Technology

At least that’s not how I’ve been taught in school

If you had a bad teacher that doesn't mean everyone else had a bad teacher.

You’re not teaching kids how to prove the quadratic formula, do you?

We teach them how to do proofs, including several specific ones.

No, you teach them how to use it instead.

We teach them how to use everything, and how to do proofs as well. Your whole argument is just one big strawman.

Again, with the order of operations

Happens to be the topic of the post.

It’s not a thing

Yes it is! 😂

I’ve given you two examples that don’t follow any

So you could not do the brackets first and still get the right answer? Nope!

2×2×(2-2)/2=0

2×2×2-2/2=7

That’s kinda random, but sure?

Not random at all, given you were talking about students understanding how Maths works.

2+3×4 then it’s not an order of operation that plays the role here

Yes it is! 😂 If I have 1 2-litre bottle of milk, and 4 3-litre bottles of milk, there's only 1 correct answer for how many litres of milk of have, and it ain't 20! 😂 Even elementary school kids know how to work it out just by counting up.

They all derive from each other

No they don't. The proof of order of operations has got nothing to do with any of the properties you mentioned.

For example, commutation is used to prove identity

And neither is used to prove the order of operations.

2 operators, no order followed

Again with a cherry-picked example that only includes operators of the same precedence.

You have no property that would allow for (2+3)×4 to be equal 2+3×4

And yet we have a proof of why 14 is the only correct answer to 2+3x4, why you have to do the multiplication first.

Is that not correct?

Of course it is. So what?

It literally has subtraction and distribution

No it didn't. It had Brackets (with subtraction inside) and Multiplication and Division.

I thought you taught math, no?

Yep, and I just pointed out that what you just said is wrong. 2-2(1+2) has Subtraction and Distribution.

2-2 is 2 being, hear me out, subtracted from 2

Which was done first because you had it inside Brackets, therefore not done in the Subtraction step in order of operations, but the Brackets step.

Also, can you explain how is that cherry-picking?

You already know - you know which operations to pick to make it look like there's no such thing as order of operations. If I tell you to look up at the sky at midnight and say "look - there's no such thing as the sun", that doesn't mean there's no such thing as the sun.