While Common Core has often been rolled out poorly, when I actually saw the content it teaches, I realized it is teaching kids to think exactly how I have always intuitively processed numbers, as a math-y person. Same with a lot of the math-y people I know. So I think the idea is to produce better/deeper understanding of mathematical theory, something the old system didn’t do (and some of us just happened to figure out thinking that way for ourselves). It seems like it’s not very effectively implemented in many cases though, maybe perhaps because often the teachers don’t even understand it very well, and many parents then can’t help since they weren’t taught that way.
Yes. The order of operations is still around, although some argue it’s broken.
Same… but that was before we graded on feelings instead of performance
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I honestly don’t even remember how I was taught addition, subtraction, multiplication, division… in the simplest sense. However, i do remember that in second grade we would do these timed tests on all of these to determine how quickly we could determine the answer. It was all memorization… it wasn’t really math…
I remember being placed in a group that did the tests faster so I was considered upper level. I look back on that now though and wonder… upper level at what exactly? memorization?
While I did end up majoring in mathematics in college (somewhat contradictory to the point I’m making), I do think kids benefit from thinking through math problems rather than memorizing the answers.
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The only thing I recall as strictly memorization were the “times tables”…I don’t think there’s any other way to learn those though…or at least, there used to not be. 
Today, who knows!
Well, one of the differences is stuff like if you’re trying to add 217 and 54, you can write it out and calculate it in columns doing the ones, tens, hundreds (how most of us were taught), or you can think in your head more easily by breaking it into easier to manage component parts, like 210 + 50 = 260, 4+7 = 11, so 277. Or if you had 97 + 36, if you recognize immediately that 97 is 3 less than 100, you can get to 133 so much faster (almost instantly). I’m pretty sure most people who can calculate things quickly in their head use those types of methods, just without formal training, and those approaches are part of what Common Core tries to teach. It also facilitates deeper understanding how numbers work to think about that way vs memorizing. Similar strategies can apply to other operations.
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