that whole "if it's adding, pass it subtracting; if it's multiplying, pass it dividing" thing doesn't exist anywhere. no serious math textbook teaches that. it's purely a trick some teacher made up and everyone replicated without thinking about the consequences.
i always see teachers in brazil saying this. always. as if it were an official algebra rule and nobody questions it.
the right thing is the equality principle. whatever you do to one side, you do to the other. simple as that.
like, take this equation
x + 3 = 7instead of going with that twisted idea of "pass the 3 over there changing the sign", you subtract 3 from both sides
x + 3 - 3 = 7 - 3
x = 4same thing with multiplication. if you have
2x = 10instead of "pass the 2 dividing", you divide both sides by 2
2x / 2 = 10 / 2
x = 5when you understand it's an operation on both sides, things get way clearer. especially when the math gets gnarlier and the trick of passing stuff back and forth simply stops working.
this trick creates a false feeling that math is just about memorizing rules. then the person gets to college and discovers it was never like that and thinks they're dumb. they're not dumb, they were taught wrong.
i think the equality principle should be taught from elementary school. it's more logical, more elegant, and prepares much better for whatever comes next.
plus, "pass it to the other side" even sounds kinda weird if you stop to think about it. like, pass where? why does the sign change? nobody explains. meanwhile "subtract from both sides" is self-explanatory. (≧◡≦)
idk, i think we need to stop teaching math as if it were witchcraft and start showing that it's really just logic. then maybe fewer people would have trauma from stem subjects.