By NICOLE SANTA CRUZ

When Darlene Johnson walks her granddaughter to school in the mornings, the 11-year-old honor roll student often darts toward the entrance, and Johnson smiles.

“She loves it,” Johnson said of her granddaughter, Terrisha Williams, who is enrolled in a magnet program at Orchard Villa Elementary School near the Liberty City neighborhood in North Miami.

This is the type of scene any school administrator would love to encounter, especially in a neighborhood like Liberty City, one of the toughest in Miami-Dade County. Here and elsewhere in the school system, officials face a constant struggle to bring low-income schools up to state performance standards.

Miami-Dade is the fourth-largest school district in the United States and the largest in Florida. It is situated in a region where the income gap is historically one of the highest in the nation. The poverty rate is 17 percent, according to the U.S. Census Bureau.

In 2007-08, 13 of the district’s 415 schools were given a failing grade, according to state data. Letter grades are determined by student performance on the Florida Comprehensive Assessment Test, or FCAT. They are also determined by gains and losses made by schools from one year to the next.

The 13 schools also had more than 50 percent of their students on the National School Lunch Program — through which students receive discounted or free lunches — according to October 2008 data. School lunch enrollment is often an indicator of poverty for school administrators.

It is a common belief among educators that low income and low student performance are related. Students who come from low-income backgrounds, they say, are more likely to move, have less parental guidance and grow up among people who are not educated.

“Socioeconomic background and educational attainment go hand in hand,” said Hilca Thomas, a principal at Howard D. McMillan Middle School in Miami’s middle-class Kendall neighborhood.

Holmes Elementary School in Liberty City is one example of an extreme. Currently, 98 percent of its students are on the school lunch program, the highest in the district. The school consistently fails in state ratings. At nearby Key Biscayne Community School, 9 percent of students are on the school lunch program, the lowest number in the district. Over the last 10 years the school has consistently performed above average, according to state data.

Instead of drawing boundaries based on socioeconomic factors or busing students from the inner city to the suburbs, however, district officials hope solutions can come from within the schools, Thomas said.

Thomas, who has been in education for 21 years, said it is ultimately up to principals and administrators to enforce high standards.

In some cases, educators are offering more after-school programs and incentives for students to learn. They are also transferring administrators with significant experience to help lower-achieving schools, Thomas said.

A program that pays students to attend tutoring sessions has worked for Trina Brownlee’s son Craig, 8, a third-grader at Holmes Elementary School.

Brownlee works at a fast-food restaurant and lives in the Liberty Square Housing Projects in North Miami. She said Craig receives extra FCAT tutoring at sessions on weekends and after school. The help has improved his grades from D’s and F’s to B’s and C’s, she said.

“It’s helping him,” Brownlee said, “because he’s doing good now.”

In the School District of Manatee County, in western Florida, where the poverty rate is about 10 percent, officials have taken a different approach to diversifying schools. At any given school, administrators try to keep the number of students on the lunch program within the range of 40 percent to 60 percent, said Danny Lundeen, the supervisor of student demographics for the district.

How this has affected student performance is hard to measure, Lundeen said, but the district is “pretty happy” with its efforts to create diversity.

Still, maintaining diversity among students is a delicate task, Lundeen said.

“It’s not only who you allow in, but it’s who you allow out of schools,” he said. “In helping one school, we don’t want to hurt another one.”

Education experts say that educators themselves undergo a learning process when teaching students from lower-income households.

“Every educator now recognizes that it’s much harder to educate children in high-poverty schools,” said John Powell, the executive director of the Kirwan Institute for the Study of Race and Ethnicity at Ohio State University.

Powell said mixing children of various backgrounds, no matter the method, also helps children become comfortable around diverse groups.

“It teaches students how to be citizens,” he said.