I agree with most of what you've written, particularly the sense of hopelessness around getting most students to "see" the beauty -- most simply won't. Quick s

I agree with most of what you've written, particularly the sense of hopelessness around getting most students to "see" the beauty -- most simply won't. Quick story: When I first TA'd a stats class at age 23 or so, I was sure I could transmit my own sense of excitement. I was a good teacher and got good feedback. But I got a dose of reality one day when I told the students about Buffon's needle problem, one of my favorite puzzles (that a needle as wide as one of the slats, when tossed onto a hardwood floor, has a chance of 2/pi of landing across a line). To me it was mind-blowing, but the class's reception was lukewarm. So I said I'm just curious, please answer honestly: How many think this is really cool (few hands); kind of interesting (maybe 7 hands); don't care (rest of class, like 15 hands). I thought, "Ohhhh, now I get it." > maybe that really is just the best we can practically achieve, and we have to live with it I think this is the answer honestly, but I think the incremental gains of a really good teacher are much greater than you're suggesting (eg, watch an Eddie Woo video on youtube and compare to your HS math teacher). It can be the difference between "I hate this" and "This is not so bad." Or, for that naturally apt, between "This is ok" and "I love this." I don't think "focus relentlessly on the practical applications" is the answer. Once you've accepted the frame of "What will I use this for?" you've already lost, because the truth is most kids won't need to use, say, calculus in their daily lives very often. That's not the reason to learn it, or most math subjects. The frame given here is the right answer imo: https://www.youtube.com/watch?v=RqQlXG__vGs https://www.youtube.com/watch?v=RqQlXG__vGs. The goal is to see the world differently and internalize an approach to reasoning. While developing this requires actual study of specific subjects, the particular sub-fields you study are less important. Moving the needle even a little here matters. And even if you focused on, say, basic financial literacy (which would be practically useful), they'd hate it just as much, and I doubt it would stick any better. Really we're just saying that it's hard to get people to do things they don't naturally care about.