February 01, 2005

When a math exam becomes an exercise in basic probability

The New York Post has the goods on the new but not improved Math A Regents exam standard :

High-school students taking the Math A Regents exam this week must correctly answer fewer than one-third of the questions to pass — the lowest benchmark in at least six years — because of a revised grading scale that critics charge is too generous. Students are required to earn just 26 out of a total 84 points — or 31 percent — to reach the minimum passing grade of 55.

To pass with "honors," students only need 34 points — or around 40 percent.

The state Department of Education insists the scoring is just as rigorous as previous exams and consistent with recommendations of the independent panel that devised the test. "There are somewhat more difficult questions on this exam, however, and so students need to get somewhat fewer questions right in order to pass," said state education spokesman Tom Dunn. "Anyone who looks closely at this exam will see that it is not easy."

I disagree (as does the Post), and for one simple reason. We heard a similar argument a while back, in the discussion of the UK maths GCSEs. If you recall, I said then that there might indeed be no problem with a very low passing standard, whereas here, I say there is.

The difference is that, while the UK exam is completely open-ended, the Math A Regents exam contains thirty multiple-choice items (or MCQ's, as we call them) that are worth a total of 60 out of the 84 total points - 71.4% of the exam. If the passing standard is set at a raw score of 26 points, or 13 MCQ's answered correctly. A student can pass this exam by getting 13 MCQ's and no open-ended items right, because all items are combined and scored; the conversion is done only on that final combined number-right score.

Mere guessing, at four options an item, gets a student up to 7.5 items by chance alone. It doesn't matter if the MCQ's are more difficult; no matter how difficult they are, students can still get the right answer by chance alone. So a student need get only an additional 6 items right in order to pass. They can completely bomb the open-ended part and pass. And calculators are allowed. And this represents an increase in the number of MCQ's on the exam compared to 2003. And we haven't even gotten into discussing the generous conversion table.

I'm sure you can guess the reason why the passing standard was lowered, by the way. They've been very concerned in NY over the miserable passing rates on this exam. This solution doesn't exactly address the root causes.

Others who have more math knowledge and understanding of these exams than I have been appalled by Regents math exams in the past. My guess is that they're still appalled. If you haven't visited the NYC Hold website, you should. It's a great read.

(Via Joanne Jacobs.)

Posted by kswygert at February 1, 2005 04:34 PM
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