One thing I didn't get about technical fields as a kid is that rigor is the standard ideas have to meet, not the source of them. The source is often the cheesiest sort of guessing.
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I knew a physics teacher (private school) who taught Physics as if he was teaching History of Physics, with the sparks, failures, etc. He claimed students understood it much better than: "here is the truth".
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On math, I've heard that St. John's College ("Great books school" in Annapolis) has some of that. E.g. read some Euclid, in original.
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Euclid's Elements are the opposite of what Paul is saying. It's all exposition with no motivation and no dead ends.
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Reminds me of the best technical teachers I've had. The best also emphasize how to understand the answers versus getting the answers. I had a teacher who gave us the solutions to all the homework at the start of a unit. Learned more in that class than many others.
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At the advanced level, math professors have opted for teaching the packaged finished product which makes the ideas seem natural and the connection to other ideas more apparent. Category theory pushes this culture to the extreme.
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