So what would happen if instead of teaching/learning mathematics in the standard way: how to count, arithmetic, functions and algebra, geometry-trig, cartesian coordinates, calculus.
what if instead they began with Mathematical foundations like logic, proof, set theory, etc.; Abstract Algebra; Number Theory, discrete math, combinatorics, etc.; and so on.
When we're taught mathematics in this standard way we're bound to forever poison our minds to think in that way first until we abandon it which will take much more time.
So how would we go about the most mental masturbatory way of learning mathematics?
I assume the way I've loosely some what resembles a poor but not awful idea. I'm only a mathematics undergrad so I'd like the opinion of others more educated or knowledgable.
Imagine we're reforming the entire educational standard so we start off with K-12+.
I'd figure for K graders you could introduce declarative statements to them as a soft introduction to logic, as well as the container interpretation of sets, counting and numbers. this way we can probably begin to get a good grasp of naturally gifted students.
Also if you're in a different field I'd like to know the "radical introduction" to that field you'd create.