mechanically writing it down in a legible manner is one of the main methods that your brain learns. It's one of the primary reasons that taking notes is important in the first place. This is referred to as the "encoding hypothesis" [1].

There are actually even studies [2] that show that tools that assist in more efficient note taking, such as taking notes via typing rather than by hand, are actually detrimental to absorbing information, as it makes it easier for you to effectively pass the information directly from your ears to your computer without actually doing the processing that is required when writing notes by hand. This is why many universities prefer (or even require) notes to be taken by hand, and disallow laptops in class.

1: https://www.sciencedirect.com/science/article/pii/0361476X78...

2: https://www.npr.org/2016/04/17/474525392/attention-students-...


Not that it detracts from your point, but I definitely benefited from notetaking on my computer in school. For an AP History class, I typed up—in outline style (I, II; A, B; 1, 2; a, b; etc)—all my notes on the required reading. At the end of the course, I had a few hundred pages of these notes all printed up.

I never had to go back and read any of them. Just the process of typing them up in the first place firmly fixed all the knowledge in my mind. When taking the final and AP test, I could see the notes I had taken in my mind.

Writing or typing didn’t make a difference. Just the rephrasing and condensing alone was enough. (Which, again, reënforces your point. I still had to consciously avoid “pass-thru” regurgitation)


> reënforces

What's it like working at the New Yorker?

(explanation: this is a joke based on the way nobody uses diaresis marks anymore for any word other than naive, except for the New Yorker style guide. https://www.newyorker.com/culture/culture-desk/the-curse-of-... )


Not only that but the common spelling is "reinforces", which doesn't need a diaeresis at all. It's like function_seven went very far out of the way to show that they know what a diaeresis is...


I’m not usually pretentious, but when it comes to the double-e, I lean in :)


History <> Math at all. I'm an electrical engineer (pretty good at math as that's all you do for 4 years in college), but can process a history lecture much much faster and easier. Outlines are great for History (I agree), but this isn't as easy for Math. A single equation can need more explanation than a novel.

Note that I'm not at all belittling the study of history...just trying to show the counter to the parent post isn't 100% relevant here IMO.


I was relating to the parent comment about writing v. typing, so I kinda lost the original point of the article.

Yeah, Math is a much different subject when it comes to notetaking and processing the information you learn. There are a few equations to memorize, but to really excel at the subject, you need to learn more why's than you do what's


I wonder if traditional memory techniques (e.g. method of loci [1]) would have long-term benefits over taking notes by hand?

According to this highly interesting HN thread, Alan Kay apparently doesn't take (much) notes [2]. I also found Warren Buffett's tip to focus on information that "doesn't expire or expires very slowly" an excellent rule of thumb for daily life. Obviously, with decades of books under their belts both of them are outstanding systems thinkers, so it must be true that they just don't need to take notes that much.

I'm a 30-something, but I like to trust my brain's tendency to forget more and more. Most of the stuff I don't remember probably wasn't relevant for my current mental models. If it's important, it sticks in one way or another. (I try to reinforce this by using the aformentioned method of loci, but I'm not as confident with this as I would like to be. It involves creating "sticky" images for the brain, and thus it always requires at least several seconds for me to "store" something that way.)

One probably won't be an A-level student with this approach, though -- but in trying to live a meaningful life, letting things (information) go often helps a lot. It's a great bullshit filter for everything.

1: https://en.wikipedia.org/wiki/Method_of_loci

2: https://news.ycombinator.com/item?id=11809285

3: https://fs.blog/2019/02/compounding-knowledge/


I wonder if traditional memory techniques (e.g. method of loci [1]) would have long-term benefits over taking notes by hand?

Mathematics already is a sort of hierarchical interconnected structure that allow you to easily remember everything, as long as you understand it. The understanding is the hard part, not remembering it. Mathematics is not a set of random facts that you have to memorize.


> There are actually even studies [2] that show that tools that assist in more efficient note taking, such as taking notes via typing rather than by hand, are actually detrimental to absorbing information, as it makes it easier for you to effectively pass the information directly from your ears to your computer without actually doing the processing that is required when writing notes by hand.

This might very well be anecdotal, but in my experience, note taking in class (by hand or on computer) was nearly always how you describe it here. Everyone was expected to copy out every word on the board, from 6 years old to ~20 years old. Maybe it works for some, but to me class was to some extent an exercise in mindless dactilography.


This depends heavily on the country's educational system.

I have gone through most of my middle-school and some high-school in Italy, and after that completed high-school in Moldova. Classes in Moldova were exactly how you described, and I hated it, while in Italy it was exactly the opposite.

Having the teacher explaining and expanding on the content in the course books while students take their own personalized notes is much more efficient and productive.


I definitely agree with this for mathematical notes. Writing LaTeX is so mechanically different from writing down actual mathematical expressions and proofs that I feel like it distracts more than it helps me absorb.

On the other hand for something like a psychology class where the material is mostly in English prose, then I feel like typing does help. Typing English is not so mechanically different than writing down English since each letter is still in a one-to-one correspondence.


