Concepts over computation (or well, before computation) is probably right. But New math was about learning the abstract before the concrete. This was predictably an abject failure.
I think the best way to teach math is to follow the trajectory that humanity took when discovering it. The key that's missing is that math doesn't just come out of thin air, its just a systematization of precise quantitative thinking. If we motivate the concepts using real world examples, then explain how to abstract away the particulars into a general procedure, then these connections will get made that make math "real" and relevant.
BTW, "not even wrong" is a rather rude way to point out a misunderstanding.
I find it disheartening that I have to teach my kids basic fractions, ratios, and transformation cause the teachers don't or barely touch on it. Kids are supposed to "discover" and "explore" math, whatever that means. In my opinion it's all bullshit.
Math, in many ways, is like an engine, either it works meaning the answer is correct, or it doesn't.
The way people are teaching math in the US is baffling and weird, but Pearson's textbook design has little to do with the common core per se. Most common core-labelled material is from something else with a new shiny CC cover slapped on.
Concepts of what? Without intuitive understanding of basic computation procedures, what concepts can anyone build out of nothing?
Math is concrete. It's from observation of actual quantitative phenomenon.
Modeling the world is a job that math the tool was created for, but it certainly isn't concrete just because the world that needed it was or is.
To split them, and think that, just because there is abstraction, and it's OK to develop the concept without the concrete substrates of actual experience is trying to make dream come true.
And I argue that no one should live in a dream. And it's obvious that only those dreams that have a strong connection with the real world have realistic chance of being made real.
Many problems that people have with math seem to stem from not having internalized the most basic facts about addition and multiplication. If you don't know at least to 10 by 10, each tiny step of working through a problem will tend to be interrupted by counting. Fluency requires memorization.
EDIT: As pointed out, I mistook OPs invocation of New Math to be talking about the much maligned Common Core rethinking of math education. I was briefly a high school math teacher, but before the roll out of these changes, so I can't comment first-hand on what the new curriculum looks like in the actual teaching. But I do know how poorly prepared my students were for math beyond arithmetic. They were trained with similar curriculum that I had experienced growing up in the 90s, which I think is poorly thought out.
Apologies for the confusion caused by me not recognizing the term New Math.