At the very high levels, it makes a lot of sense as to why this is occurring. In pure math, for example, to even understand a single paper in a field you need to understand an immense amount of literature that came before it. Undergraduate degrees don't even begin to cover all this specialized material since the field has gotten to the level of depth to where analogies are so hard. Grothendieck was known for his ability to "see analogies between analogies", allowing him to make such deep reformulations of old fields and develop completely new ones. While I'm no where near the upper echelon's of these subjects, I can see the immense difficulty that is to come with the attempt.
At low levels, I agree that this is a big problem. I think it's partially because students are taught to memorize in most institutions rather than deduce from principles or use their imagination. They're given the same physics problems rather than being forced to imagine the physical circumstance and then apply their knowledge of formulas by figuring out the useful parameters of the system. Or they're given the same style essay topics instead of actually being allowed to develop their own ideas and interpretations of the story, which would force them to read critically and interpret substructures, which develops logical and imaginative thinking skills.
My high school physics teacher forced us to do this and I can testify that I learned a lot about physics, and about myself, in the process, and so I think you nailed that aspect. For instance, I realized that my thinking style is incredibly visual. If I can visualize it, then I can solve it - and it doesn't have to be a concrete visualization. For subjects like economics or mathematics, using analogies to visualize often makes things much easier for me. But naturally, my interests stray towards visual subjects like physics, engineering, and computer science, which helped me figure out possible career prospects. Moreover, giving students challenging problems makes them appreciate the subject more since it isn't just about passing a class but realizing the depth of knowledge humans have uncovered. Learning how things work and what it can be used for at a principle level teaches students how to think.
Of course the problem is feasibility for this. How do we change the education system properly? I haven't investigated that system enough to tell, but I think it's important to reform that system for a number of reasons.



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