I would disagree with you on the benefits of taking notes in higher maths. If I'm taking notes, I can barely follow what is going on in the lecture. If I don't take notes I can fully concentrate on the lecture and logic, but then I have nothing to study/reference. Teachers should provide notes so you don't have to do it yourself, especially if they're just writing off a sheet of paper. They're usually just worried that people then won't show up for class.

I'm sure history is maybe different where the note taking is probably easy enough and reinforces what you learned, but with math you're not exactly comprehending everything you write down at the same speed as human language. When you're in high school: "The storming of the Bastille happened in..." is different than scribbling down the Fundamental Theorem of Calculus and wondering WTH is on your paper.


I often wonder if those studies about "copying the entire lecture by taking notes" are an example of the Simpson Paradox. Breaking them down to sub-groups of students and their experience would surely reveal another picture. At least some students can't benefit from this, as my experience mirrors yours. Courses that required me to write everything down were those where I couldn't remember anything at the end. I just can't write and listen / comprehend at the same time.


Agreed. Either lecture or tell me to read a chapter. I can't multi-task that well with learning something that detailed.


Agreed, sometimes just copying the formula takes very long and you don't want to be making mistakes. Also, sometimes wording for explanation takes me long enough that I miss a few sentences from my lecturer.

The best I think is still to come prepared for class by having read the required readings before hand.


> The mechanical task of taking notes is one of the most important parts of actually absorbing the material. It is not an either-or. Hearing/seeing the information, processing it in a way that makes sense to you individually, and then mechanically writing it down in a legible manner is one of the main methods that your brain learns. It's one of the primary reasons that taking notes is important in the first place. This is referred to as the "encoding hypothesis" [1].

There's almost certainly an advantage to learning to think about math using a publishable symbol set like LaTeX.

We learn by reinforcement; with feedback loops that may take until weeks later in a typical university course.

> There are actually even studies [2] that show that tools that assist in more efficient note taking, such as taking notes via typing rather than by hand, are actually detrimental to absorbing information, as it makes it easier for you to effectively pass the information directly from your ears to your computer without actually doing the processing that is required when writing notes by hand.

Handwriting notes is impractical for some people due to e.g. injury and illegibility.

The linked study regarding retention and handwritten versus typed notes has been debunked with references that are referenced elsewhere in comments on this post. There have been a few studies with insufficient controls (lack of randomization, for one) which have been widely repeated by educators who want to be given attention.

Doodling has been shown to increase information retention. Maybe doodling as a control really would be appropriate.

Banning laptops from lectures is not respectful of students with injury and illegible handwriting. Asking people to put their phones on silent (so they can still make and take emergency calls) and refrain from distracting other students with irrelevant content on their computers is reasonable and considerate.

(What a cool approach to math note-taking. I feel a bit inferior because I haven't committed to learning that valuable, helpful skill and so that's stupid and you're just wasting your time because that's not even necessary when all you need to do is retain the information you've paid for for the next few months at most. If course, once you get on the job, you'll never always be using that tool and e.g. latex2sympy to actually apply that theory to solving a problem that people are willing to pay for. So, thanks for the tips and kudos, idiot)


Glad to see this at the top, agree 100%. I’m definitely going to copy some of OP’s setting and snippets, but not for real time use during a lecture.

A textbook is an infinitely better reference than any notes one could take in class. Read the damn book. Lecture time should be for asking questions when you have a freaking live expert professor literally presenting the material to you. Ask all the small, nuanced questions that you can think of in the moment, which you can’t find answers to easily online or in the book.

Not to downplay the efficient workflow here, but there is zero chance that this person’s notes are actually better than a real textbook.


That's fine amd dandy from a US perspective, but many European universities are different. I don't know about this guy's exact class, but some (many?) undergrad classes are 500 people in a lecture hall with the professor orating, no textbook, and the content on the exam is pretty much whatever was covered during the lectures. So accurate note taking is very important because those notes essentially are your textbook. Hence the small business of students assembling high quality lecture notes and selling them to people who have't been to class (much).


Undergrad maths classes with 500 people? That must be one hell of a course. Either way, all undergrad classes I attended in Germany were based on some kind of textbook (usually (co-)authored by the lecturer, and occasionally self-published, i.e. as photocopies of a set of more or less neatly typewritten pages, with equations scrawled in by hand).


At that point smuggling an audio recorder to the class might lead a better reproduction of the material.


You'd still have to transcribe them, and you'd miss what's on the blackboard.


onenote can transcribe in real time and save the audio recording as well... you can even save notes at particular timestamps so you can mark something you didn't understand for later.

all of these things are solved problems


Note: Europe: the continent where most of the lectures are still not in English. And where are many languages. Not to mention the accents and the dialects in the same non-English language.

I also doubt you are aware how seriously distorted the result of the speech to text conversion would be for a non-professional recording of any non-trivial lecture given in English (e.g. domain specific terms).


yes it was totally my mistake to assume a comment on an english speaking american site would be in the context of american english. also one note picks up domain specific terms just fine in STEM fields...

also remember how i said it records audio and logs in real time? yeah, just listen back to it and correct the one or two words it garbles. works just fine. people want to complain not use the solutions that exist. i'm sure writing in latex is trivial and doesn't have you googling issues every 2 hours lol


audio recording != text book ;) It still would need significant time to transcript, and then OPs workflow comes back into picture ...


