The City’s public schools are not keeping up with federal mandates established under the federal No Child Left Behind Act, despite the fact that its overall scores on standardized tests have been higher than the state’s for eight years in a row.

Each year, schools and districts are given a numerical ranking, from a low of 200 to a high of 1,000, that reflects students’ test performance — with a state goal of reaching a rank of 800 or more. The number is called the Academic Performance Index, or API.

This year the San Francisco Unified School District was given an API of 777. The state API was 755.

However, nearly half of the district’s schools — 48 percent — did not meet federal benchmarks, called “Adequately Yearly Progress,” required under NCLB.

Under the federal goal, elementary and middle schools needed to show that at least 46 percent of students are proficient in English and 47.5 percent are proficient in math. The percentage mandates for high schools are 44.5 for English and 43.5 for math. Under NCLB, districts are expected to have 100 percent of students at proficiency, or grade level, by 2014. In recent years, California’s schools have been expected to boost their proficiency percentages by about 10 points every year, according to state officials.

Schools that do not reach Adequate Yearly Progress goals for two years in a row are designated as “Program Improvement” schools and face increasing sanctions every year thereafter, eventually facing the possibility of staff overhauls, new governance or restructuring.

“That’s the historic rub,” State Superintendent of Public Instruction Jack O’Connell said. “Now that we have this dramatically increasing bar, the reality is it’s going to be more difficult for our schools.”

Officials with the San Francisco Unified School District said they’ve tried overhauling school leaders and staff in the past, and that changing the curriculum is the best way to improve student test scores.

This year the district’s most notable success story is at Malcolm X Academy, which was in its fifth year of Program Improvement.

The elementary school of about 120 students was showered with more hands-on resources, which have proven to be more effective in the past, school district spokeswoman Gentle Blythe said.

Practicing mathematicians were brought in to teach alongside math teachers, showing how math applies to real-life situations, for example.

The district also had a program that helped parents become more involved in their children’s academics, among several other “interventions,” Blythe said.

“We tried that approach of taking all the teachers and changing them entirely, but that has not been proven to be a long-term effective strategy,’’ Blythe said. “Different schools have different needs.”

Last year 28 of San Francisco’s public schools were designated as Program Improvement schools; 31 are on the list this year. Malcolm X was the only school that got off the list, meaning it met proficiency for two years in a row.

Two other SFUSD schools that had notable score increases are E.R. Taylor and Robert Louis Stevenson elementary schools, which were named “Blue Ribbon” schools by the U.S. Department of Education.

SFUSD ranks higher than overall state scores

The Accountability Progress Index, or API, is a number assigned to California schools that falls between 200 and 1,000 that reflects student performances on English and math tests. The state goal is an API of 800.

table, td { border: 1px solid #ccc; }