A couple of question on writing good

[Chronos]

@Thudlow_Boink

Or you’re forgetting that, like the way English is written, the way math is written is full of arbitrary rules and mutually-agreed-upon conventions. What would you tell a student who argued that, logically, the symbol 9 should mean negative six, or one-sixth, because it’s 6 upsode-down?

I would ask them how they intend to represent the number 9, and how they would represent the additive or multiplicative inverse of 8 or 101. Then, one of two things would happen: Either the student would decide that the notational idea they came up with is impractical, and I would have dealt with the question just as quickly as if I had told them “no, because The Rules say so”. Or, the student would come up with answers to those questions, and develop a new system of notation for numbers, and would in the process learn a great deal about how systems of notation of numbers work.

You’re not going to be able to gotcha me by asking “But what if a student starts to think for themself?”. That’s the whole point: I want students to think for themselves. That is the primary fundamental purpose of education.

[GreysonCarlisle]

More to the point, if a student decided to forgo My Dear Aunt Sally and just did every operation in the order it was written, they would be flouting a convention to the detriment of their finished product. The logic behind the order of operations and the logic behind the guidelines for punctuation are similar: be clear without being cluttered.