[advice_thrwawy9]

It's worth pointing out that virtually every math teacher I had growing up, in retrospect, had no knowledge or experience with any actual math.

I recall wondering out loud in hs geometry if one infinity could be bigger than another in typical early high school "big brain" thinking, and at the time my high school geometry teacher basically shrugged their shoulders.

Years later when I discovered cardinalities of infinite sets, which comes up pretty quickly when studying math in college, I was fairly disappointed that such a great potential teaching moment was passed over. I'm pretty sure early high school me would have been dramatically more engaged with math if a teacher has said "funny you should mention that, do you know about the difference between integers and real numbers..."

The tragedy of this is that most Americans, even the ones teaching math, believe mathematics is calculation, and even at the advanced levels will only rarely be exposed to real mathematical thinking.

[d3ckard]

It's interesting, because I was introduced to cardinal numbers and alef zero, plus Cantor proof, precisely during highschool mathematics class. In Poland though.