[IAEP] versus, not

[Albert Cahalan]

Maria Droujkova writes:

> I think it may be useful to distinguish tracks, and destinations to
> which they lead. The real deal destinations are to make mathematics:
> coin definitions and refine them, pose problems, form conjectures,
> construct example spaces, create models and so on. Activities with
> real deal destinations invite students to make mathematics; this is
> the part where I get pretty "religious" and I suspect Tim does, as well.

I don't think this is a proper expectation.

Gym class isn't expected to create pro or Olympic athletes.
Music class isn't expected to create pop stars. Native language
class isn't expected to create a J. K. Rowling, Shakespeare,
or Tom Clancy.

Math isn't any different.

A student who is **solidly** prepared for calculus is doing well.
This would include word problems with a minimum of 4 steps,
some algebra, geometry, trigonometry, etc.

Here in the USA, most students get nowhere near that level.

For the very best students we may hope for completing calculus early
enough to use it for physics, followed by statistics with calculus.
Maybe one could throw in a tiny bit about game theory or aliasing.

A desire to have students "make mathematics" can't be allowed to
get in the way of ensuring that non-ideal students learn the existing
math that they need. Math isn't just for people like Euler.