We had a very famous MIT professor on a 6 month sabbatical at our lab in the early 90's. He remarked on the difference between US and our institution in Belgium being that here you can just assume undergrad students would be fluent in basic math subjects, whereas in the US (in this case MIT) you would have to explain even very basic math.
Now 3 decades later we are also at a US level as math has in general been completely de-emphasized at all levels of education.
As for textbooks, at the time EU ones were pretty clean, mostly definitions, axioms, proofs and conjectures, plots etc, layed out in simple black on white, whereas US textbooks were extremely wordy, full of colour and irrelevant photos blasting away at your senses.
Sadly this seems to be the style that commercially won, but I doubt very much it is beneficial to the student.
I don't think just plopping all the subject material in front of a student and expecting everyone to immediately "get it". Some people may have the intuition to read a group of definitions or a proof and suddenly understand the higher level concepts gluing everything together, but that certainly doesn't work for everyone.
Anecdotally, having a textbook that explains a concept via examples without jargon and informative pictures, then throwing all the definitions and proofs at me has been much more helpful to my understanding in multiple subject areas.
I'd also throw "extremely wordy passages" in there as well because having something repeated & reframed multiple times has help me understand something from multiple perspectives - and remind me of a previous definition at a crucial point in the text.
Now 3 decades later we are also at a US level as math has in general been completely de-emphasized at all levels of education.
As for textbooks, at the time EU ones were pretty clean, mostly definitions, axioms, proofs and conjectures, plots etc, layed out in simple black on white, whereas US textbooks were extremely wordy, full of colour and irrelevant photos blasting away at your senses.
Sadly this seems to be the style that commercially won, but I doubt very much it is beneficial to the student.