One of the reasons common core math is so controversial is because it's one of these "shared experience" topics for which everyone has personal experience and considers themselves an expert, yet most don't realize that their own experience is probably quite different from nearly everyone else's. And the reason theirs is different is in large part because their mind works differently and they naturally fell into using skills matched to their own strengths and weaknesses. Take 20 people and pair them off into 10 pairs, and have one person in each pair walk the other through how they calculate 876 - 381 in their head. You will 10 different results[1]. The problem with common core is that it teaches a handful of these approaches rather than letting the student develop their own customized approach.
[1] I have actually done this experiment. Of the 8 pairings, I think we had 7 different algorithms. Only two people did something close enough to be called the same thing.
The implementation and communication about what Common Core is doing needs a little work. The author mentioned this, and I think he's absolutely right. The fact that math-educated parents like you are reacting negatively to Common Core is a symptom of the plan not being very well explained to parents, even though once people see it clearly, they often agree that it looks like a superior way to teach math.
I guess I'll just add a side note that fostering this appreciation for different approaches might actually be getting more directly at the universality you mentioned above. There's a deeper truth behind the meaning of subtracting two numbers than any one algorithm holds, and perhaps the only way to see it is to be familiar with multiple algorithms.
From the article, "the Common Core State Standards in the U.S. still requires student fluency with these algorithms"
> Being able to mentally estimate numbers or do simple arithmetic is a good skill
It's not just about the ability to estimate or do simple mental arithmetic. Look at this example from the article: "Describe three ways to see why 35 x 12 is 420". Knowledge of these 'three ways' provides a deeper conceptual understanding of multiplication. I want my students to have a shot at deriving the algorithm for multiplication, not just implementing it.