The lectures will contain content from text books, even if they aren't referenced. Reading around the topic will give a better understanding and better results.


It does not make too much sense to compare textbooks and class notes, specially when you get to higher level classes where the textbooks are reference textbooks, hardly readable by someone who is not already familiar with the material.

Your study notes will contain parts of the textbook, of course, but also explanations that are not in the book, maybe examples that you find useful and that might not be in the book, counterexamples, doubts, schematics... No textbook will have 100% of the contents you need to study.


>A textbook is an infinitely better reference than any notes one could take in class.

but...

>Ask all the small, nuanced questions that you can think of in the moment, which you can’t find answers to easily online or in the book.

and then what, forget them by the time you go back to the book? Why was the book so good again if it doesn't answer all the questions? It makes more sense to record the answer to those useful questions you ask, maybe in the form of some notes.


Not everybody learns in the same way. For myself, I get essentially nothing out of just sitting in a lecture hall listening to a professor drone on. It literally just goes in one ear and out the other. The only way I am able to learn is by reading and by working through the material on my own, either from notes taken in class or (preferably) a textbook.

So I can appreciate what OP has done here. I took notes in LaTeX for most of my undergraduate math courses (and some graduate ones), and I found it to be a fairly valuable exercise.


But surely taking notes on the fly when you have been barely introduced to the subject isn't going to help with that.

I found that taking structured, detailed notes in lectures forced me to pay close attention & work constantly to keep up with the lecturer. For the courses I did that for, it felt like it was equivalent to doing an entire extra revision session with the lecture material for me - I had to do much less work to go over the material after the lecture in order to make sure I understood it, so it was a far more efficient use of my time that just 'attending' the lectures and then doing revision work afterwards.

Some people can maintain that level of connection with the lecture without taking notes of course, but that’s what worked for me.


I found I couldn’t take notes fast enough. But if learning online, pausing the video and taking notes is very effective for me.


> I found I couldn’t take notes fast enough.

Me neither. However, what I do once in a while is after I've sat through a tutorial (in person or video) I recall and make notes. It helps me immensely to a) Structure my thoughts b) Recall the actual content which reinforces it in my memory.

As a student, I always found that writing notes/answers on a topic/question made me understand the concept that much better as well as connect them to form a larger picture (e.g., connect concepts in math and physics).


It must be admitted that I got a lot quicker at taking notes in a very short time!


Learning is learning. He has clearly learnt how to do something. And do it well.

The entire article is very clear and well thought out. To me it signals a disciplined and methodical mind, that learns from doing. And we are lucky it's willing to share.


Lucky indeed. Who hasn't dreamt of being a stenographer for Math lectures in grad school, using the hardest tools for the job, including the most obscure window manager known to Linux. I mean, if one don't kill a week getting bspm to work on their laptop, is lecture note taking even worth it?


You don't need to demean the effort of anyone to put focus on how to do something better.


I'm not demeaning anyone. Sometimes, we can all look at the things we deify, including obscurity and complexity, and laugh a bit at ourselves. Tell me with a straight face that this article isn't quintessential fodder for the show "Silicon Valley".

I fully agree with your parent comment that this article is a demonstration of multiple positive traits of the author, I respect him/her a lot. But also, I cannot help but laugh a bit at myself and the others who up-voted the article. That in no way diminishes my respect for anybody, including the author.

FYI - I've relied on LaTex for submitting to multiple peer reviewed journals, my thesis and my thesis defense presentation (LaTex Beamer), so I fully understand and appreciate the skill level of the author here

Cheers!


i bet he looks really cool doing it though+whoever convinces him to share his notes is on easy street


I did this in a Biochemistry course minus the Vim. It is definitely counterproductive and I started to do better once I switched back to traditional notes.


OP describes exactly how he abstracts away the mechanical task of writing LaTeX and can focus on the content. I did a similar thing in my classes and after a little bit of practice and tool adjustment you just don't think about LaTeX more than you think what pen to use or how to highlight something when handwriting.

And precisely because math is so content-dense, having your notes is important, as they will be organized in a similar way to how the content is organized in your mind. Yeah, there is a lot of study material but most of the time, unless the class follows a textbook literally, you'll want your own set of notes with only the class contents, and you'll want to organize that in a way that is easy for you to understand.


The only alternative I see is getting the lecture notes from your professor. I had one (math) lecturer who used to make his notes on the fly with his convertible Thinkpad (x230t or similar) and shared those notes with us afterward. In addition, he also had a clean script. That combination was awesome as you could focus on what he was explaining (or take additional notes if necessary).


I remember things much better if I write them down during a lecture, rather than just listen. I seldom actually used my notes afterwards beyond a quick recap, except in a few classes where the lecturer had prepared the lecture very well. Still, just writing it down allowed me to remember better by orders of magnitude.


Exactly. Any decent lecturer is going to give you printed lecture material with this kind of detail already, your written notes are exactly that: notes on the material of important information and extras to help recollection.


I live-TeXed notes for some of my math classes and it was absolutely a great idea.




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