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It is determined largely by partisan political motivations. To keep it lounge-safe, I'll just say that where you are is a different political side than the national political side that is giving/taking money from local political bodies for accepting or rejecting this political agenda.
There... I didn't argue about politics.
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I think the idea is to move from the lower number to the larger number in small steps that are each easy to do:
3 + 5 = 8,
8 + 10 = 18,
18 + 2 = 20
Yay! There is the answer!
The old way way was obviously way too complicated where you have to do:
The "ones" column: 2 - 2 = 0
The "tens" column: 3 - 1 = 2
...and then you wrote the "tens" answer followed by the "ones" answer to get 20
Yay! There is the answer!
Of course, you could make it even easier by only incrementing the lower number by 1 until you reached the larger number and then counting how many times you had to do that. 20 Yes! That should be the new method! Much simpler!
Or, for future programmers using nice round, easily remembered numbers:
12 + 4 = 16
16 + 8 = 24
24 + 8 = 32
____
20
- I would love to change the world, but they won’t give me the source code.
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Quote: Of course, you could make it even easier by only incrementing the lower number by 1 until you reached the larger number
You can borrow my fingers if you need to. 
There are only 10 types of people in the world, those who understand binary and those who don't.
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Quote: You can borrow my fingers if you need to
No thanks; I hate to think where they might have been!
- I would love to change the world, but they won’t give me the source code.
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I'm flattered to be in your dreams but really, this has got to stop.
There are only 10 types of people in the world, those who understand binary and those who don't.
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Dreams, dreams? Now the nightmares begin...
 
- I would love to change the world, but they won’t give me the source code.
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My son's going through this now and it's driving my wife crazy. I've reviewed it and I think I understand the "why" behind it. I've started thinking I look at numbers differently than her. Most Americans learn math by memorization - flash cards, repetitive tables, etc. They don't think about what the numbers actually mean. They are stuck as they have only memorized base 10.
What happens when you need to understand base 2, 8, 16, 535? The majority of Americans can't figure those out. They never had flash cards for that. However, this is teaching kids early how to understand the value of the number outside of what they have memorized.
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Now I don't mean to defend this nonsense. Understanding how to subtract properly is clearly important and the 'count up in increments' method is generally longer and therefore more error prone. However, this is how people often count out change ("that's £6.52, sir" ... *hands over tenner* ... "and your change ... six fifty two, six sixty, seven, eight, ten" as he hands me the 8p, a 10p, two 20s, two £1s and a £2) and it may be a good way in for people who aren't getting it, or want a way to confirm their 'proper' subtraction is working correctly.
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That is well and good for counting UP in money, where you end on a larger denomination of base 10.
But how will common core work on fractions and algebra/calculus, etc where you have to determine multiple variables, which may or may not be easily expressed as a base 10 whole number 
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BobJanova wrote: "that's £6.52, sir" ... *hands over tenner* ... "and your change ... six fifty two, six sixty, seven, eight, ten" as he hands me the 8p, a 10p, two 20s, two £1s and a £2
So you score £1.20? I can see the value in this method. 
What is this talk of release? I do not release software. My software escapes leaving a bloody trail of designers and quality assurance people in its wake.
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No, he only scores £1.10. £0.08 + £0.10 + £0.20 + £0.20 + £1.0 + £1.0 + £2.0 = £4.58
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Skitt's Law strikes again. 
What is this talk of release? I do not release software. My software escapes leaving a bloody trail of designers and quality assurance people in its wake.
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I knew I should have checked that more carefully ...
The counting out is correct, the coinage isn't. Should be 8p, 2x20p, £1, £2 obviously.
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I haven't had anyone count out change since the mid 80's.
".45 ACP - because shooting twice is just silly" - JSOP, 2010
-----
You can never have too much ammo - unless you're swimming, or on fire. - JSOP, 2010
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When you pry the gun from my cold dead hands, be careful - the barrel will be very hot. - JSOP, 2013
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Still happens moderately often on market stalls, I find, and in some independent shops too.
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I am not sure how this is better way. If someone claims this is helpful in real World calculations, I do not get how. I mean how can it be easy to subtract using 10 steps instead of traditional? If they are really after an alternate way, why not Vedic Maths[^]? I did a beginner course in middle school on it and did find it weird at first. But once I became habitual, it was quick.
As far as this method is concerned, this[^] is what I found.
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I homeschool my kids.
My son is waaaaay ahead of grade level in math. But I don't think he enjoys it and everything is quite tedious. I would like some additional ways of approaching problem solving. I think this may be a nice fit. Thanks for the link to vedic.
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Now do
12
- 32
----
I think I saw that crap on one of my kid's math papers (7th grade) a while back. It's nonsense.
We need to teach these kids 2s-complement -- it's the only true path!
You'll never get very far if all you do is follow instructions.
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?????
No wonder kids can't count back change. They're purposely trained to be morons.
My theory is that this is done to distract people from realizing that the teachers are illiterate and incapable of working simple arithmetic. If anybody seriously evaluated their skills, they'd be immediately fired, and we can't afford to retrain all of them to flip burgers.
Will Rogers never met me.
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*cough*innumerate*cough*
Did you ever see history portrayed as an old man with a wise brow and pulseless heart, waging all things in the balance of reason?
Is not rather the genius of history like an eternal, imploring maiden, full of fire, with a burning heart and flaming soul, humanly warm and humanly beautiful?
--Zachris Topelius
Training a telescope on one’s own belly button will only reveal lint. You like that? You go right on staring at it. I prefer looking at galaxies.
-- Sarah Hoyt
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I was quite specific, and accurate. They can't write, either, though the OP didn't mention that fact. The two skills go hand in hand, and those lacking either are doomed to failure.
Will Rogers never met me.
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I use that method to help students who think subtraction is too hard, and in-fact I will sometimes use it in my head for rapid math. I definitely prefer the long-hand version when writing, however, as it is less error prone. I think the biggest gap is that most of the teaching methods now are so focused on trying to teach below average students methods of how to understand simple concepts it leaves every one else in the cold. Certainly takes quite a while to think dumb enough to understand many of the common core methods.
Sadly, they make sense if you are lost or clueless but as as student who was left out to dry using the really old methods because it was too easy, I really feel for the top 55% now who will be left out with this. Private school if I ever have kids, I swear.
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Spot on the money. I know a few retired teachers, including one who was only teaching 'gifted' students. In order to get the most $$ from the gov't, the schools are aiming at the lowest performing students. It doesn't matter how good the gifted students are... only how many students are above the line.
The more kids you get to pass a -basic- skills test, the more $$ the school system gets.
My friend watched the budget for the 'gifted' students get cut to where they couldn't even have enough teachers for accelerated classes. All the while, more teachers aids were hired to help problem students.
We are becoming a society of mediocrity... and by mediocre... it is an average that has a lower bar every year.
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