This is an issue that would occur regardless of CC, I believe. Unless you can differentiate them into separate classes fairly early, and are constantly checking to see if everyone is in the correct group (for instance, I have several students who are labeled as gifted in math who can't do simple addition without a calculator... they were listed as gifted in third grade, and then never tested again), one of the two is always going to suffer. Either you help the higher level kids at the expense of the lower, or the lower at the expense of the higher.
As for 'students see the new methods as being...' it's because they just mimic how their parents see them. Now, I don't teach elementary school so I don't know what they do, but reading comments here it seems they basically teach students how numbers work. And that's a good thing. I have high school students who didn't know that to multiply a number by 15, you could multiply it by 10 and by 5 then add the results. Along the same lines, they didn't know you could multiply by 10 then divide by 2 (or divide by 2 then multiply by 10) to get multiplication by 5. And this impacts them a lot more when we discuss variables and polynomials (which is mostly what Algebra II should be). They have no concept of how numbers work, so they don't understand why x^3/x = x^2.
Despite her spending tremendous care at trying to neatly diagram exactly as she was taught, the methods apparently do not scale well past 3 significant digits.
It becomes an exercise in frustration which can take up to 10 minutes trying to solve a multiplication problem which she knows how to do properly in the blink of an eye.
There’s lots of graphite going on the page, but I’m highly skeptical of any learning. Certainly any love of math quickly goes out the window during the process.
The Common Core doesn't specify curriculum. Period. Anyone who cites a specific problem or worksheet as evidence the Common Core is bad doesn't know what they're talking about. It's just evidence of an incompetent teacher.
Often she will do the problem the “new” way taking up maybe 10 minutes and a whole sheet of paper which looks more like an art project, and then when she’s done check her work the “old” way in a few seconds, and then go back and find the mistake in the drawings.
She’s happy to do it “because that’s the way [my teacher] wants us to” but she’s faster and better at doing it the traditional way.
My personal opinion is that CC is perhaps better at teaching basic math skills to the bottom 50% and is less likely to lose students along the way, but at the cost of holding back the top 50% of students approximately 1 full grade-level by the time they graduate high school. From my limited sample sized poll students see the new methods as being just as ridiculous as parents see them.
And parents are generally pretty frustrated about this whole fiasco: https://youtu.be/wZEGijN_8R0