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... I ran across this criticism of this movement courtesy of a rather annoyed Arne Duncan, and frankly, I laughed out loud.

Arne Duncan: White Suburban Moms upset that Common Core shows their kids aren't brilliant.

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U.S. Education Secretary Arne Duncan told a group of state schools superintendents Friday that he found it “fascinating” that some of the opposition to the Common Core State Standards has come from “white suburban moms who — all of a sudden — their child isn’t as brilliant as they thought they were, and their school isn’t quite as good as they thought they were.”
cool Yes, yes, yes.

Criticism about the implementation is one thing. But most of these parents ranting and raving about Common Core are just mad that their precious snowflakes don't look so good now that actual standards are involved...
As I understand it, the precipitating event was NY parents calling out the system on the mis-match of the test and the curriculum being taught. You may have recently shared a similar concern of toxic educational practices regarding curriculum which doesn't seem to support the content that is evaluated by assessments?

In NY, Spring 2013 standardized testing was that for Common Core, while students were being taught with unrelated curriculum and content. Some have said the Common Core standardized tests were not more rigorous per se, just different, and may have made an example of how poorly students (as well as their teachers, schools, districts, and States) will fare if they do not follow Common Core and "teach to the test".

Meanwhile on the Official Blog of the U.S. Department of Education, "Homeroom", Arne Duncan issued a bit of an apology for his earlier statements, calling it "some clumsy phrasing that I regret... I singled out one group of parents". (link- http://www.ed.gov/blog/2013/11/high-standards-for-all-schools-and-students-everywhere)