system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: The "Old Math" in Tom Lehrer's New Math

If you haven't heard the song, he describes the way they used to do math as follows:

>Consider the following subtraction problem, which I will put up here: 342 minus 173. Now, remember how we used to do that:

>Three from two is nine, carry the one, and if you're under 35 or went to a private school, you say seven from three is six, but if you're over 35 and went to a public school, you say eight from four is six ...and carry the one, so we have 169.

He then proceeds to the song, which explains regrouping, the way I learned to do math growing up in the 90s. How did they teach it before?
gpt
Before regrouping, arithmetic was taught as a mechanical procedure to follow and practice religiously, without any regard to why it works.

     3 4 2
    -1 7 3
    -------

When subtracting a larger number from a smaller number, you'd pretend there's an extra 1 before the larger number, so 2 - 3 becomes 12 - 3. Then after writing down 9, you'd "carry" that extra 1 to the next line. Then you can either subtract one from the top number, or add one to the lower number - they're equivalent, and continue.

It's pretty much exactly the same as regrouping, but the idea of "carry the 1" doesn't really give you any insight into how it works.