I came across this method to perform subtraction using addition and not using the "borrow" concept, apparently because it is harder to learn it that way.

Video - https://www.youtube.com/watch?v=PKOd6S4-iXk

This method is referred to as "Austrian method" in wikipedia article

  1. Is it really hard for students to learn subtraction using "borrow method"
  2. Is the "austrian method", better than the borrow method?
  3. Are there any studies into which methods of teaching subtraction are more/less helpful to students?

I found reference to this method in the book "The Teaching of Arithmetic; a Manual for Teachers" by Paul Klapper, published in 1921

enter image description here.

Has this "controversy" been settled by now?

  • 2
    $\begingroup$ When I read the title I thought you meant the nine complement which is easier than the standard method. $\endgroup$
    – user5402
    Apr 30 '18 at 15:50
  • 1
    $\begingroup$ See also my answer on MESE 11093 here. $\endgroup$ Apr 30 '18 at 21:00
  • $\begingroup$ @BenjaminDickman thanks for linking that question. It is not clear if that book provides any "conclusions" as to which method is better. $\endgroup$
    – user13107
    May 2 '18 at 5:13
  • $\begingroup$ Watching the first few minutes of Salil Gadgil's video (linked in the Q), I don't see how the concept of adding-with-carry is any less difficult than the concept of subtracting-with-borrow. $\endgroup$
    – shoover
    May 30 '18 at 16:41
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    $\begingroup$ It may be worth noting that "addition with carries" and "subtrating with borrowing" were introduced with the New Math in the 60s(?), and were seen as strange and confusing at the time. $\endgroup$ Sep 17 '19 at 15:45

Wikipedia says the Austrian method is now used in some countries in Europe.

I looked up what the Austrian method is. I recognized it from the patter in one of Tom Lehrer's comic songs, "New Math". Here it is:

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;

So perhaps the Austrian method was still used in America up to 25 years before that song, whenver that was...

  • 1
    $\begingroup$ That song was first performed in 1965. So , based on those lyrics, it would have looked like the Austrian method after 1940 if you checked their work, except that the Americans were memorizing subtraction facts (mod 10) instead of leveraging the addition facts they already knew. Before 1940, their "carry" would have been somehow subtracted from the minuend instead of added to the subtrahend, so that was a beneficial change at least. $\endgroup$ Sep 18 '19 at 10:28

I have been taught both methods. By different teacher, and at different age, although I do not remember in which method first.

Today I am using both indifferently, sometimes changing of method in the middle of the subtraction. I noted a tiny preference for the Austrian method, but I think it is purely esthetic, because most of the time the choice is totally unconscious.

There is no harm in teaching both methods, and let the student decide.

  • 1
    $\begingroup$ I have to say that the Austrian method won my vote at around 4:50 in the video when he calculated 5000-2468 without drama. That's unpleasant to do with the borrowing-and-regrouping method, and more unpleasant yet to explain to a student IME. $\endgroup$ Sep 17 '19 at 22:56
  • $\begingroup$ One way to explain carry/borrow is to move out of the decimal system. Try to find the time elapsed between 10h45mn and 11h30, i.e. subtract 11h30 - 10h45. Because there is not enough minutes in 30 to subtract 45, you have to borrow 1 hour to 11, and convert it in 60mn : 10h90 - 10h45 (American method) or to carry 1 hour from 45mn : 11h30 - 11h(-15)mn (Austrian method). $\endgroup$
    – AlainD
    Sep 28 '19 at 11:27

Both these methods suffer from the same problem: they work from right to left, despite our reading numbers from left to right. That's why children have trouble with long sums.

I discovered as a small child that I could always be the first kid in class to put my hand up when the teacher wrote a subtraction (or addition) sum on the blackboard, by working from left to right, so that (if necessary) I could do the sum in my head while giving the answer.

.69 from 1.00 is (round the 60 up to 70 and take from 100 = 30; 9 from 10, no need to round the last digit up, is 1) hence thirty-one. It worked beautifully when I worked weekends as a sales clerk as a teenager.


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