Here’s a back-to-school idea to think about: A new study published in the journal Science found that black students who wrote a short essay on their values at the start of the school year got a lasting boost in academic performance. The study, conducted over the course two years at a suburban middle school, asked randomly selected students to write a brief explanation of the values that are most important to them. A control group was instructed to write about values that they rated the least important. Each year, the black students who wrote about positive values scored about one-third of a letter grade better than black students in the second group. Perhaps more significantly, they also closed the achievement gap with white students by 40 percent. The researchers believe the assignment helped the students affirm their self-worth and negate the negative stereotypes that many black students feel in school. “Our performance is really affected by what other people think of us,” said Geoffrey Cohen, a psychologist at the University of Colorado, who coauthored the study.