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This is a philosophical question.

From undergrad (which I did stem), I have noticed that in some classes, the teachers taught the absolute bare minimum, almost like overviews of a topic, often times with no examples (as they are allocated to the tutorials), whereas the exam coverage often involves material that are usually much more advanced, with details far surpassing the lectures or even the textbooks.

This trend gets even more extreme in grad school. Sometimes the classes (say a math class) simply involves a lecturer jogging down a few key results, write a few equations on the board. Proofs, if ever even given, tend to be handwavy. Whereas in the assignments or exams, these equations and proofs for these results may need to be derived from scratch.

In other words, there are many things that students need to fill by his/her self. Much of the learning do not occur because of lecture but rather from preparation for exams.

So in a sense, "taking a class" is not to learn from the lectures or to gain some panoramic understanding of a subject, as much as to wrestle with the assignments and exams, which may be very narrow in scope.

Is this the correct way of thinking about the purpose of taking courses, i.e., just to pass the exam of these courses, however narrow they might be in the context of the entire subject that's taught?

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No, the purpose of teaching is not for students to be able to pass an exam and be done with it. That makes it not a correct way for you the student to think about the purpose of taking courses.

Yes, in university students are supposed to work on subjects on their own. This is not necessarily a modern development. It is bit less intense for freshman/sophomore years, however.

There are cases where a professor has to teach a lot in a very limited time, so they'd make a heavy use of homework. There are also cases when they succumb to giving just cursory understanding of the subject and invite people to join a more advanced class. In that type of classes, we'd typically had a "prepare at home and come have a talk about some topic" type of exam. If that's the case - "narrow at scope" these assignments might seem, it's actually probably the best attempt of getting you a panoramic view of the subject by giving various assignments which are supposed to highlight some links and important properties. The entire point of that "calculate wind shear ..." assignment is obviously not so that you know its numerical value and not so that you memorize the formulae by which it is derived but rather so that you can reason about it. Since we're talking STEM, going through the technicalities of applying some laws is usually the less important part, the more important is figuring out which one is applicable and why, which values should you put into it and what are the limitations of that approach.

And sometimes, well, people just teach poorly. But still, your goal is to learn the subject and be able to reason about it. Taking the least effort path of just doing the bare minimum to get a pass is a shortcut.

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