Zoe Bellars and Brad McGann, eighth-graders at Swanson Middle School in Arlington, Va., do their homework faithfully and practice their musical instruments regularly. In a recent delayed-gratification experiment, they declined to accept a dollar bill when told they could wait a week and get $2.

Those traits might be expected of good students. But a study by University of Pennsylvania researchers suggests that self-discipline and self-denial could be a key to saving U.S. schools.

Self-discipline is a better predictor of academic success than even IQ, according to a recent article by Angela L. Duckworth and Martin E.P. Seligman in the journal Psychological Science.

"Underachievement among American youth is often blamed on inadequate teachers, boring textbooks and large class sizes," the researchers said. "We suggest another reason for students falling short of their intellectual potential: their failure to exercise self-discipline. ...

"We believe that many of America's children have trouble making choices that require them to sacrifice short-term pleasure for long-term gain, and that programs that build self-discipline may be the royal road to building academic achievement."

But how, educators, parents and social scientists want to know, do you measure self-discipline?

Duckworth, a former teacher studying for a doctorate in psychology, and Seligman, a psychology professor famous for books such as "Learned Optimism," used an assortment of yardsticks, including questions for the students (such as how likely they are to have trouble breaking bad habits, on a 1-to-5 scale), ratings by their teachers and parents and the $1-now-or-$2-later test, which the researchers call the Delay Choice Task.

The results: "Highly self-disciplined adolescents outperformed their more impulsive peers on every academic-performance variable, including report card grades, standardized achievement test scores, admission to a competitive high school and attendance. Self-discipline measured in the fall predicted more variance in each of these outcomes than did IQ, and unlike IQ, self-discipline predicted gains in academic performance over the school year."

The study looked at one group of 140 eighth-graders and another group of 164 eighth-graders in a socio-economically and ethnically diverse magnet school in a Northeast city. The names of the city, the school and the students were not revealed.

At Swanson, when students were approached for an unscientific version of the Delay Choice Task, eight of 10 eighth-graders chose to forgo $1 right away in exchange for $2 in a week.

The mothers of Zoe and Brad, who both declined the $1 offer, said they were not surprised by their children's decisions and thought the correlation of self-discipline with academic success made sense.

"I remember when Zoe was in the second grade, they had to do this poster of what they would do with $1 million," recalled her mother, Arlene Vigoda-Bellars, a former journalist. Her daughter said she would use it to go to Harvard. In preparation for that college competition, Zoe is taking intensified algebra and second-year Spanish, has a voice scholarship at a music school and plays first flute in Swanson's symphonic band.

Bertra McGann, a technical writer married to a Foreign Service officer, said that when Brad was 4, the family lived in Kenya, and he was put in a class with older students. "He would come home from school and hand me the flash cards and work on his sight-reading — an extraordinary amount of self-discipline for a 4-year-old," she said. Now 13, Brad plays clarinet and basketball and earned his black belt in tae kwon do by practicing two hours a day, six days a week, for two years.

Some educators said schools can teach self-discipline. Rafe Esquith, an award-winning Los Angeles teacher, often tells his low-income fifth-graders about a study that showed that hungry 4-year-olds willing to wait for two marshmallows were more successful years later than those who gobbled up one marshmallow immediately.

Ryan Hill, director of the TEAM Academy Charter School in Newark, N.J., said students at his school, a Knowledge Is Power Program middle school in a low-income neighborhood, are required to stay at school until their homework is done if TV interfered with study the night before. "Over time, they learn to just do their homework before watching TV, delaying gratification, which becomes a habit of self-discipline," Hill said.

However, some experts expressed doubt about the Delay Choice Task. "I'd assume it was some kind of scam, take the buck and run," said Bob Schaeffer, public education director of FairTest, the National Center for Fair & Open Testing, a nonprofit group that is critical of over-reliance on testing in U.S. schools.

Zoe refused to take the $2 at the end of the experiment. "I think it is rude to take money from strangers," she said.