That's the wrong way to do it according to Common Core [ijreview.com]. No, instead you need to do this:
Instead of citing a silly youtube video that's part of the FUD campaign against the common core (motivated by political dogmas that have nothing to do with math or education), why don't you try referencing the actual common core state standards say is that 2nd graders should be taught to:
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Note "strategies" (plural). Good "common core" activities take a class of problem and look at multiple ways of solving it. As others have pointed out, your 'common core' subtraction method is one perfectly valid strategy for doing a subtraction in your head. Its not a replacement for the traditional way (which, as you can see, is perfectly compatible with the common core definition. If any teachers really are teaching "your" method, rote, as "the way" to do do subtraction, and marking the traditional method wrong, then they really don't have a clue about common core. More likely someone with an axe to grind has cherry-picked the example from an activity in which students are specifically told to try different methods, or explore strategies for mental arithmetic, and presented it out of context.
Also, please bear in mind that the current 'status quo' in US schools is not:
32
-12
------
20
....but more like:
What is 32 - 12?
(a) 44,
(b) 30,
(c) 20,
(d) -44
Shade the correct bubble.
...and its logically impossible to get any more insane than that (plus, the kids still can't do it).
This isn't even as insane as it gets. My son was given the problem: 1.62 / 0.27. Instead of actually dividing, he was told to draw 162 "tenths segments" Then he had to redraw them, but in groupings of 27. The number of groupings was his answer. Does this work? Yes, but it doesn't teach kids to work with numbers.
From the common core state standards:
Grade 6 The Number System Compute fluently with multi-digit numbers and find common factors and multiples. 3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Either your son urgently needs to change school or, more likely, you've again picked out part of an activity designed to help kids understand a topic from different perspectives and weed out common misconceptions. In this case, lots of kids would answer '0.06' or '0.6' because they think division always makes things smaller. This sort of activity helps them understand why that is not true.
A good activity might have kids repeating a method like this with 1.62/27, 162/27 and 162/0.27, maybe using manipulatives or some software, and reflecting on the result sandwiched between more traditional problems using the standard algorithms.
and yet kids are being taught that THIS is how you solve math problems and doing it any other way is WRONG (even if it works and gives you the right answer).
[Citation Needed]. There's certainly nothing of the sort here. If anything, the thrust of the common core is that there isn't just one right way of doing something (read the Common Core Math Practices).
If any teacher is actually doing as you describe then they are emphatically not teaching the common core, and someone, somewhere along the line has either pulled a massive TL:DNR (not impossible) or is deliberately spreading (or unwittingly retweeting) political FUD.
And remember, the status quo is that millions of kids fail to learn the good 'ol fashioned way of doing things.
Anybody who's actually any good at math (including most of slashdot) will tell you that the great thing about math was that they didn't have to remember lots of stuff because it all fitted together and made sense. The challenge is, how to make that happen for the other 90% of the population who are desperately trying and failing to learn math by rote. Back in the good old days of the 1950s, being able to add up, multiply and divide reliably without understanding it might land you a job as a clerk. Not any more - understanding is required, and a good way to achieve understanding is to slow down and spend some time looking at concepts from different angles... except then some dork comes in, takes a snapshot of what is visible that second and presents it as "what our kids are doing now instead of proper maths".