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.

> 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.

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.

> 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.

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.