[zsz]

> I’m totally convinced that a new idea or a new plan or a new technique is never really understood when you just explain it. > People will often think they understand, and they’ll say they understand, but then their actions show that it just ain’t so.

Isn't this the very reason that homework assignments exist? When I was in college, it took me two years to realize that I could have easily gotten As and Bs (instead of Bs and Cs) in my various math classes, physics, chemistry, etc. had I simply bothered to do my homework properly--or, to put it differently, had I only properly applied the knowledge which I passively acquired by reading the associated textbook sections. Notably, I was always convinced that I "understood" everything I had read, only to find out otherwise when I tried to solve any of the problems. It was only after I actively applied the knowledge I had picked up, that my understanding transitioned from superficial (as in, understanding the underlying logic itself) to concrete (being able to apply the logic toward other problems).

If you apply this to abstract and esoteric technical concepts, it is easy to see why someone might say they understand--and even believe that they do--while in reality only having a superficial understanding at best. The problem then becomes getting the other person to spend the effort to properly internalize the concepts being conveyed, before they have built up the requisite interest in the idea to be sufficiently motivated to carry out said effort.

It's probably also true, however, that this may only apply to sufficiently esoteric and complex ideas in the first place.

[koyote]

> When I was in college, it took me two years to realize that I could have easily gotten As and Bs (instead of Bs and Cs) in my various math classes, physics, chemistry, etc. had I simply bothered to do my homework properly--or, to put it differently, had I only properly applied the knowledge which I passively acquired by reading the associated textbook sections.

I took this realisation to the extreme and decided to completely deprioritise classes in favour of homework and doing the reading in my own time. I figured the cost-benefit, at least for me, was much higher if I spent an hour doing as opposed to an hour listening.

This actually worked really well for me but that might also be because I often struggle with large classroom learning: the pace is either too slow and I get distracted or too fast and I can't keep up. But even when the learning is 'one-to-one' I feel like there's always the tendency for people to zone out and not raise an issue when they are either bored or did not keep up/understand.

I think you're right in that some of that might be the brain pretending that it understood when in fact it did not. Could it also be a social thing? Maybe because the other person expects you to understand and this causes your brain to try its best to believe that it understood when it did not.

[smaudet]

Classroom experience is so rarely useful, the ONLY time you benefit is when either a) you already studied the subject and the professor is good and mentions something tangential/extra credit, or b) the classroom size is small, so when you don't understand something you can say so without fear of class disruption and the teacher can spend more time tailoring their curriculum to their class.

Otherwise yes, you are often better off with the book and homework and actually completing both.

And this is where I usually go off on my rant how college is useless for education - you can 'learn' peer interaction but even this way nothing forces you to make friends or connections, so the inherent use is close to nill.

[Ntrails]

I believe this may be true for you, but it is not true for me.

I find classrooms engaging and I actually internalise information in a way that reading is only ever surface level.

[Aeolun]

I don’t find classrooms particularly engaging, but an open book in front of me is even less so. Classrooms are basically the only way I get any not-immediately-interesting learning done.

[TRiG_Ireland]

It does depend what you're learning, too. Anything practical (chemistry lab skills, for example) will need a classroom. And languages probably do too.

(If you do Deaf Studies in Trinity College, University of Dublin, one of the lectures is on Deaf Culture, Perspectives on Deafness, Working with the Deaf Community. The lecturer is himself Deaf, and will lecture in ISL. There's an interpreter present to voice the lecture for the hearing students (and to interpret any questions, of course). In third year, you lose the interpreter. By that stage, you should be fluent enough in ISL from your ISL classes to no longer need one.)

[anonymousDan]

I can't say I agree with this. If there is anything I learned from COVID it is the value of in-person teaching.

[chalst]

I had the luxury of going to Oxford, when colleges gave tutorials to two or three students at a time. For most topics, I figured out what had been covered in the lectures from the tutorial problems, read up that material in the book I was using, and then solved the tutorial problems.

There were a few topics that I attended the lectures, either because the lecturer was very good or because no book was adequate. The subject was mathematics, but I knew people from other fields who approached study in a similar way.

[Mezzie]

It's wildly dependent on the topic.

I never went to my physics classes in college - there was no attendance requirement outside of lab and I saw no reason to since math and science were easy for me to grok on my own.

