## Wednesday, March 30, 2016

### More quality control issues -- Regents exams edition

Math teacher and blogger Patrick Honner has been looking closely at the NY State Math Regents exams and found questions like this:

If

Find

If you remember your junior high algebra, you probably spotted the mistake here. This function doesn't have an inverse. Honner goes into detail on this point but I suspect everyone reading this knows where he's going, Sufficed to say, unless we add a condition like "for x greater than or equal to zero," the correct answer would be "does not exist."

Here's the answer that gets the student full credit (which is definitely not a function).

They get half credit if they leave off the plus-minus (which would actually have been the right answer if we had included the previously mentioned condition).

As Honner puts it:

In summary, you get full credit for the wrong answer, but if you forget the worst part of the that wrong answer (the plus-minus sign), you only receive half credit!  So someone actually scrutinized this problem and determined how this wrong answer could be less correct.  The irony is that this conceptual error might actually produce a more sensible answer.  The further we go, the less the authors seem to know about functions.
It gets worse. Following an outcry from teachers:

The next day, the state gave in and issued a scoring correction:  full credit was to be awarded for the correct answer, the original incorrect answer, and two other incorrect answers.  By accepting four different answers, including three that were incorrect, you might think the Regents board would have no choice but to own up to their mistake.  Quite the opposite.

Here’s the opening text of the official  Scoring Clarification from the Office of Assessment Policy:

Because of variations in the use of $f^{-1}$ notation throughout New York State, a revised rubric for Question 32 has been provided.

There are no variations in the use of this notation, unless they wish to count incorrect usage as a variation.  I understand that it would be embarrassing to admit the depth of this error, which speaks to a lack of oversight in this process, but this meaningless explanation looks even worse.  This is a transparent attempt to sidestep responsibility, or, accountability, in this matter.

I realize New York is a big place, but between Eureka Math, the Success Academy schools and this, the state is more than pulling its weight when it comes to blog fodder.