Should Zermelo-Fraenkel Set Theory be taught to elementary school children?

[WalterWhite]

This is the foundation of mathematics and logic. Should ZFC and its axioms be taught to elementary school children?

[Inverted Things]

Absolutely not.  Two reasons: (1) I have doubts as to whether most under-11-year-old brains can really get it, and (2) ZFC is completely worthless to almost everyone, including most mathematicians.

Regarding my first point: See, if you're going to teach someone something, you've got to use what they know already as a hook.  We are born with an innate sense of numbers, and with a visual cortex.  If you're going to teach math to elementary school kids, you use those assets.  This is why arithmetic and geometry are quite good choices.  You don't try to appeal to their logical reasoning and abstraction skills -- those won't be sufficiently formed until adolescence.

Naive/intuitive set theory can be taught quite well at that age -- you can draw Venn diagrams to engage the visual cortex, and make sets out of physical objects, and so on.  But an axiom-deductive abstract system like ZFC is going to have trouble getting absorbed -- the mental equipment is just not matured enough yet.

(Side note: Geometry makes a great first proof-based course because you get to use that powerful visual cortex to help exercise and strengthen the developing logical reasoning faculties.)

And for my second point: Unless a mathematician explicitly works on foundational math, the only axiom they might care about is the Axiom of Choice (and even then, this is rare).  Naive set theory is good enough for almost all working mathematicians.  And if even most professional mathematicians don't need to know about ZFC, why on earth would you teach it to fifth graders?

If you must expose elementary school students to set theory, just do naive/intuitive set theory.  Don't do ZFC.

[Antonio the Sixth]

The idea of set theory as a foundation for mathematics might make sense in an abstract sense, but if it takes a 400-page book to prove that 1+1=2 (and even then people still aren't sure if you actually succeeded), it's not actually a good introduction to it.

[President Punxsutawney Phil]

The idea of set theory as a foundation for mathematics might make sense in an abstract sense, but if it takes a 400-page book to prove that 1+1=2 (and even then people still aren't sure if you actually succeeded), it's not actually a good introduction to it.

Quoted for truth.