Over time, this adds up. By third grade, children who can’t read at their grade level (a whopping 73 percent of students eligible for free or reduced-price lunch) begin to struggle with other subjects. Students living in poverty who cannot read proficiently by third grade are 13 times less likely to graduate from high school. By ninth grade, some have estimated that two-thirds of the reading achievement gap can be explained by unequal access to summer learning opportunities.

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There is good news: Stemming the summer slide isn’t impossible. Students who read just four to six books over the summer maintain their skills (they need to turn more pages to actually become better readers.)

Schools have tried to enforce this with a summer reading list. Students are assigned several books that they must write a report about or take a test on once they return in the fall. These programs often include a mailed package of books selected by well-intentioned educators, who evaluate the material on educational and literary merits and then ship books home sight-unseen by students.

I wondered if there was a way to make this program more effective. So in 2013, I tested a small tweak in two low-income classrooms in Rochester, N.Y.: I asked the teachers to let the kids choose the books they read over the summer.

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We started with two second-grade classrooms in schools with low-income students. Although 84 percent of students in the Rochester City School District qualify for the free and reduced-price lunch program, this school had a particularly high concentration of poverty, with 96 percent of students eligible for the program.

For one class, researchers ran a book fair, where each student picked 13 books to take home at the end of the school year. The fair featured a broad range of selections — fiction and nonfiction, classics and newer works — and students eagerly passed the books back and forth, reveling in the opportunity to pick those matching their personal interests while chattering with one another about familiar stories. (An adaptation of Disney’s “Frozen” was especially popular.) Many also chose works considerably above or below their reading levels so they could share with siblings.

The other class of students received books by mail from the already-in-place community program.

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Both classes were given literacy tests before summer vacation and again when they returned in the fall. Sure enough, the students who chose their own books did better, improving from the previous summer. Those in the community program showed no improvement.

A follow-up study involved six classes, with a total of 87 students, and compared those who selected all of their summer books with those who chose some of their own books, while educators picked the rest. There was no significant difference between the two groups. Seventy-five percent of the students either maintained or improved their reading levels over the summer, which is much better than typically expected.

Clearly, the small sample size is a limitation, but other reading research backs this up. A three-year study of Florida students found that kids who selected books to take home for the summer had significantly higher reading proficiency scores compared to students who received nothing.

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A Scholastic Corp. study of 1,000 readers found that middle and high school students who are given the opportunity to choose the books they read are more likely to read more frequently for fun. “You become a lifelong reader when you’re able to make choices about the books you read, and when you love the books you read,” Pam Allyn, a literacy advocate, told The Washington Post. “You tend to get better at something you love to do.”

The Rochester City School District seems to agree. This summer, for the first time, all kindergarten through second-grade students will receive five books selected by educators and five more they will pick themselves.