"Those who know, do. Those who understand, teach." -unknown
I strongly question the validity of this woman's bachelors degree if she couldn't figure out the answer to the question. I would hope that any college worth its salt would teach problem solving, critical thinking, and acceptance of there being more than one right way to solve a problem. Second, this woman clearly has no idea what goes into effective teaching. So while you can't "destroy the common core" with one sentence on a kid's assignment when you obviously have no idea what the common core actually is, I am going to completely destroy her "argument".
If you're too lazy to click the link, the article is ridiculously titled: "Angry Mother Destroys Common Core by Writing This on Her Son's Test", and the image that goes along with it is this:
First, let me solve the problem that was oh so difficult for this alleged Electronics Engineer who has done extensive training in "higher math applications" and differential equations (neither of which is relevant because your elementary school kid is obviously not being taught either of those things). Side note: I have plenty of brilliant friends with bachelors degrees and more who have commented that they have completely forgotten how to do long division. So the fact that you may or may not be able to solve differential equations has literally no bearing on why you can't solve an elementary-level math problem.
Let me break it down for you:
That line with tick marks is a student created number line. Jack wanted to visualize this subtraction problem, and used one of many strategies he was likely taught to do so. Because he was working with hundreds, it is much easier to skip count when possible, than count back 316 by ones. He recognized that 316 has 3 hundreds, 1 ten, and 6 ones. So he started by counting back by hundreds. Starting at 427, he jumped back to 327, 227, then 127. Now he's taken care of the hundreds, so he moves on. But oh no! Jack you silly boy, you forgot about the tens and went straight to ones! Jack merely counted back 6 from 127: 126, 125, 124, 123, 122, 121. Had he counted back by 10s, he would have jumped from 127 to 117, and then the ones, to end up with 111.
It is true that you can use the simple method of lining up the numbers to do 427-316. But this is not what Jack did. Because Jack, like many students, is still developing some of his number sense, especially number sense with large numbers. The traditional method is abstract, and if you learn those quick tricks, you may completely miss the important parts: why the trick works, when you can and cannot use said trick, and what subtraction even is. So, yes, maybe once you graduate into the work force, simplicity is valued over "complication" (even though what Jack was doing was not that complicated.)
But your child is in SCHOOL. Not the work force. We don't want kids taking the easy way out. We want kids to understand what they are doing, and be able to apply these concepts to new problems in creative ways. If they just know the quick tricks, and have no concept of what is actually going on with numbers, they won't amount to much in a work force that increasingly values problem solving and creativity. This process might result in termination if you are an Electric Engineer and using it daily on the job, because you should no longer need scaffolds such as using a number line to visualize a problem. You will not, however, be terminated from a school for solving a problem a different way from the kid sitting next to you, in order to fully understand a concept. How fast your kid can solve something is NOT the point. The point is understanding, and persevering to solve problems. Not every problem can be solved in 5 seconds, and if you teach your kid that he should be able to solve math fast to be successful, I'm afraid you are setting your kid up for failure.
Okay, so now that I've done your son's homework for him, you may be saying, hey, you didn't address the issue with the Common Core! Don't worry, I shall now. This is not "common core math". The Common Core is a set of standards that covers what a student should understand by the end of each year in school. It does not tell teachers HOW to teach. This strategy may be addressing a standard, but I'm pretty sure this strategy has been taught for longer than the Common Core has been around. The issue you are having is more with the math curriculum that is being used, not the Common Core. And that's the main issue. Many curriculums slap on a sticker that says "Common Core Aligned", and that sticker is the most Common Core thing about it. Slowly, we are seeing more effective curriculums pop up to provide teachers with resources to teach to the new standards. But again, the standards are much more about problem solving and justifying reasoning than about specific strategies teachers must teach. The Common Core is NOT a curriculum. There is no such thing as "Common Core Math" in the context that this frustrated, and frustratingly ignorant, mother uses it. So before you have a little fit about the common core, please educate yourself. Let me make it easy for you: HERE is the website for the common core standards. You can go read the standards themselves, or read the page that's about what parents should know.
Maybe you'll realize that your son's teacher actually knows what he or she is doing, and is effectively teaching your son math at a level that is developmentally appropriate for him. But hey, I'm just a teacher with a bachelors degree in psychology, a teaching credential, and a masters degree in education. What do I know?