[whlr]

I'm curious how you envision a calculus class that would make the topic more tangible. I think we can agree that typical calculus classes are more abstract (for lack of a better term) than typical english, history, or science classes.

[inimino]

Physics and calculus should be taught as a single class, it's a mistake when they are separated.

[vincent-toups]

I'm a physicist and it happens to be the case for me that I didn't really _get_ math until I understood I could do physics with it. So you'd think I'd agree.

But after I was sensitized to it by physics, I've come to see pure mathematics as just as interesting and worthy of being taught standalone. In fact, one does mathematics an enormous disservice by suggesting that its tightly coupled with physics. Roger Penrose himself points this out in The Road to Reality: mathematics is actually substantially larger than that part of it which we require for physics. That fact alone is fascinating.

The pitch I'd give for pure mathematics is that its really the study of precisely what we all do on a daily basis when we "reason" about things. Our daily experience suggests reasoning is useful and in many ways concrete, but a detailed study of the process almost immediately produces challenges and paradoxes and great landscapes of mystery.

[inimino]

I agree that mathematics is much bigger than applied mathematics. However, for precisely this reason, pure mathematics, like philosophy, isn't for everyone.

The main argument for teaching it this way is a pedagogical one. If it took physics to prompt the geniuses of the day to discover calculus, then following in their footsteps is probably the easiest way for us to get there as well.

[vincent-toups]

I think philosophy is much more for everyone than physics or mathematics. I can't conceive of a model of the human condition which I would want to adhere to that said philosophy wasn't for everyone.

We _all_ think about value and about the relationship between what we think and what happens in the world and these are the fundamental elements of philosophy. If people feel that philosophy isn't for them, its a failure of the teachers rather than the people.

Its my opinion, anyway, that children don't always know or appreciate what they ought to learn and that adults do them a disservice when they fail to teach them that which is not immediately interesting just because they don't want to learn it.

[inimino]

Some amount of practical philosophy or received wisdom is necessary for everyone, just like some amount of mathematical awareness. The formal study of philosophy as a discipline, like that of pure mathematics, is not for everyone. For most people it would be deeply unpleasant for almost no benefit.

[whlr]

I'm not 100% sure if I agree with this or not, but a related idea is that physics shouldn't be taught without the necessary math as a pre- or co-requisite. I'm thinking particularly of non-calc-based mechanics classes, which I loathe.