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Comment by ozim | Hacker News Reader

Why do we expect school or university to teach „understanding”.

It is like teaching snowboarding. You can get the pointers but students have to actually do the snowboarding - there is no shortcut.

The same with knowledge and understanding, you can organize material so they don’t end up in unproductive rabbit holes - but they have to work out their understanding on their own.

Classroom setting is also not really good one unless you have small groups on the same level - larger group and you are just pulling slow ones up and fast ones are getting bored.

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As someone teaching in higher education, I’d say that you can certainly incentivize the students to learn "understanding", although I agree that a lot is up to the student.

Some basic examples:

- Don’t give test and exam questions that are too similar to examples and problems in the text book and homework. Then they’ll know that learning to generalize is a better pay-off than memorizing the textbook problems, and may choose to change their strategy when studying for exams.

- Reduce the amount of curriculum. By studying in depth instead of in breadth, you have time to focus on how things really work instead of just rushing through material on a surface level, and in my experience that improves understanding more. (But I know many disagree with me on this one.)

- Focus on problem solving as part of the lectures (student-active learning). I’m not an extremist, like some advocating that we shouldn’t lecture at all, but the pedagogical literature is pretty clear that small doses of lectures interspersed with problem solving enhances understanding.

- Try to teach intuition and conceptual models, not just facts. For example, as a student, I really struggled understanding eigenvalues and eigenvectors because our linear algebra textbook defined it by Αv = λv but made no attempt at explaining what it means intuitively and geometrically. Similarly, integration by parts has a simple and beautiful geometric interpretation that makes it obvious why this is correct, but we were only taught the opaque symbolic version in my calculus classes. When I teach myself, I try to lean on such visualizations and intuitive pictures as much as possible, as I think that really enhances «understanding»; not necessarily being able to cough up a solution to a problem you’ve seen before as fast as possible, but being able to generalize that knowledge to problems you haven’t seen before.

But who knows, maybe I’m just biased by how I myself perceive the world. I know there are some people who for example eschew geometric pictures entirely and still do very well. My experience is that most students seem to appreciate the things listed above though.

You are absolutely right on all points!

Students need to take responsibility for themselves and Teachers need to point them in the right direction and help/steer as needed.

A Chinese Martial Arts saying which i keep in mind goes;

To show one the right direction and the right path, oral instructions from a Master are necessary, but mastery of the subject only comes from one's own incessant self-cultivation.

A good authoritative book can be the stand-in for a Master in which case there is more discipline and effort required of the Student.

These days different types of books/videos focusing on different aspects of the same subject are so easily available/affordable that the Teacher/Student can both work together and focus on understanding. A handful of real-world problems modeled and worked through beats pages of mere symbol manipulation. We need to start stressing quality over quantity i.e. deliberate effort via deliberate practice in the right way.

The Feynman essay here is all about the teachers NOT pointing the students toward understanding.

And it is all about the students being disciplined and putting in effort, but toward rote memorization rather then understanding, because that is what teachers told them to do.

I was agreeing/elaborating on "setopt's" comment (which lists specific approaches) on how to solve the problem detailed in the essay.

I had submitted the original article for discussion since the observations seem to apply to how Physics/Science has been taught/studied in most countries and not just Latin America.

I think you’re right and especially in regards to abstract concepts like linear algebra I don’t know anyone serious about learning who didn’t struggle with what turned out to be relatively simple things when viewed intuitively.

The problem as I see it

1. Professors themselves don’t understand it and are regurgitating pedagogy from books.

2. The material load is so high for your average bachelors degree you’d spend 8 years in school otherwise. I would hazard to say this is necessary and sufficient but schools wouldn’t get funding and our job oriented society would have it so then only the wealthiest could get education (like it was for centuries).

3. Tests are a benchmark and very expensive. You can consider a class’ total value to be loaded on the final exam. I recently wanted to go back to school casually. One of the cheapest universities available wanted 2600 dollars for a partial differential equations course. If I fail the course I lose 2600 dollars since I would need to retake it to proceed to higher mathematics. This alone does not allow a person time to explore - and that’s just one class!

4. Schools are simply a money laundering vehicle that takes money from students and moves it into administrator pockets. Education costs have skyrocketed yet education and pedagogy remains the same. This is money laundering by any other name.

- understanding leads intuition. There’s very little of either, anywhere.

> Why do we expect school or university to teach „understanding”.

Having been taught in different systems that emphasize understanding vs memorization, I'd have to disagree. The teachers and the overall academic system can encourage, test for, and reward rote memorization. Or it can encourage, test for, and reward problem-solving, critical thinking, and understanding.

Everything from the way teachers lecture, to assigned reading, to assignments, to tests will influence how students think and what they optimize for. There will always be exceptions who forge their own path, but most students like most people just go with the flow.

Students study to pass exams, teachers teach to enable students to pass exams. If your grading is based mostly on correctly reproducing facts and applying algorithms you memorized then that’s the outcome your education system optimizes for.

> If your grading is based mostly on correctly reproducing facts and applying algorithms you memorized then that’s the outcome your education system optimizes for

My favorite college class was compilers.

The whole semester you worked on a compiler for a simplified Pascal. Each homework added a feature.

The final exam was 4 hours. Open textbook, open internet. No chat with classmates. You got a description of 3 features to add to your compiler. Grade is number of tests passed.

Fantastic way to teach understanding.

My uni claimed grading was something like:

~ 40% bookwork. Rote learned facts ~ 30% standard questions. Do in an exam hall standard variants of what was done in class/homework/tutorials. ~ 30% New applications and logical extensions.

I don't know how well they achieved that split, I suspect it was mostly aspirational. Seemed like a reasonable ideal though!

I agree with your both of your observations; And I also think what's missing is the acknowledgement that connects the two. Students come with the expectation of "chew it for me" and schools have the expectation of "I'm going to throw the material at you, you can & will handle it yourself".

But it doesn't need to be that hopeless. Learning is a skill and schools can help each individual find the ways working best for them. Starting by not packing gazillion number of people in a class.

As a university level educator I am pretty confident most universities worth their salt do in fact teach you by "actually doing the snowboarding" to stay with your analogy.

But it is also true that (1) not all universities (or all departments, or all professors) are worth their salt and (2) snowboarding may not be a skill that is highly sought after in the society you live in.

Gladly most academic skillsets are highly transferable if the student isn't totally dull.

I will say you are right.

But ;)

At the same time Universities worth their salt also get students that are most likely going to be more self staring. Likely good professors will fail students that need more hand holding because it will be waste of their time.

So there is no magic trick to scale up. Besides getting more people to understand school/university is not going to do hand holding. You will get tools to learn how to learn and curated resources all the other things depend on you.

Studying at an university level is about building the skill to aquire new knowledge and methods yourself. Of course you will get guidance by the educators, but with too much guidance you're no longer learning the most essential lesson of them all.

As someone who teaches at an infliction point between theory and practise I can't stress enough how important it is that students go at issues themselves. You can have them understand all the theory, nod along, give the right answers when asked and then give them the real problem and they will look buzzled like they have never seen it. Because yes, they haven't.

That means studying and assuming they will hammer the knowledge into you is silly. You need to be the person that cares about understanding, like anybody who is good at what they are doing is, university level study or not.

> The same with knowledge and understanding, you can organize material so they don’t end up in unproductive rabbit holes - but they have to work out their understanding on their own.

Problem sets with feedback.

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