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Apr 7 '21 at 6:39 comment added ancient mathematician @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 added Steven Alexis Gregory @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 added ancient mathematician 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 added Matthew Christopher Bartsh @ancientmathematician What do you think about "new math"?
Apr 6 '21 at 6:41 comment added ancient mathematician 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 added Matthew Christopher Bartsh @ancientmathematician Is it a good way to teach math?
Apr 5 '21 at 7:11 comment added ancient mathematician 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 added ancient mathematician @MatthewChristopherBartsh we were all being trained up to be double-entry bookkeepers ;-)
Apr 5 '21 at 2:37 comment added Matthew Christopher Bartsh @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 added ancient mathematician 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 added Tommi 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 Steven Alexis Gregory CC BY-SA 4.0
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Apr 4 '21 at 9:14 history edited Steven Alexis Gregory CC BY-SA 4.0
added 521 characters in body
Apr 4 '21 at 8:55 history answered Steven Alexis Gregory CC BY-SA 4.0