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Did Americans, before new math came in to schools, really say, 'three from two is nine carry the one", instead of borrowing ten from the tens column?

Tom Lehrer claims and the audience seems to agree with him that the 'old way', before new math to do subtraction was to say, for example, 'three from two is nine carry the one' and put a miniature one on top of the tens column. I never heard of this method. Does anyone still use it? What is it called? https://www.youtube.com/watch?v=UIKGV2cTgqA is the video showing Tom Lehrer's bit. Does it really not involve understanding what you are doing as the new math activists claimed (I presume).

Lehrer's example is 342 - 173.