PE(MD)(AS) Now just remember to account for those parentheses first
Those Brackets don't matter. I don't know why people insist it does
I did not flip any signs
Yes you did! 😂
merely reversed the order in which the operations are written out
No, merely reversing the order gives -3-2+1 - you changed the signs on the 1 and 3.
If you read the right side from right to left, it
Starts with -3, which you changed to +3
it has the same meaning as the left side from left to right
when you don't change any of the signs it does 😂
Hell, the convention that the sign is on the left is also just a convention
Nope, it's a rule of Maths, Left Associativity.
a single sentence of a wikipedia article without me handfeeding it to you
And I told you why it was wrong, which is why I read Maths textbooks and not wikipedia.
I’m sorry for your students
My students are doing good thanks
The notation is not intrinsically clear
It is to me, I actually teach how to write it.
Exactly! It’s in math textbooks, in both ways!
And both ways are explained, so not ambiguous which is which.
inside radicals
I had to look up what that meant (should've done that the first time - sorry) - have never heard that before, must be a local terminology.
So, square roots (or other roots) can be expressed as an exponent - e.g. the square root of 2 is the same as 2 to the power ½ - so that's covered by "E", exponents! (or I for Index, or O for to the Order of, depending on your area)
I appreciate your mention of the importance of teaching the difference between operators and terms
Thank you.
My pedagogical background is in the sciences and I’m much better at doing math than teaching it
Oh god, welcome to why I have so many people argue with me, a Maths teacher, about it. There's a whole bunch of Youtubes and blogs out there by Physics majors. I'm like "OMG, why are you trusting someone with a Physics major over someone with a Maths major - god help me".
I would like if math classes (in my area) did more explicitly teach the difference between terms and operators
So what area are you in? A country will do. You said PEMDAS so I'm guessing the U.S.? I've heard via Youtubes/blogs that indeed there is more confusion with what is taught there, but I ended up Googling for U.S. textbooks, and found the same thing being taught in the textbook, so I'm not sure where this "that's not what they teach in the U.S." is coming from (why I was Googling for U.S. textbooks in the first place). Is the standard of teachers there actually worse than elsewhere? Or is it perhaps (possibly more likely) that there's just more U.S. people posting, therefore more people who've forgotten the actual rules, and are just (as I've seen many times) they're just blaming it on what they were taught (which I've usually found isn't true at all).
it was decided that it would be easier to change how the equation was interpreted
No, it wasn't. The claim that the rules were changed is a debunked myth.
Yes, the guy who should mind his own business.
How about his reference for historical use
Are you talking about his reference to Lennes' letter? Lennes' letter actually completely contradicts his claim that it ever meant anything different.
Elizabeth Brown Davis
Haven't seen that one. Do you have a link?
He also references a Slate article by
...a journalist. The article ALSO ignores The Distributive Law and Terms.
I wouldn’t disagree with that.
Thank you. And also thank you for being the first person to engage in a proper conversation about it here.
I’ve heard Presh respond to people in the past over questions like this
I've seen him respond to people who agree with him. People who tell him he's wrong he usually ignores. When he DOES respond to them he simply says "The Distributive Property doesn't apply". We're talking about The Distributive LAW, NOT the Distributive Property. It's called "law" for a reason. i.e. ALWAYS applies. I've only ever seen him completely unwilling to engage in any conversation with anyone who points out he's wrong (contradicting his claim that he "welcomes debate").
I have a lot of respect for him
Really?? Why's that? I'm genuinely curious.
I’ve never heard the variant where there was a clear change in 1917
Me either. As far as I can tell it's just people parroting his misinterpretation of Lennes' letter.
Instead, it seems there was historical vagueness until the rules we now accept were slowly consolidated
I can't agree with that. Lennes' letter shows the same rules in 1917 as we use now. Cajori says the order of operations rules are at least 400 years old, and I have no reason to suspect they changed at all during that time period either. They're all a natural consequence of the way we have defined the symbols in the first place.
The Distributive Law obviously applies
Again, thank you.
I’m seeing references that would still assert that (6÷2) could at one time have been the portion multiplied with the (3)
If it was written (6÷2)(1+2), absolutely that is the correct thing to do (expanding brackets), but not if it's written 6÷2(1+2). If you mean the latter then I've never seen that - links?
6/2=3
3(1+2)=9
You just did division before brackets, which goes against order of operations rules.
For me to read the whole of 2(1+2) as the denominator in a fraction
You just need to know The Distributive Law and Terms.
You probably missed the part where the article talks about university level math,
This is high school level Maths. It's not taught at university.
Why would I read something that I know is wrong? #MathsIsNeverAmbiguous
They don't. It's irrelevant that they have the same priority. MD and DM are both correct, and AS and SA are both correct. 2+3-1=4 is correct, -1+3+2=4 is correct.
And there's absolutely nothing wrong with doing that, for example. You still always get the correct answer 🙄