PEMDAS --- > Order of Operations am I confused or is my professor wrong!

I just want to get down to the truth, although I'm pretty sure I'll google this myself I want other opinions.
So I'm in college math and while using the order of operations my professor swears up & down the correct way to do the operation when it comes to multiplication,division & addition,subtraction is to go from left to write of the math problem. I'm having a very hard time understanding this for the simple reason all through out high school & middle school I was told by my teachers this :

Do multiplication before division & do addition before subtraction

now all of a sudden my professor teaches me:
when we get down to doing division & muliplication we do the problem from left to right
when we get down to doing addition & subtraction we do the problem from left to right

I'm highly confused, so I guess when there's division before multiplication I'll do it in that order
when there's subtraction before addition I'll do it in that order

He's a wise man who seems to know his stuff but I just utterly don't think it's right, I mean why would they have us remember PEMDAS(Please Excuse My Dear Aunt Sally) in middle school & high school. I'm pretty sure all the teachers I've had for math DID know their stuff when teaching me this but again I'm a freshman in college stuff may be different! but idk, this is just a itch I'm dying to scratch!

Also, if he's wrong I'm just going to have to do "HIS" way of teaching for my tests, I don't want to fail knowing what I was taught to do is wrong by 1 professors perspective of it.

I'm not sure why people are saying that the order doesn't matter.
Consider: 12 / 4 x 3
If you go left to right, you get:
(12 / 4) x 3 = 9
If you do multiplication first, you get:
12 / (4 x 3) = 1

Obviously, order matters.