Thank you, Bostonian, for posting this excerpt. It piqued my curiosity to consider that the influence of a teacher in NY has determined policy and practice on the opposite coast... a national influence. Being the author of several books extends her reach. I did a web search on Carol Burris. She has written two books sharing her viewpoint against grouping students by ability:
1) Detracking for Excellence and Equity (2008)
2) On the Same Track (2015)

To her credit, she currently does NOT support Common Core.
To her dismay, the Common Core has turned out to be a way to standardize curriculum and testing across the nation and to generate uniform data.
Two thoughts on this:
1) Ironically, before flip-flopping her viewpoint, she made money by publishing a book on how to implement core (2012).
2) Some of us were aware of the development of these tests from early on, and the roles which they would play, even as common core "standards" were being crafted to usher these tests and data collection methods in:
Originally Posted by DOE Factsheet, 2009
With such comprehensive data systems, states will be able to monitor their reforms and make specific changes to advance them.
What other views does she hold?
She opposes the use of test scores to evaluate teachers, and she cites what is known as Campbell’s Law:
“When test scores become the goal of the teaching process, they both lose their value as indicators of educational status and distort the educational process in undesirable ways.”
Many people oppose common core, including some who once supported it. Many people also oppose excessive standardized testing, and data collection. Often these viewpoints are found to be philosophically consistent with respecting each student as an individual with unique talents, challenges, and learning needs... therefore not philosophically compatible with promoting a one-size-fits-all classroom.

Who is Diane Ravitch, author of the articles on Carol Burris & Common Core, quoted earlier in this post?
Originally Posted by dianravitch.net
I am the mother of two sons. They went to private schools in New York City. I have four grandsons: two went to religious schools, the third goes to public school in New York City, and the fourth will go to the same wonderful public school in Brooklyn.
How might she feel if "the wonderful public school in Brooklyn" which two of her grandsons attend were to announce discontinuation of any selection criteria and advanced academics? Yet these may be the ideas foisted on other families, partly by influence of Network for Public Education (NPE), of which Diane Ravitch is president and to which she recently appointed Carol Burris as executive director of the NPE fund.

Here I see two ladies "playing" with education policy, as long as it affects someone else's kids.

What about NPE? According to statements on its webste, it was co-founded in 2013 by Diane Ravitch and Anthony Cody.

Here's the list of ideas which NPE supports. I do not see a statement against grouping students by ability.

The NPE website states that
In 2011, she received the Daniel Patrick Moynihan award from the American Academy of Political and Social Sciences for her careful use of data and research to advance the common good.
(emphasis added)

In supporting Carol Burris' anti-tracking message (and furthering a policy and practice of teaching students in classrooms which encompass all ability levels) possibly Diane Ravitch, was unaware of, overlooked, or discounted this important data and research, which indicates that students learn more when grouped with others of similar ability:
1) http://www.casenex.com/casenet/pages/virtualLibrary/gridlock/groupmyths.html
2) http://www.gifted.uconn.edu/nrcgt/reports/rbdm9204/rbdm9204.pdf