Favorite field of Math?

abstract1
Sat, 20 Sep 2014 15:27:20 +0000

@Ctesiphon‌ @MITer94‌ Yep. The American education is just abysmal when it comes to mathematics. Basically, they take really rich, interesting fields of study and reduce them to their most mechanical, computational elements- presumably so they’ll be more ‘palatable’ to high school kids. But honestly I think people would like math more if they saw the wonder and theory in it, if the focus was on delving into theorems versus memorizing their applications.

Personally, when I took my first higher level, proof-based math course, I was shocked: I basically had to throw out all the technical garbage I had learned before, in my normal high school math classes, and start all over. That way of approaching mathematics- not solving arbitrary problems, but grappling with the overarching ideas- was completely new to me. Plane geometry only begins to scratch the surface.

Case in point: the whole fact that we go through the calculus sequence AGAIN to teach it right (in the form of real analysis) is indicative of just how barren our math is becoming. High school math is basically prep for engineering and more applied realms of science, and that’s about it.

If we started tweaking the way we do things- which we probably won’t, because of stubbornness and also because most high school math teachers really don’t have the training- I would suggest we start with proofs and conceptual math straight from the get go, let everything else be secondary. Teach more set theory in algebra, as this is the foundation of actual algebra, as @MITer94 pointed out. Maybe work in some non-euclidean geo in a typical geometry class to jazz it up. Teach calculus more like introductory analysis.

Sigh… a math nerd can dream.