A Daily News report this week cast doubt on the validity of the state’s math scores. A major problem the News pointed to is that the math tests seem to repeat themselves, broken-record style, making it easy for teachers to coach their students on how to give correct answers — without necessarily understanding the underlying math. A second problem is that the tests may be getting easier over time, the story said.

Here’s a graphical portrait of what this means in practice, courtesy of Jennifer Jennings, the doctoral student at Columbia University whose analysis informed the News’s story.

A math question seventh-graders answered in 2009:

picture-21A math question for seventh-graders in 2008:

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And finally a question from the same test’s 2007 version, assessing the same concept, but in a much more difficult way:

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Here’s another set of “clones,” as Jennings calls them.

From the 2009 seventh-grade math test:

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From the 2007 seventh-grade test:

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