On the other hand, I also studied languages and classroom and face to face time is almost essential for in-depth language study. Language study isn't usually lecture based, though. Not going to my Chinese or Arabic classes would have been a bad time.

[asimpletune]

This is a super interesting strategy. Also going to classes can lead one into a false sense of mastery. It almost makes more sense to do homework before class, and attend lecture as a review. It would just become pre-work then and would essentially be considered mandatory. This would also really fix the problem of lectures not being useful, since the lecturer could assume you did the work and then spend more time on things that are a better use of their expertise.

[travisjungroth]

> I often struggle with large classroom learning: the pace is either too slow and I get distracted or too fast and I can't keep up.

This is a problem for everyone. People may not experience the struggle directly, but it's there. It's the inherent problem with any group class.

> I feel like there's always the tendency for people to zone out and not raise an issue when they are either bored or did not keep up/understand.

Tight loops of interaction will make this nearly impossible. What you'll have to watch out for instead is overwhelming students to the point of distress (speaking from experience).

[a2800276]

Not only is this a problem with everyone, it's also one of the "soft" skills you learn to deal with in school. It occurs in professional and social interactions as well and school prepares for dealing with it.

[anthomtb]

> completely deprioritise classes in favour of homework and doing the reading in my own time

I had two mathematics teachers in high school that took this approach to class time. They would lecture for 10 minutes then have the class do work in groups on homework assignments for the remaining 45 minutes. Exact times varied based on the complexity of the material, of course. And I do not believe their format was sanctioned by the administration. But it sure helped me retain more of the information.

As an extra bonus, it really helped with procrastination. It was a lot easier to get to work on an already-started homework assignment compared to staring at a blank page and a daunting list of problems.

[funcDropShadow]

> I took this realisation to the extreme and decided to completely deprioritise classes in favour of homework and doing the reading in my own time. I figured the cost-benefit, at least for me, was much higher if I spent an hour doing as opposed to an hour listening.

That depends very much on the lecturer. If he or she just follows one book for the whole semester and doesn't add any additional insight, explanation of tradeoffs, or enlightening anecdotes, then by any means skip the lecture. But if you have a lecturer giving you all from above and the possibility to ask questions, lectures can be invaluable. Luckily I experienced many of the latter kind, although some of the first.

[lordnacho]

I think it's to do with the nature of tests. Exam questions in the mathy subjects are sort of two varieties in my experience. One is simply book proof: here's an equation, here's another one, plug one into the other and rearrange and there's this useful result. Come exam time, you just need to remember the steps and you get points.

You'll think you get it.

But there are questions that are about a deeper understanding. For these there's some point to the question that isn't obvious from just reading. I remember the first few question sheets I got in uni, there would be questions that appeared to have nothing to do with what was presented at all. Only by asking around did I discover what the cryptic connections were. If you don't do the question sheets, you won't see this.

[fulltimeloser]

>I often struggle with large classroom learning: the pace is either too slow and I get distracted or too fast and I can't keep up.

Yes, this is my biggest gripe with learning as well. It's so individual that you almost need one teacher per student.

[andai]

Finally, we have the "Digital Aristotle". KhanAcademy is testing out a ChatGPT integration.

Well, it was astonishing when I read the news. Now, at the end of this crazy week, all I can think is "well of course they are!"

[einpoklum]

From my experience both as a student and as a teacher (formal and informal settings; the formal ones in academia): Different people respond differently to different modes of teaching / exposure to information.

* Some only "get it" when it's explained to them in a classroom, preferably by an engaging teacher; while others have to read it in the book.

* Many, perhaps most, won't really get it unless they do the homework; but others can do all of the exercises you give them, and still fail to get the bigger picture, and will be lost if faced with something slightly different than what they exercised.

[gboss]

I did this when I accidentally enrolled in the astronomy 101 class for astronomers when I meant to enroll in the “fun” astronomy class for non-majors. The professor was extremely uninterested in teaching and I decided to just do the assignments and stop going to class. Still got an A.

[crdrost]

Yes. Well, examples. Good homework assignments give you some examples to sit in your head, not all homework assignments are good though.

The way I like to tell people this is, you know that thing where you want to take your kids or your students and make sure that they don't have to go through the same pain that you did to learn what you had learned? That feeling?

