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The Chicago Public Schools, the third largest system in the country, has decided to buck a mandate to give all its students a new Common Core test known as PARCC this school year, a decision that could have implications across the country for Core testing.

The Chicago Tribune reported that school district chief Barbara Byrd-Bennett, with support from the school board, made the decision not to give the Partnership for Assessment of Readiness for College and Careers test to all students. Instead, students in just 66 of more than 600 schools in the Chicago system would take the PARCC test. The other schools will use standardized tests that they have already been using.

The decision came just as Mississippi pulled out of the PARCC, one of two federally funded multi-state consortia tasked with creating new Common Core tests. (The other is the Smarter Balanced Assessment Consortium.) PARCC, which had 26 states in 2010, has suffered major defections in recent years, and now it has fewer than a dozen states — including Maryland — plus the District of Columbia. PARCC officials have said the consortium will not collapse but continued defections could challenge that assessment.

The decision by Chicago could also affect the national discussion with mandated annual standardized testing, perhaps the most contentious subject in the debate about rewriting No Child Left Behind. Sen. Lamar Alexander, the Tennessee Republican who just became the chairman of the Senate Committee on Health, Education, Labor and Pensions, has said he will push legislation rewriting NCLB, the current version of the Elementary and Secondary Education Act, onto the Senate floor by the end of February, and has suggested abandoning annual standardized testing that is imbedded into the law. The Obama administration has pushed to continue annual testing.

Byrd-Bennett asked Illinois education officials last summer for permission to delay the implementation of the PARCC exam, which is being given officially to millions of students for the first time this school year, because she still had too many questions about the test and its value. The Illinois Board of Education, concerned about a loss of federal funding, rejected the request. Other public school districts in Illinois are planning to give the PARCC this spring.

But the Tribune reports that Chicago education officials feel they have to delay implementation of the PARCC test, designed to be given on computers,  because of technology capacity concerns. (Although PARCC test was designed for the computer, paper versions are available and many schools are planning to them.)

“We’re not asking to be exempt, we’re not saying ‘Dump PARCC, dump Common Core ,’ ” Byrd-Bennett said.

“Too many of our children, over 400,000 of them, don’t have regular access to the technology that is needed. And we find that is particularly so in the younger grades,” she said.

The federal government requires that public schools test students for accountability purposes every year, and failure to do so can result in loss of federal funding.

PARCC and the other consortium’s new Common Core-aligned exam were field-tested on thousands of students last spring, and many districts reported computer problems.

There has been a growing backlash to the Common Core tests among students, parents, teachers, principals and superintendents, with tens of thousands of amilies choosing not to allow their children to take them and some teachers opting not to administer it. This weekend, an organization called United Opt Out is having its first conference, in Fort Lauderdale, Fla.

The Tribune quoted Wendy Katten, of the parent group Raise Your Hand, as saying she hopes that other school districts in Illinois and other parts of the country will push back on giving PARCC if they are not adequately prepared to give it.