Anecdotally, I was not very good at math in school (enough to pass, but not much better), mainly as a result of a lack of motivation. I got interested in math (and subsequently better) when I learned set theory (not in school), as I felt like I understood more about why arithmetic works the way it does. It was hard to motivate myself to learn math when it felt like pointlessly executing algorithms that computers are so much better at anyway. This is obviously just an anecdote, but I feel some sort of exposition to set theory in schools, though maybe not at the beginning of math education may be beneficial. I am now better at math than I used to think, and actually enjoy it, and I think that you are right that many more people could be also.
Could you please be more specific about how the set theory motivated you? (Was it set theory specifically, or just the general feeling of “there is a secret kind of math they do not teach at school, and I know it”?)
What I remember from my elementary-school textbooks, we drew some Venn diagrams and calculated a few inclusion-exclusion exercises, but most of the time it was “set theory as attire”, where you said: “this set contains two apples, and this set contains three apples, therefore their union contains five apples” which was just a complicated way of saying: “two apples, plus three apples, equals five apples”. That’s all.
On the other hand, the set theory I read about as an adult, is mostly about how you can construct sets starting from an empty set using the ZF axioms, how you can simulate all kinds of mathematical objects using such sets, how to compare infinite cardinals, and whether the axiom of choice is a good idea.
From my perspective, the usage of set theory at the elementary school was just an applause light, because the main thing that fascinated mathematicians about sets—how you can use them to simulate everything else (so hypothetically, if you could prove any statement about sets, you could prove everything) -- or the thing that fascinates amateurs and crackpots—infinity!, more real numbers than integers (or maybe not) -- is unrelated to what is taught at school. And counting to 20 could be taught without sets just as effectively.
Anecdotally, I was not very good at math in school (enough to pass, but not much better), mainly as a result of a lack of motivation.
I got interested in math (and subsequently better) when I learned set theory (not in school), as I felt like I understood more about why arithmetic works the way it does.
It was hard to motivate myself to learn math when it felt like pointlessly executing algorithms that computers are so much better at anyway.
This is obviously just an anecdote, but I feel some sort of exposition to set theory in schools, though maybe not at the beginning of math education may be beneficial.
I am now better at math than I used to think, and actually enjoy it, and I think that you are right that many more people could be also.
Could you please be more specific about how the set theory motivated you? (Was it set theory specifically, or just the general feeling of “there is a secret kind of math they do not teach at school, and I know it”?)
What I remember from my elementary-school textbooks, we drew some Venn diagrams and calculated a few inclusion-exclusion exercises, but most of the time it was “set theory as attire”, where you said: “this set contains two apples, and this set contains three apples, therefore their union contains five apples” which was just a complicated way of saying: “two apples, plus three apples, equals five apples”. That’s all.
On the other hand, the set theory I read about as an adult, is mostly about how you can construct sets starting from an empty set using the ZF axioms, how you can simulate all kinds of mathematical objects using such sets, how to compare infinite cardinals, and whether the axiom of choice is a good idea.
From my perspective, the usage of set theory at the elementary school was just an applause light, because the main thing that fascinated mathematicians about sets—how you can use them to simulate everything else (so hypothetically, if you could prove any statement about sets, you could prove everything) -- or the thing that fascinates amateurs and crackpots—infinity!, more real numbers than integers (or maybe not) -- is unrelated to what is taught at school. And counting to 20 could be taught without sets just as effectively.