If you have ever had that feeling you must understand that it was horribly mistaken. The problem is precisely that learning and pain go hand-in-hand. We learn abstractions precisely because they relieve a sort of confusion, a sort of difficulty, they organize the pain that we have experienced and make it tidy and less painful. Even as kids abstractions like “this is what it means for the stove to be on” work this way, not that you have to get burned, maybe you just need to be yelled at, but it organizes that pain of being yelled at and tells you when are you getting yelled at and why.

Not all learning is this way, for example memorization and repetition... but to a first approximation you have to get lost in the forest before the landmarks on the map are recognizable.

Corollary: you CAN tell people things, but it might be more involved than just a casual conversation. Either you have to establish a shared context, tap into the pain/confusion that they already have... Or you have to get them interested enough that they will follow you down a rabbit hole of confusion and difficulty so that you can finally explain the thing.

[moring]

> The way I like to tell people this is, you know that thing where you want to take your kids or your students and make sure that they don't have to go through the same pain that you did to learn what you had learned? That feeling?

I am not yet convinced. Let me take the following example because I remember it well: I tried to learn about geometric optics and lenses. To do so, I downloaded multiple lecture PDFs from the internet and read them.

All of them started to explain lenses by describing how large the image of a real object is, defining focal length and such. Literally not a single one of them even defined what an image is. The whole talk about image size and focal length and magnification and what not was totally worthless because it was all based on the same fundamental word that had no meaning. In the end, I tried to make up my own definition that was consistent with all those PDFs, but it left me unsure if I got it right.

The "pain" was there, but there was no relief from it, and I am still convinced that that simple definition could have avoided it. If I were to teach optics, I would give such a definition, and I am still convinced that it would help with the pain.

The other example was one of those PDFs that showed a real object that was "wide" along the distance axis from the lens, and so by my understanding should have an image whose magnification changes along the distance axis, but the explanatory picture in the PDF showed equal magnification everywhere. Today I am convinced that this "explanatory picture" was simply wrong.

Again, there was "pain", no relief (because I could not be sure), and I am still convinced that a learner can be saved a lot of pain when you just exlucde factually wrong content from the learning material.

[melagonster]

this why Socratic questioning is good when you have a personal teacher.

[jrumbut]

I strongly agree with your main point that sometimes valuable learning is painful. I've found a lot of mathematics is painful beyond "this is frustrating and difficult," but in a more profound way.

I would say though, about abstractions, I'm not sure hot stove is an abstraction. I think hot is an abstraction that allows you to apply the lesson you learned on the stove to the toaster and the coffee maker and all the other hot appliances you encounter.

[maCDzP]

If you wouldn’t mind, could you elaborate your point about mathematical being painful?

[jrumbut]

I don't have a great way to put it in words, but the intuition is that you are putting enormous mental energy into something that doesn't give anything back. Being able to solve heat equations doesn't make you warm.

Other subjects are the same, obviously, but when writing a history essay you can BS and not think too hard and skate by with a C. With a math problem, if it's difficult for you, you need to really put your whole self into solving it to make any progress at all. And I think that can be painful, in a certain way.

[andai]

I was studying calculus not too long ago and arrived at the conclusion that drawing is actually way harder than math. In math, you learn how something works, and then you can do it. In drawing, you can literally see the "solution" right in front of you (e.g. your own hand that you are drawing) and still get it wrong for years (and even then, only asymptotically approach perfection).

That discrepancy between the goal (photorealism, or at least beauty) and the result (ugly art) is very painful for me, to such a degree that it discouraged me from putting much effort into art, despite my love for it.

[jrumbut]

Drawing is similar (and a lifelong source of frustration for me). I can see the same experience playing out in different disciplines.

I would say that in the kind of math you study after calculus it becomes more common to have that "I know what the solution should look like but I can't seem to get there" feeling.

[wizzwizz4]

Don't try for photorealism straight away. Pick a more abstract style, and work on that: change things around until you find it fun. When you learn to follow your whims, that's when you'll start getting better (perhaps even quite rapidly).

This isn't to say give up on photorealistic drawing: but don't bludgeon yourself with it. If you don't find it fun, you're probably not at a point where practice will make perfect.

[weinzierl]

> Isn't this the very reason that homework assignments exist?

