Every day for the last four years, Leah Alcala has greeted her Berkeley, California, middle-school students with an exercise she calls "my favorite no."

As students enter class, they see a math problem on the whiteboard and are instructed to solve it on index cards. After they finish, Alcala immediately sees which answers are right or wrong -- "yes" and "no" -- and chooses her favorite incorrect response, the one most liable to be repeated. She then explains the mistake to the class -- never identifying its culprit -- and demonstrates how it can be avoided.

"At this point, I can almost predict the mistakes they're going to make in a way that I never used to be able to," Alcala says. In addition to helping her students understand that "mistakes are natural," she says, she has seen their test scores rise since she started the activity.

As it turns out, Alcala's students aren't the only ones who can benefit from exercises like "my favorite no." A new study by two French researchers published in the Journal of Psychology: General shows how telling students that failure is a natural element of learning -- instead of pressuring them to succeed -- may increase their academic performance.

"Teachers should not hesitate to tell children that what they're going to do is very difficult," said author Jean-Claude Croizet, a University of Poitiers professor. He conducted the study with Poitiers postdoctoral student Frederique Autin.

The study's findings, publicized by the American Psychological Association, come amid mounting cries against high-stakes standardized tests in the U.S. As more and more states seek to tie students' standardized test scores to teacher evaluations, statisticians often question the validity of those exams. According to Croizet and Autin, high-stakes test trigger a psychological mechanism and lack of confidence that makes it harder to assess aptitude.

Croizet has previously studied "stereotype threat," a concept identified in the U.S. by researchers Claude Steele and Joshua Aronson that refers to how often intangible social circumstances can affect academic performance. "That convinced us there was more going on in performance situations than just poor abilities," Croizet said. "We wanted to show that even if you put children in a situation where there's no pressure, the simple fact that they're confronted with difficulty could trigger a disruption in their performance."

To verify this hypothesis, Croizet and Autin conducted three studies among sixth graders in their city, Poitiers. In one experiment, they gave 111 sixth graders an impossible set of anagrams to solve. Then Autin told one group of kids that "learning is difficult and failure is common," but hard work will help, "like riding a bicycle." Autin asked a second group of kids how they attacked the problems after the test. When both groups, plus a control group, then took an exam that measured working memory -- a capacity often used to predict IQ -- the students Autin had counseled performed "significantly better" than both groups, especially on the tougher questions.

In the second setup, the researchers added an additional group of kids who were first presented with an easier anagram problem set before giving all groups a reading comprehension test. Once again, the kids Autin had advised bested the other groups, even the one that performed well on the easier anagram test. "This finding is indicative that motivation or involvement alone cannot easily account for the gains observed" after kids are told that failure is natural, the researchers wrote.

For their third experiment, the researchers organized the kids into similar groups, and before a reading comprehension exam, had them write self-descriptions about their intelligence. The group that had been advised on the difficulties of learning once again outscored their peers -- and also reported, overall, fewer feelings of ineptitude.

And while the researchers conducted their experiments in France, they think it's applicable to all high-stakes test-taking Western countries. Aronson, a New York University psychology professor, agrees. He noted that similar studies in the U.S. have found that college students perform better after reading positive messages, and that he replicated the experiment by having older students tell younger students that they should "expect middle school to be difficult but doable" -- and found that state test scores increased dramatically.

So far, Croizet said, teachers have been very receptive. "Some of them are willing to implement it in their classrooms," he said. "They have also told us it's very difficult in the long run to implement because the educational system is geared toward ranking students." Student rankings, he says, "reinforce what we think we should avoid in the classroom: who's smart and who's not smart."

The researchers also found that test relaxation techniques that seem obvious to most teachers, such as telling students that they can perform well, can actually make kids more anxious -- and thus perform at lower levels.

"It makes sense to me," Alcala, the Berkeley teacher, said of the study. "I've been doing it [my favorite no] for four years now, and my kids' understanding is significantly better than before, as measured by test scores."