# Timeline for 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?

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Apr 7 '21 at 6:39 comment @StevenGregory: of course you are right. But I've just been describing how it was done many years ago in a society where the mechanical skills were necessarily more valued than they need be today. The redeeming feature was that it was called Arithmetic, and was an entirely different subject from Mathematics; in the same way that (hand)Writing was a completely different subject from English.
Apr 7 '21 at 3:30 comment @ancientmathematician: This was actually a senior-level theory of arithmetic class. Mathematics isn't about remembering addition and multiplication tables. It's about recognizing and exploiting patterns. At the most abstract level, yes, that includes efficient processing of strings of digits. Out of context it's gibberish. It takes more than a good teacher for it to mean more.
Apr 6 '21 at 19:13 comment I think I knew what "new math" was in 1965 when I gave classes on it for English schoolteachers, but I'm not sure what "new math" means today. ;-)
Apr 6 '21 at 19:07 comment @ancientmathematician What do you think about "new math"?
Apr 6 '21 at 6:41 comment In my opinion, No, not nowadays. In a pre-computer society, when every craftsman, farmer, shopkeeper, whatever had to daily perform many calculations then things were different. I've been looking at my old Arithmetic books and noticing what a lot they tell us about society.
Apr 6 '21 at 6:35 comment @ancientmathematician Is it a good way to teach math?
Apr 5 '21 at 7:11 comment If I may make one more comment. @Steven says "You start by saying 9 plus 3 is 12". That's not how I remember it: you start by saying "3 is bigger than 2, so borrow 1 " [here you write the little ones], "now 12 take away 3 is 9". In other words, we knew by heart two independent facts: (i) 3 add 9 is 12 (ii) 12 take away 3 is 9. In an addition sum you used the first, in a subtraction sum the second. It was years before I realised that it was more than a coincidence that these look so similar: we didn't waste time on semantics, we were being trained as efficient processors of strings of digits!
Apr 5 '21 at 6:59 comment @MatthewChristopherBartsh we were all being trained up to be double-entry bookkeepers ;-)
Apr 5 '21 at 2:37 comment @ancientmathematician That method is awesome. It's like doing the same thing to each side of an equation so it remains true.
Apr 4 '21 at 11:28 comment My recollection (Scotland in the 1940s/50s) is that the full-blown notation for beginners puts a little one at the top of the units as well as a little one at the foot of the tens (etc). I still do. The first subtraction then looks like 12 take away 3, so we write 9. Etc.
Apr 4 '21 at 9:54 comment This is the method and notation I learned in Finland: youtube.com/watch?v=HhldRs8Hkdw . I have no idea what it would be called or how it would be said in English, but it is certainly European.
Apr 4 '21 at 9:19 history edited