what i wish i had been told about math in school
i have to know something well enough to be able to explain it to another person before i feel like i understand it.
I had a great math teacher in grade school, and we used an abacus to help conceptualize what was happening in multiplication and division which was super helpful for me i could feel like i really understood why and how.
but in later classes i began to be told things like
"we do it that way because that's the way it's done" and
"because if you do it any other way you get the wrong answer"
and, like, okay but if you do FOIL out of order you do get an answer, like you can do the math that way and you do get an answer, why is that answer wrong? What makes this answer right?
Clearly it IS the right answer, everyone seems to agree on that, but can you please for the love of all that is holy tell me how do we know that?
but nobody would tell me, and i stopped feeling like i understood what was going on, because i didn't know why we were doing the things we were doing
and that made math really hard for me.
So here's what i wish i could go back and tell myself
the answer is that a lot of math, maybe even almost all of it, is used to describe or prove observable phenomena.
so we see observable behavior number one, let's call it Snowballs Flying
and we see observable behavior number two, let's call that one Kids Walking By
and we do Bonkers Level Math that describes those behaviors, measurements for position, math that describes a changing rate of speed, math that describes the way gravity effects the snowballs, maybe even throw some wind force and air flow dynamics in there, all kinds of math
and that math lets us make predictions. Predictions like Snowball 37a and Kid-JS4 will be in the same place at the same time. And when JS4 goes down with an ear full of 37a, it proves all our math was right! (or at least that it was only off minutely)
So the reason you have to do FOIL (or whatever) when you encounter that kind of equation is because when you're doing Bonkers Level Math you have to do it that way to be able to accurately describe the things we can see happening around us
if someone had just fucking told me that, istg