upworthy

standardized tests

Education

In the early 80s, there was one SAT question that was literally impossible to answer

Everyone got it wrong and it wasn't their fault.

Photo by Nathan Dumlao on Unsplash

Teenager is baffled.

As if the SAT didn't already have a less-than-stellar reputation in terms of racial bias and the possible inability to truly measure a student's cognitive abilities, now a story about an expensive blunder is once again making the rounds on social media. Back in 1982, one math question on the test was completely impossible to answer on the multiple-choice Scantron. How was that possible? Because the correct answer hadn't even been listed.

Pencil, SAT test, Scantron, testing, SATsClassic SAT test. Photo by Nguyen Dang Hoang Nhu on Unsplash

Here was the question: Picture two circles, a large one marked B and a smaller one next to it with an arrow, marked A. "In the figure above, the radius of Circle A is 1/3 the radius of Circle B. Starting from the position shown in the figure, Circle A rolls around Circle B. At the end of how many revolutions of Circle A will the center of the circle first reach its starting point?" Is it A, 3/2; B, three; C, six; D, 9/2; or E, nine?

On the Veritasium YouTube page, they explain that if you were to look at the problem logically, you'd conclude the answer was B, three. Because the circumference of a circle is 2πr, and the radius of Circle B is three times that of Circle A, "logically it should take three full rotations of Circle A to roll around." However, that answer is wrong.

- YouTubewww.youtube.com

In Jack Murtagh's piece "The SAT Problem that Everyone Got Wrong" for Scientific American, he conveys it all came down to the Coin Rotation Paradox (take note of this if you want to sound super intelligent on your next date or job interview).

You can try this yourself. Murtagh writes, "Here's how the paradox works: Place two quarters flat on a table so that they are touching. Holding one coin stationary on the table, roll the other quarter around it, keeping edge contact between the two without slipping. When the moving quarter returns to its starting location, how many full rotations has it made?"

Again, most test takers assumed that the answer was three. But "in fact, Circle A makes four rotations on its trip—again, exactly one more rotation than intuition expects. The paradox was so far from the test writers’ awareness that four wasn’t offered as an option among the possible answers, so even the most astute students were forced to submit a wrong response."

Why in fact was this the case? On the Scientific American YouTube page, it's explained again: "If you replace the larger circle with a straight line of the same length, then the smaller circle would indeed make three rotations. Somehow the circular path creates an extra rotation. And to see why, just imagine rotating a circle around a single point. There are two sources of rotation here. One from rolling along a path—and the longer the path is, the more rotations. And another from revolving around an object, which creates one extra rotation, no matter its size."

- YouTubewww.youtube.com

Okay, one more try. Here, it's relayed in terms of actual astrophysics: "This general principle extends far beyond a mathematical fun fact. In fact, it's essential in astronomy for accurate timekeeping. When we count 365 days going by in a year—365.24, to be precise—we say we're just counting how many rotations the Earth makes in one orbit around the Sun. But it's not that simple. All this counting is done from the perspective of you on Earth. To an external observer, they'll see the Earth do one extra rotation to account for its circular path around the Sun. So while we count 365.24 days in a year, they count 366.24 days in a year."

What might be equally interesting is that out of 300,000 SAT test-takers who got that question at the time, only three wrote in to the College Board to challenge the answer. Ultimately, they had to fix the test, which cost them over $100,000. (In 1982, that's at least ten Happy Meals.)

The comment section on YouTube was buzzing.

gif, wrong, reaction, reaction gif, math problemYoure Wrong John C Mcginley GIFGiphy

This person suggests following your gut, even if that does mean challenging a professor or other authority figure: "In college, I took a poetry class and once had an answer marked wrong on a test. Confident in my response, I reached out to the poet themselves, who affirmed I was right and even communicated this to my professor. Despite not being a fan of poetry, that moment made me quite proud!"

Another person commented on the reasoning behind the paradox itself: "That part about the circle rotating around the triangle was mind-blowing. You instantly understand why it's not the same if the circle rolls on a flat line or rolls on a curved line."

And for this person, it brought peace of mind: "This was the one SAT I took, and I remember the question that didn't have a correct answer, and it wasn't until today that I understood the right answer. I can die happy now."

From Your Site Articles
standardized tests
Most Shared

The sad reasons why women may perform worse on tests than men.

Standardized tests: sexist by nature?

If mock college-entrance exams were the actual exams, more women might get top scores, new research has found.

But the same wasn't true for men in the study. And that could add to the idea that the way standardized tests work is gender biased.

Photo via iStock.

Researchers at the National University of Singapore analyzed how 8,000 young men and women performed on China's national college-entrance exam. They tracked the scores for both the actual exams and the mock ones, which students took a month beforehand.

They found that women were much more likely to perform better on the mock exam than the actual one. Nearly 1 in 6 women who didn't qualify for entry into a top school would have qualified if the mock exam scores had been the ones that counted.

But what's to blame for this discrepancy?

While the study didn't pinpoint a clear reason why this disparity exists, previous research may give us a hint.

And as NPR noted, the big c-word may be a culprit. Competition, that is; it favors guys.

Many studies have found that "women on average are simply not drawn to competition as much as men are drawn to competition," NPR social science correspondent Shankar Vedantam explained. "So studies in the United States, for example, show that if you have a highly competitive setting, fewer women will step forward — and this is the really important bit to remember — even when the women are likely to do really well in the competition."

Photo via iStock.

This gender disparity could play a role in how women approach (and feel during) a real college entrance exam — arguably one of the biggest "competitions" a person can participate in.

So, are women to blame for their own shortcomings? Do they need to just, you know ... up their competitive edge with the big boys?

Not really. As Vedantamnoted while citing other research, it's not that men are naturally more competitive than women. They tend to be more so in more patriarchal (read: sexist) societies.

Photo via iStock.

So, as one theory goes, the more patriarchal a society, the more competitive the men are, which may collectively have a negative effect on the women they're among.

But there are other factors that can hurt women in the test-taking process, too.

In the U.S., scores from the SAT tend to underpredict the success of women once they're actually in higher education. That may be because many standardized tests operate in ways that put girls and women at a disadvantage.

Men tend to score higher on multiple-choice questions (they're more willing to guess on questions they don't know the answer to). They also benefit from timed testing; one study found that when time limits were removed from the SAT, girls were far more likely to see their scores increase than boys.


Photo via iStock.

Negative stereotypes don't help, either. When a girl takes a math test, the stereotype that girls are worse at that subject may (subconsciously) give her more anxiety because the pressure's on for her to disprove the negative assumption. The same stereotype can apply to say, a black or Latino student who's been told by society they're somehow less "college material" than their white counterparts.

This has been dubbed "stereotype threat." And, ironically, it only perpetuates these fallacies by increasing test-taking anxiety among oppressed groups. Stereotype threat may help explain why research found that girls were more likely to do worse on their AP calculus exams if they checked the gender box before completing the exam rather than after.

Something needs to change.

If research tells us one gender (or any group, for that matter) is at a disadvantage when it comes to the way we test, shouldn't we be rethinking our ways?

It's not a matter of life and death, but it is a matter of passing or failing. And that can make a world of difference.

From Your Site Articles
Trending Stories