[nh23423fefe]

imagining that alpha is what stops people from being good at math is a useless take. why pretend that such a low bar could prevent anyone from understanding? its some fake generosity towards "newcomers" that is completely unwarranted. math notation is by and for professional mathematicians.

are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R"

[tenacious_tuna]

> why pretend that such a low bar could prevent anyone from understanding?

I don't know why this is a startling take. If you encode your ideas in an unfamilar symbology, of course that's going to make it more difficult for someone who isn't familiar with the space.

I'm not arguing that we should teach real analysis this way, or any other high level math class. I'm only contesting GP's comment that there is NO value to be had in using more familiar language to explain a new concept to an unfamiliar audience.

This is the entire reasoning behind "word problems" at the elementary level; they're meant to ground the abstract modeling of a math problem (193 - 3 * 12 = ?) into something more intuitive for a child to understand (If you start with 193 eggs, and you take three dozen away to bake a cake, how many are left?)

> are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R"

No, I'm saying the there's tradeoffs on either side, and our educators ought to be aware of this.

> math notation is by and for professional mathematicians.

I agree, but we teach math to plenty of people who aren't professional mathematicians. I wouldn't want to do formal abstract algebra proofs in a more verbose form, I'm perfectly happy using the domain notation, but my friends from biological sciences who have to take a calculus course now have to learn both a new symbology alongside the problem domain. I've watched enough of my (clearly intelligent) biology friends slam face first into calculus and spin out. They're not dumb, they can do circles around me when it comes to chemistry, yet they Just Can't wrap their heads around calculus-style math, which leads me to wonder what the difference is between how we teach complex chemistry vs complex math. Questioning the pedagogy is a fairly logical extension of that.

[globular-toast]

If there was some better notation that allowed biology people to understand calculus more easily, what do you imagine they'd do with it?

It's hard for me to imagine it without any special notation. It makes me think of the general relativity in words of four characters or less that was posted recently. Sure, it might be possible, but does it really make it easier to understand? Understanding is normally built up in layers. We learn things using big words because that makes it easier than learning with small words. And we learn maths with funny symbols because it makes it easier than learning it with words (or colours or mime or other things you already know).