I personally don't know enough about the Common Core (CC) to make an informed judgement about it - but from the Reader Comments at the article (a fair number of which I've been through, not all by any means), it appears that there are plenty of people who're "'Against' the 'Against'", i.e., they're "For the Common Core". (That's assuming one accepts the contention "my enemy's enemy is my friend". We should keep in mind that this contention may not *necessarily* be true: the logic of life in the real world may be somewhat more complex than that).
What does seem to be clear in any case is that the stakeholders in the US educational system - the 'for the Common Core' as well as the 'against' - really don't know how to design themselves an effective math educational system.
The New Yorker piece (when read along with its Reader Comments) does not seem to be of much help in terms of enabling the stakeholders find out what to do about the CC or how to go about resolving the underlying problem(s) posed by the CC:
"How to develop and design an effective math educational system for the nation's schools?" -
or, for that matter,
"How to develop and design an effective (school) educational system?"
Remarkable! We in India are confronted by the very same problems - and our stakeholders in the educational systems here are just as clueless as are the stakeholders in the USA! (Notwithstanding the huge differences between the two countries and their respective circumstances).
However, we must acknowledge that the US seems to have developed a 'higher education system' that had appeared in the past to be the envy of rest of the world - though there are murmurs (and, indeed, shouts, roars, bellows - and, perhaps moos and miaows also) against the 'higher education system' as well.
It appears that all of the above really represents a 'system problem': stakeholders in 'systems' do not know how to cope with issues and problems confronted in the complex systems within which they have to live and work and play!
Remarkably enough, it was a US scientist, the late John N. Warfield, who developed practical means that could help stakeholders in complex systems take control of the systems around them, within which they have to live. More information about Warfield's developments is available at http://www.jnwarfield.com and at the "John N. Warfield Collection" held at the library of George Mason University, where Warfield was Professor Emeritus - see http://ead.lib.virginia.edu/vivaxtf/view?docId=gmu/vifgm00008.xml.
Though Warfield provided the basic modeling tools and showed the general approach required to enable people "take better charge" of their own systems, some further developments were needed. One of those developments is the 'One Page Management System' (OPMS), which enables people to articulate any 'system Mission' and then to develop, from their own available good ideas, an *effective* Action Plan to accomplish it. More information about the OPMS is available at the attachments to my post heading the thread "Democracy: how to achieve it?" - see http://mathforum.org/kb/thread.jspa?threadID=2419536. There is something more required (I think), and I'm using the OPMS to figure out just what this something might be.