SAT Error Means Math Scores Will Rise for 45,000 Students

Guess who flunked the SAT?

The College Board itself.

Admitting that it made a mistake in a math problem, the organization that oversees the Scholastic Assessment Test, the most widely used college admissions exam, is adjusting the scores of 45,000 students--upward, by as much as 30 points.

The mistake was detected by a student who alerted the College Board and the Educational Testing Service, which devises the questions, that an algebra item had more than one correct answer, depending on how part of it was interpreted.

“We knew we had a problem after three college math experts confirmed the student’s perception,” Brian O’Reilly, director of the SAT program, said Wednesday. “Not only did this exceptional student find a flaw that had been overlooked by internal and external math specialists during extensive reviews, but he did so while taking the SAT.”

As a result, most scores will be increased 10 points, but a “very few” will be raised 20 or 30 points, the College Board said, without saying how one question could make such a difference. No scores will be lowered, and the flawed item will be omitted from future tests, the board said.

The error affects about 13% of the 350,000 students who took the three-hour test that was given in October.

The College Board said it will finish recalculating scores this week and rush out the revised results to the students and to all schools, colleges and scholarship organizations that received the earlier scores.

The College Board said it has not found a flawed item on the SAT since 1982.

The announcement comes at a crucial time, when colleges are reviewing applications for admission to the fall class.

“I’m glad they found the error and that acceptance and rejection letters haven’t gone out yet,” said Susan Bonoff, a college counselor at North Hollywood High School. “Ten or 20 points could make a significant difference. Hopefully, it will help some students.”

The questionable question--one of the most difficult on the test, according to the College Board--asked students to determine the relationship between two quantities. The confusion stemmed from how a test-taker determined the median of an algebraic sequence and whether an integer--”a”--was seen as positive or negative.

The original “correct” answer assumed that the “a” in the sequence was positive--and did not account for the possibility that it was negative.

Anti-testing groups jumped on the College Board’s admission of error as proof of the need for public oversight of standardized testing.

“No matter how often this happens, even if once a decade, it provides further evidence of the need for truth in testing,” said Bob Schaeffer of the Cambridge-based National Center for Fair & Open Testing, a nonprofit group that questions the accuracy and fairness of standardized exams such as the SAT. “Whatever you think of the test, it’s still not a perfect product.”

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SAT Snafu

Here is the math problem from the Oct. 12, 1996, SAT that led to the revision of scores for 45,000 test-takers:

DIRECTIONS: The following question consists of two quantities in boxes, one in Column A and one in Column B. You are to compare the two quantities and on the answer sheet fill in oval:

A if the quantity in Column A is greater,

B if the quantity in Column B is greater,

C if the two quantities are equal,

D if the relationship cannot be determined from the information given.

*

The first two terms of the sequence are 1 and a , and each succeeding term is the product of a and the preceding term.

*

THE GOOF: Here is the College Board’s explanation of what went wrong with the question:

* This was one of the most difficult math questions on the test, and it worked well if students thought the value of “a” was positive or viewed the median of a sequence as the middle term. In these cases the “correct” answer was C, which is what the test designers intended.

* However, if students considered that the value of “ a “ could be negative and then reordered the numbers in the sequence to find the median, they would arrive at a different answer. For example, if a = -1 and n = 6, the terms of the sequence would alternate between 1, -1, 1, -1, 1, -1, 1. When the numbers in this sequence are placed in numerical order (-1, -1, -1, 1, 1, 1, 1), then the median (or middle term) is 1. In this same example (a = -1 and n = 6), the value in column B is -1 (-1 to the third power). So if students considered both positive and negative values for “a” they would probably have chosen D as the “correct” answer (since D indicates that the relationship cannot be determined from the information given.) Thus the answer to the question depends upon what is meant by “the median of a sequence” as well as whether the value of “a” could be either positive or negative.

Source: The College Board