I rarely skipped math lectures in university (only when the prof was really bad; but then I watched video lectures taught by a different prof from a previous term).
The lectures in the hardest math classes I took did not feature any “working through problems.” They were 50 minute pedal-to-the-metal proof speedrun sessions that took me 2-3 hours of review and practice work to fully understand. I don’t know how anyone can see a lecture like that and not see it as an inefficient note delivery system.
I did have math classes where profs worked through problems but those were generally the much easier applied math classes. Those were the ones I least needed to attend lectures for because there you’re just following the steps of an algorithm rather than having to think hard about how to synthesize a proof.
For language learning it’s hard to beat full immersion. When we learn our first language (talking to our parents as children) we don’t learn it by theory (memorizing verb conjugations), we learn it by engaging the language centre in our brains. I think language classes are more useful if you want to learn to write and translate in that language, where you need a strong theoretical background. If your main goal for language learning is being able to speak with loved ones or being able to travel and speak fluently with locals, then sitting in a classroom listening to a lecture seems like a very difficult way to do that.
The lectures in the hardest math classes I took did not feature any “working through problems.” They were 50 minute pedal-to-the-metal proof speedrun sessions that took me 2-3 hours of review and practice work to fully understand. I don’t know how anyone can see a lecture like that and not see it as an inefficient note delivery system.
I did have math classes where profs worked through problems but those were generally the much easier applied math classes. Those were the ones I least needed to attend lectures for because there you’re just following the steps of an algorithm rather than having to think hard about how to synthesize a proof.
For language learning it’s hard to beat full immersion. When we learn our first language (talking to our parents as children) we don’t learn it by theory (memorizing verb conjugations), we learn it by engaging the language centre in our brains. I think language classes are more useful if you want to learn to write and translate in that language, where you need a strong theoretical background. If your main goal for language learning is being able to speak with loved ones or being able to travel and speak fluently with locals, then sitting in a classroom listening to a lecture seems like a very difficult way to do that.