I’ll never understand these approaches to learning. They require remembering the phrase, and then require remembering how the phrase translates to the rules you need to remember
Yeah, exactly, but the U.S. seems to have a chip on it's shoulder about always doing everything differently to the whole rest of the world. "Maths? We're not going to use BEDMAS, and we're not going to call them Brackets, and...".
That's because it's already clear as is, as per the rules of Maths.
I think someone told me that order of operations is like a natural law
It's a natural consequence of the definitions of the operators. e.g. Multiplication is shorthand for repeated Addition - 2x3=2+2+2 - so if you don't do it before addition you end up with wrong answers. The order of operations rules is in fact just breaking everything down into Addition and Subtraction and then solving from there.
not a convention
There are some conventions, like left to right, but in that case that's only because students tend to make mistakes with signs when they don't go from left to right, so it's there to preserve teachers sanity.
that there was a multiplication there since it isn’t explicit
There isn't a Multiplication there, only Addition and Brackets, and Subtraction inside Brackets. It's never Multiplication unless there is a Multiplication sign.
The engagement comes from people not remembering the rules of Maths
(8-5)5
That's an invalid syntax. it's 5(8-5) or 5x(8-5), nothing else. Why is it invalid? Imagine (8-5)-5 - am I multiplying what's in the brackets by -5 (which gives -15), or subtracting 5 after doing the brackets (which gives -2)? Invalid syntax
Far easier for most people
Nope, it's wrong for everyone, due to being an invalid syntax.
Yeah, exactly, but the U.S. seems to have a chip on it's shoulder about always doing everything differently to the whole rest of the world. "Maths? We're not going to use BEDMAS, and we're not going to call them Brackets, and...".