Math isn't flexible like that though. You're asking for flexibility where there is none. Sure pemdas is technically arbitrary but having a set convention for that is strictly necessary and good teaching.

But there is logic behind them.

1+2+3=6 and 2+3+1=6 also.

But 1+2*3 and 2*3+1 won't come out the same if you do the calculations in just any order. It's not always possible to order them left to right like in the second version, and if we use parentheses for everything we can end up with an illegible mess. I actually tried to type an example of how silly it could look and lost track of my own parentheses nesting before I got very far.

Do you have any other suggestion for how to notate an equation which would make memorization of PEMDAS unnecessary?

🤨

Not understanding the logic doesn't mean it doesn't exist.

We created math and devised a method to ensure that equations can be solved in a way that leads everybody to the same result. If you don't use the rule, you don't get the same answer as someone who does. In this circumstance, yes, you do teach by nailing down a strict rule as it's foundational to the language (math) that we've created.

Bro doesn't know how math works