But there is a way to teach mathematics from axioms that is intuitive: geometry. Euclid's Elements was the key mathematics textbook for about 2000 years.
Of course, you simply can't cover as much ground if you must derive everything.
But I do wonder if the collapse in public discourse is partly because of faith-based mathematics. i.e. taught as: it's true because we tell you it's true, not because you can see for yourself that it's true.
But there is a way to teach mathematics from axioms that is intuitive: geometry. Euclid's Elements was the key mathematics textbook for about 2000 years.
Of course, you simply can't cover as much ground if you must derive everything.
But I do wonder if the collapse in public discourse is partly because of faith-based mathematics. i.e. taught as: it's true because we tell you it's true, not because you can see for yourself that it's true.