When does 2 + 2 = 5?
When you're taking the state math test.
Despite promises that the exams -- which determine whether students advance to the next grade -- would not be dumbed down this year, students got "partial credit" for wrong answers after failing to correctly add, subtract, multiply and divide. Some got credit for no answer at all.
"They were giving credit for blatantly wrong things," said an outraged Brooklyn teacher who was among those hired to score the fourth-grade test.
State education officials had vowed to "strengthen" and "increase the rigor" of both the questions and the scoring when about 1.2 million kids in grades 3 to 8 -- including 450,000 in New York City -- took English exams in April and math exams last month.
But scoring guides obtained by The Post reveal that kids get half-credit or more for showing fragments of work related to the problem -- even if they screw up the calculations or leave the answer blank.
Examples in the fourth-grade scoring guide include:
* A miscalculation that 28 divided by 14 equals 4 instead of 2 is "partially correct" if the student uses the right method to verify the wrong answer.
* Setting up a division problem to find one-fifth of $400, but not solving the problem -- and leaving the answer blank -- gets half-credit. (See Photo Above)
* A kid who subtracts 57 cents from three quarters for the right change and comes up with 15 cents instead of 18 cents still gets half-credit.
* A student who figures the numbers of books in 35 boxes of 10 gets half-credit despite messed-up multiplication that yields the wrong answer, 150 instead of 350.
These questions ask students to show their work. The scoring guidelines, called "holistic rubrics," require that points be given if a kid's attempt at an answer reflects a "partial understanding" of the math concept, "addresses some element of the task correctly," or uses the "appropriate process" to arrive at a wrong solution. Despite flubbing the answer, students can get 1 point on a 2-point problem and 1 or 2 points on a 3-pointer.
The Brooklyn teacher said she and peers who had trained to score the tests were stunned at some instructions.
"Everybody in the room was upset," she said.
The teacher had scored tests with some "controversial questions" for several years, but "this time it was more outrageous," she said. "You feel like you're being forced to cheat."
Scorers joked about giving points to kids who wrote their names, brought a pencil or shared gum.
However, score inflation is not funny, the whistleblower said.
"The kids who really need the help are just being shuffled along to the next grade without the basic skills to have true success. They are given a hollow success -- that's the crime of it. The state DOE is doing a disservice to its children."
Some testing experts are also troubled.
Ray Domanico, a former head of data analysis for city schools, said kids deserve a little credit for partial knowledge but agreed the scoring system "raises some questions about whether it's too generous."
State Education Department spokesman Tom Dunn defended the scoring.
"All teachers who score exams receive clear training and rubrics that detail scoring criteria for every question on the tests," he said. "Students who show work and demonstrate a partial understanding of the mathematical concepts or procedures embodied in the question receive partial credit."
But a few extra points can let a failing kid squeak by.
A year ago, Chancellor Joel Klein boasted that the city was making "dramatic progress" when 82 percent of city students passed the state math test and 69 percent passed in English, up sharply from 2002. And fewer kids have been left back in recent years.
What officials didn't reveal was that the number of points needed to pass proficiency levels has, in most cases, steadily dropped.
The state Board of Regents, which oversees the tests, has postponed the release of results until late July, but let the city Department of Education set its own "promotional cut scores" to decide which kids may be held back. The DOE will release those scores in the next two weeks, a spokesman said.