There was previously a question/rant here on MESE about why so many are still using the PEMDAS/BODMAS/BIDMAS/BEDMAS mnemonics to teach order of operations. The question was deleted (still viewable by 10K+ users), but there were some comments and an answer that had a link to an argument against PEMDAS, from which an interesting and useful question can be extracted.
Like the author of the linked argument, I, who attended government-run schools in the suburban US in the 1970s, also had never heard of PEMDAS until I was an adult. In fact, I probably first encountered the mnemonic while reading edu-blog posts and/or MESE or MSE. I don't remember how we were taught, but I know that I have internalized the rules so I don't have to think about them, whereas I encounter adults who have to write down "PEMDAS" before they can begin.
I realize this may be several questions, but they are interrelated:
Why, and less importantly when and where, did mathematics educators begin to use mnemonics to teach order of operations?
Note: there is a related question about why the mnemonic rule works, but that doesn't get into the justification for teaching order of operations in this way.