Absolutely. It is also why I will never understand why it is considered a virtue (especially in the maths and physics community) to set assignments without exemplary solution. I'm not asking to give this exemplary solution to students right away, but it should definitely exist and be given when students have shown honest effort and especially to weaker students that are struggling.

Instead the "left as an exercise to the reader" mentality is celebrated when in reality - in my opinion - it is almost always just a convenient excuse for the laziness of the professor at the expense of their students.

[Aune]

I have seen plenty of miss-use of solutions of the following though:

1. Struggle with exercise.

2. Check proposed solution.

3. Thinking that your understanding of the proposed solution constitutes an ability to solve it yourself.

This is analogous to the original problem, where you assume the ability to follow reasoning translates to being able to reproduce it.

The main use of exercises without solutions is to try and force students to go to their teachers and interact, so that someone can try to pinpoint what exactly the missunderstanding is.

This can probably be better done with assigned homework. However grading can be time consuming, so trying to filter so that only those that have problem with specific exercises come to see you is one way to try and get some time economy going.

Also yeah. This is better in course specific work sheets than in books, since books should be self contained enough to be usable without the guidence of TAs or professors.

[tormeh]

IMO mathy homework should always come with the correct end result to the questions. It allows the student to get instant feedback on whether they’re right or wrong. They’ll still have to work out the derivation of the answer.

[kaashif]

That works fine for some kinds of questions, but not for questions like "prove this group is cyclic" or "prove this function is holomorphic" - in those cases there is no answer separate from the derivation.

And those questions tend to be the hardest and most prone to bullshittery by students. Many times in exams I made up proofs that made no sense and hoped no-one would notice.

Often when given the end result of a computation students just make up some nonsense integral or something and pretend they evaluated it, even if they didn't. Not having the answer immediately at least forces an honest attempt.

Let's not kid ourselves, we were all students at one time and we know students are lazy.

[alex-moon]

Yes and also https://build-your-own.org/

I had a boss years ago who would encourage me, whenever I was interested in e.g. a new library or framework, to go and reinvent the wheel in my spare time i.e. build it myself from scratch first to understand what the problems it solves actually are.

I've never built my own anything quite as low level as the build-your-own.org projects, but doing things like implementing a PHP web server with a class loader without any frameworks, or a JS templating system which stores the state of the UI in a big ol' object and updates the DOM automatically, has given me the deeper understanding of these things that I've later needed to debug weird issues and find creative fixes.

[FrontierPsych]

Yes, 100%.

A friend of mine was going to graduate, and had one required class that she had to take. She had dropped it twice before because she said it was too difficult for her. If she didn't pass, she couldn't take the class again, or maybe for a year, not sure exactly.

Well, at the start of the semester at the first mid-term, she failed the first one. At that point, I decided to step in. I made her read every single chapter, completely, and understand most of it, before going to class, where the teacher went over everything and she could ask the one or two very incisive and important questions that she honestly didn't understand in the book.

I also "made" her do an extra credit paper (meaning I really just put the screws to her to do it, no mercy. For her own good - ie not graduating and failing out with one semester to go.)

As you might expect, she got perfect scores on her next two mid-term tests, and her report she also had an A+.

Reading to understand and working hard at it, you will understand. And reading it before each class, in order to ask the one or two or four honest questions that you have to fill in the honest few things you just can't understand.

And actually, with the internet, for almost all things, you can look up multiple sources on the topic and read them all - because each author has a different perspective and when you see the concept from many different perspectives, you really do understand deeply.

I got pretty much all C's, but then started doing this and then got all A's. Plus I leared memory mnemonics - Tony Buzon - for perfect memory. Learning mnemonics required a lot of work, but so worth it I would make it a required topic to teach starting in 1st grade, and every grade after that. Just like everyone should be required to take probability and statistics classes starting in 7th grade to 12th grade. Just those two.

[inopinatus]

The irony here is that bypassing active learning early, means one only discovers how valuable it is much later in life.

As per article above in which the hubris is its own comeuppance.

[ianai]

At my undergrad you had to do the homework and attend all the lectures to get a C+/B-. As/Bs were the realm of studying the class beforehand or, preferably, having taken it once before the time.

[scotty79]

Hear and forget. See and remember. Do and understand.

[tricksforfree]

I've seen this time and time again when attempting to implement a centralized design system across a group of existing apps.